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Moritz Schubotz

Publications and source records attributed to Moritz Schubotz.

At least 37 records · Page 2Linked to original sources

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.

cs.DL↗

TEIMMA: The First Content Reuse Annotator for Text, Images, and Math

This demo paper presents the first tool to annotate the reuse of text, images, and mathematical formulae in a document pair -- TEIMMA. Annotating content reuse is particularly useful to develop plagiarism detection algorithms. Real-world content reuse is often obfuscated, which makes it challenging to identify such cases. TEIMMA allows entering the obfuscation type to enable novel classifications for confirmed cases of plagiarism. It enables recording different reuse types for text, images, and mathematical formulae in HTML and supports users by visualizing the content reuse in a document pair using similarity detection methods for text and math.

cs.IR↗

Neural Machine Translation for Mathematical Formulae

We tackle the problem of neural machine translation of mathematical formulae between ambiguous presentation languages and unambiguous content languages. Compared to neural machine translation on natural language, mathematical formulae have a much smaller vocabulary and much longer sequences of symbols, while their translation requires extreme precision to satisfy mathematical information needs. In this work, we perform the tasks of translating from LaTeX to Mathematica as well as from LaTeX to semantic LaTeX. While recurrent, recursive, and transformer networks struggle with preserving all contained information, we find that convolutional sequence-to-sequence networks achieve 95.1% and 90.7% exact matches, respectively.

cs.CL↗

Methods and Tools to Advance the Retrieval of Mathematical Knowledge from Digital Libraries for Search-, Recommendation-, and Assistance-Systems

This project investigated new approaches and technologies to enhance the accessibility of mathematical content and its semantic information for a broad range of information retrieval applications. To achieve this goal, the project addressed three main research challenges: (1) syntactic analysis of mathematical expressions, (2) semantic enrichment of mathematical expressions, and (3) evaluation using quality metrics and demonstrators. To make our research useful for the research community, we published tools that enable researchers to process mathematical expressions more effectively and efficiently.

cs.IR↗

Introducing Peer Copy -- A Fully Decentralized Peer-to-Peer File Transfer Tool

It allows any two parties that are either both on the same network or connected via the internet to transfer the contents of a file based on a particular sequence of words. Peer discovery happens via multicast DNS if both peers are on the same network or via entries in the distributed hash table (DHT) of the InterPlanetary File-System (IPFS) if both peers are connected across network boundaries. As soon as a connection is established, the word sequence is used as the input for a password-authenticated key exchange (PAKE) to derive a strong session key. This session key authenticates the peers and encrypts any subsequent communication. It is found that the decentralized approach to peer-to-peer file transfer can keep up with established centralized tools while eliminating the reliance on centralized service providers.

cs.NI↗

Discovery and Recognition of Formula Concepts using Machine Learning

Citation-based Information Retrieval (IR) methods for scientific documents have proven effective for IR applications, such as Plagiarism Detection or Literature Recommender Systems in academic disciplines that use many references. In science, technology, engineering, and mathematics, researchers often employ mathematical concepts through formula notation to refer to prior knowledge. Our long-term goal is to generalize citation-based IR methods and apply this generalized method to both classical references and mathematical concepts. In this paper, we suggest how mathematical formulas could be cited and define a Formula Concept Retrieval task with two subtasks: Formula Concept Discovery (FCD) and Formula Concept Recognition (FCR). While FCD aims at the definition and exploration of a 'Formula Concept' that names bundled equivalent representations of a formula, FCR is designed to match a given formula to a prior assigned unique mathematical concept identifier. We present machine learning-based approaches to address the FCD and FCR tasks. We then evaluate these approaches on a standardized test collection (NTCIR arXiv dataset). Our FCD approach yields a precision of 68% for retrieving equivalent representations of frequent formulas and a recall of 72% for extracting the formula name from the surrounding text. FCD and FCR enable the citation of formulas within mathematical documents and facilitate semantic search and question answering as well as document similarity assessments for plagiarism detection or recommender systems.

cs.IR↗

Collaborative and AI-aided Exam Question Generation using Wikidata in Education

Since the COVID-19 outbreak, the use of digital learning or education platforms has significantly increased. Teachers now digitally distribute homework and provide exercise questions. In both cases, teachers need to continuously develop novel and individual questions. This process can be very time-consuming and should be facilitated and accelerated both through exchange with other teachers and by using Artificial Intelligence (AI) capabilities. To address this need, we propose a multilingual Wikimedia framework that allows for collaborative worldwide teacher knowledge engineering and subsequent AI-aided question generation, test, and correction. As a proof of concept, we present >>PhysWikiQuiz<<, a physics question generation and test engine. Our system (hosted by Wikimedia at https://physwikiquiz.wmflabs.org) retrieves physics knowledge from the open community-curated database Wikidata. It can generate questions in different variations and verify answer values and units using a Computer Algebra System (CAS). We evaluate the performance on a public benchmark dataset at each stage of the system workflow. For an average formula with three variables, the system can generate and correct up to 300 questions for individual students based on a single formula concept name as input by the teacher.

cs.IR↗

Mining Mathematical Documents for Question Answering via Unsupervised Formula Labeling

The increasing number of questions on Question Answering (QA) platforms like Math Stack Exchange (MSE) signifies a growing information need to answer math-related questions. However, there is currently very little research on approaches for an open data QA system that retrieves mathematical formulae using their concept names or querying formula identifier relationships from knowledge graphs. In this paper, we aim to bridge the gap by presenting data mining methods and benchmark results to employ Mathematical Entity Linking (MathEL) and Unsupervised Formula Labeling (UFL) for semantic formula search and mathematical question answering (MathQA) on the arXiv preprint repository, Wikipedia, and Wikidata, which is part of the Wikimedia ecosystem of free knowledge. Based on different types of information needs, we evaluate our system in 15 information need modes, assessing over 7,000 query results. Furthermore, we compare its performance to a commercial knowledge-base and calculation-engine (Wolfram Alpha) and search-engine (Google). The open source system is hosted by Wikimedia at https://mathqa.wmflabs.org. A demovideo is available at purl.org/mathqa.

cs.IR↗

Caching and Reproducibility: Making Data Science experiments faster and FAIRer

Small to medium-scale data science experiments often rely on research software developed ad-hoc by individual scientists or small teams. Often there is no time to make the research software fast, reusable, and open access. The consequence is twofold. First, subsequent researchers must spend significant work hours building upon the proposed hypotheses or experimental framework. In the worst case, others cannot reproduce the experiment and reuse the findings for subsequent research. Second, suppose the ad-hoc research software fails during often long-running computationally expensive experiments. In that case, the overall effort to iteratively improve the software and rerun the experiments creates significant time pressure on the researchers. We suggest making caching an integral part of the research software development process, even before the first line of code is written. This article outlines caching recommendations for developing research software in data science projects. Our recommendations provide a perspective to circumvent common problems such as propriety dependence, speed, etc. At the same time, caching contributes to the reproducibility of experiments in the open science workflow. Concerning the four guiding principles, i.e., Findability, Accessibility, Interoperability, and Reusability (FAIR), we foresee that including the proposed recommendation in a research software development will make the data related to that software FAIRer for both machines and humans. We exhibit the usefulness of some of the proposed recommendations on our recently completed research software project in mathematical information retrieval.

cs.SE↗

Design and Evaluation of IPFS: A Storage Layer for the Decentralized Web

Recent years have witnessed growing consolidation of web operations. For example, the majority of web traffic now originates from a few organizations, and even micro-websites often choose to host on large pre-existing cloud infrastructures. In response to this, the "Decentralized Web" attempts to distribute ownership and operation of web services more evenly. This paper describes the design and implementation of the largest and most widely used Decentralized Web platform - the InterPlanetary File System (IPFS) - an open-source, content-addressable peer-to-peer network that provides distributed data storage and delivery. IPFS has millions of daily content retrievals and already underpins dozens of third-party applications. This paper evaluates the performance of IPFS by introducing a set of measurement methodologies that allow us to uncover the characteristics of peers in the IPFS network. We reveal presence in more than 2700 Autonomous Systems and 152 countries, the majority of which operate outside large central cloud providers like Amazon or Azure. We further evaluate IPFS performance, showing that both publication and retrieval delays are acceptable for a wide range of use cases. Finally, we share our datasets, experiences and lessons learned.

cs.NI↗

Electronic Laboratory Notebook: A lazy approach

Good research data management is essential in modern-day lab work. Various solutions exist that are either highly specific or need a significant effort to be customized appropriately. This paper presents an integrated solution for individuals and small groups of researchers in data-driven deductive research. Our electronic lab book generates itself out of notes and files, which are generated by one or several experiments. The generated electronic lab book is then presented on a Django-based website. The automated gathering of metadata significantly reduces the documentation effort for the lab worker and prevents human error in the repetitive task of manually entering basic meta-data. The skilled user can quickly adapt the electronic lab book software to his needs because the software employs widely used open-source software libraries with active communities and excellent documentation.

cs.CY↗

Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems

Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously eveloped conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.

cs.DL↗

Detecting Cross-Language Plagiarism using Open Knowledge Graphs

Identifying cross-language plagiarism is challenging, especially for distant language pairs and sense-for-sense translations. We introduce the new multilingual retrieval model Cross-Language Ontology-Based Similarity Analysis (CL-OSA) for this task. CL-OSA represents documents as entity vectors obtained from the open knowledge graph Wikidata. Opposed to other methods, CL-OSA does not require computationally expensive machine translation, nor pre-training using comparable or parallel corpora. It reliably disambiguates homonyms and scales to allow its application to Web-scale document collections. We show that CL-OSA outperforms state-of-the-art methods for retrieving candidate documents from five large, topically diverse test corpora that include distant language pairs like Japanese-English. For identifying cross-language plagiarism at the character level, CL-OSA primarily improves the detection of sense-for-sense translations. For these challenging cases, CL-OSA's performance in terms of the well-established PlagDet score exceeds that of the best competitor by more than factor two. The code and data of our study are openly available.

cs.CL↗

Academic Storage Cluster

Decentralized storage is still rarely used in an academic and educational environment, although it offers better availability than conventional systems. It still happens that data is not available at a certain time due to heavy load or maintenance on university servers. A decentralized solution can help keep the data available and distribute the load among several peers. In our experiment, we created a cluster of containers in Docker to evaluate a private IPFS cluster for an academic data store focusing on availability, GET/PUT performance, and storage needs. As sample data, we used PDF files to analyze the data transport in our peer-to-peer network with Wireshark. We found that a bandwidth of at least 100 kbit/s is required for IPFS to function but recommend at least 1000 kbit/s for smooth operation. Also, the hard disk and memory size should be adapted to the data. Other limiting factors such as CPU power and delay in the internet connection did not affect the operation of the IPFS cluster.

cs.DB↗

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

We have developed an automated procedure for symbolic and numerical testing of formulae extracted from the NIST Digital Library of Mathematical Functions (DLMF). For the NIST Digital Repository of Mathematical Formulae, we have developed conversion tools from semantic LaTeX to the Computer Algebra System (CAS) Maple which relies on Youssef's part-of-math tagger. We convert a test data subset of 4,078 semantic LaTeX DLMF formulae %extracted from the DLMF to the native CAS representation and then apply an automated scheme for symbolic and numerical testing and verification. Our framework is implemented using Java and Maple. We describe in detail the conversion process which is required so that the CAS can correctly interpret the mathematical representation of the formulae. We describe the improvement of the effectiveness of our automated scheme through incremental enhancement (making more precise) of the mathematical semantic markup for the formulae.

cs.DL↗

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

Document preparation systems like LaTeX offer the ability to render mathematical expressions as one would write these on paper. Using LaTeX, LaTeXML, and tools generated for use in the National Institute of Standards (NIST) Digital Library of Mathematical Functions, semantically enhanced mathematical LaTeX markup (semantic LaTeX) 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 LaTeX 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 LaTeX, semantic LaTeX, and now CAS representations as well.

cs.IR↗

MathTools: An Open API for Convenient MathML Handling

Mathematical formulae carry complex and essential semantic information in a variety of formats. Accessing this information with different systems requires a standardized machine-readable format that is capable of encoding presentational and semantic information. Even though MathML is an official recommendation by W3C and an ISO standard for representing mathematical expressions, we could identify only very few systems which use the full descriptiveness of MathML. MathML's high complexity results in a steep learning curve for novice users. We hypothesize that this complexity is the reason why many community-driven projects refrain from using MathML, and instead develop problem-specific data formats for their purposes. We provide a user-friendly, open-source application programming interface for controlling MathML data. Our API is written in JAVA and allows to create, manipulate, and efficiently access commonly needed information in presentation and content MathML. Our interface also provides tools for calculating differences and similarities between MathML expressions. The API also allows to determine the distance between expressions using different similarity measures. In addition, we provide adapters for numerous conversion tools and the canonicalization project. Our toolkit facilitates processing of mathematics for digital libraries, without the need to obtain XML expertise.

cs.DL↗

Towards Explaining STEM Document Classification using Mathematical Entity Linking

Document subject classification is essential for structuring (digital) libraries and allowing readers to search within a specific field. Currently, the classification is typically made by human domain experts. Semi-supervised Machine Learning algorithms can support them by exploiting the labeled data to predict subject classes for unclassified new documents. However, while humans partly do, machines mostly do not explain the reasons for their decisions. Recently, explainable AI research to address the problem of Machine Learning decisions being a black box has increasingly gained interest. Explainer models have already been applied to the classification of natural language texts, such as legal or medical documents. Documents from Science, Technology, Engineering, and Mathematics (STEM) disciplines are more difficult to analyze, since they contain both textual and mathematical formula content. In this paper, we present first advances towards STEM document classification explainability using classical and mathematical Entity Linking. We examine relationships between textual and mathematical subject classes and entities, mining a collection of documents from the arXiv preprint repository (NTCIR and zbMATH dataset). The results indicate that mathematical entities have the potential to provide high explainability as they are a crucial part of a STEM document.

cs.IR↗