Content-based research paper recommendation (CbRPR) has seen advances in computer science and biomedicine, but remains unexplored for mathematics, where paper relatedness is more conceptual than explicit textual or citation-based similarity. Mathematics papers may be connected through shared proof techniques, logical implications, or natural generalizations, yet exhibit minimal textual or citation overlap, rendering existing CbRPR ineffective. To address this gap, we first conduct an expert-driven study characterizing mathematical recommendations, revealing that relevance is inherently \textit{aspect}-driven. Grounded in this insight, we introduce GoldRiM (small, expert-annotated) and SilverRiM (large, automatically derived), the first datasets for \textit{aspect}-aware CbRPR in mathematics. Recognizing that LLM embeddings of mathematical content alone yield suboptimal representation, we propose AchGNN, an \textit{aspect}-conditioned heterogeneous GNN that jointly models textual semantics, citation structure, and author lineage. Across GoldRiM and SilverRiM, AchGNN consistently outperforms prior \textit{aspect}-based CbRPR methods, achieving substantial gains across all evaluated \textit{aspects}. We conduct ablation studies to analyze the contributions of individual \textit{aspect} supervision, authorship lineage, and graph-structural signals to AchGNN's performance. To assess domain generality, we further evaluate AchGNN on the \textit{Papers with Code} dataset of machine learning publications, demonstrating that our \textit{aspect}-aware approach effectively transfers beyond mathematics. We deploy our system on the MaRDI platform to help mathematicians with recommendations and release datasets and code publicly for reproducibility.

The centralization of web services has raised concerns about critical single points of failure, such as content hosting, name resolution, and certification. To address these issues, the "Decentralized Web" movement advocates for de-centralized alternatives. Distributed Hash Tables (DHTs) have emerged as a key component facilitating this movement, as they offer efficient key/value indexing. The InterPlanetary File System (IPFS) exemplifies this approach by leveraging DHTs for data indexing and distribution. A critical finding of previous studies is that DHT PUT performance for record storage is unacceptably slow, sometimes taking minutes to complete and hindering the adoption of delay-intolerant applications. To address this challenge, this research paper presents three significant contributions. First, we present the design of Optimistic Provide, an approach to accelerate DHT PUT operations in Kademlia-based IPFS networks while maintaining full backward compatibility. Second, we implement and deploy the mechanism and see its usage in the de-facto IPFS deployment, Kubo. Third, we evaluate its effectiveness in the IPFS and Filecoin DHTs. We confirm that we enable sub-second record storage from North America and Europe for 90% of PUT operations while reducing networking overhead by over 40% and maintaining record availability.

Large Language Models (LLMs) have demonstrated exceptional capabilities in various natural language tasks, often achieving performances that surpass those of humans. Despite these advancements, the domain of mathematics presents a distinctive challenge, primarily due to its specialized structure and the precision it demands. In this work, we follow a two-step approach to investigating the proficiency of LLMs in answering mathematical questions. First, we employ the most effective LLMs, as identified by their performance on math question-answer benchmarks, to generate answers to 78 questions from the Math Stack Exchange (MSE). Second, a case analysis is conducted on the LLM that showed the highest performance, focusing on the quality and accuracy of its answers through manual evaluation. We found that GPT-4 performs best (nDCG of 0.48 and P@10 of 0.37) amongst existing LLMs fine-tuned for answering mathematics questions and outperforms the current best approach on ArqMATH3 Task1, considering P@10. Our case analysis indicates that while GPT-4 can generate relevant answers, it isn't consistently accurate. This paper explores the current limitations of LLMs in navigating complex mathematical question-answering. We make our code and findings publicly available for research: https://github.com/gipplab/LLM-Investig-MathStackExchange

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 L A T E X to Mathematica as well as from L A T E X to semantic L A T E X.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.

Wikipedia combines the power of AI solutions and human reviewers to safeguard article quality. Quality control objectives include detecting malicious edits, fixing typos, and spotting inconsistent formatting. However, no automated quality control mechanisms currently exist for mathematical formulae. Spell checkers are widely used to highlight textual errors, yet no equivalent tool exists to detect algebraically incorrect formulae. Our paper addresses this shortcoming by making mathematical formulae computable. We present a method that (1) gathers the semantic information surrounding the context of each mathematical formulae, (2) provides access to the information in a graph-structured dependency hierarchy, and (3) performs automatic plausibility checks on equations. We evaluate the performance of our approach on 6,337 mathematical expressions contained in 104 Wikipedia articles on the topic of orthogonal polynomials and special functions. Our system, [Formula: see text], verified 358 out of 1,516 equations as error-free. [Formula: see text] successfully translated 27% of the mathematical expressions and outperformed existing translation approaches by 16%. Additionally, [Formula: see text] achieved an F1 score of .495 for annotating mathematical expressions with relevant textual descriptions, which is a significant step towards advancing searchability, readability, and accessibility of mathematical formulae in Wikipedia. A prototype of [Formula: see text] and the semantically enhanced Wikipedia articles are available at: https://tpami.wmflabs.org.

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.

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.

Peer Copy is a decentralized, peer-to-peer file transfer tool based on libp2p. 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.

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.

Documents from science, technology, engineering and mathematics (STEM) often contain a large number of mathematical formulae alongside text. Semantic search, recommender, and question answering systems require the occurring formula constants and variables (identifiers) to be disambiguated. We present a first implementation of a recommender system that enables and accelerates formula annotation by displaying the most likely candidates for formula and identifier names from four different sources (arXiv, Wikipedia, Wikidata, or the surrounding text). A first evaluation shows that in total, 78% of the formula identifier name recommendations were accepted by the user as a suitable annotation. Furthermore, document-wide annotation saved the user the annotation of ten times more other identifier occurrences. Our long-term vision is to integrate the annotation recommender into the edit-view of Wikipedia and the online LaTeX editor Overleaf.

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.

This paper presents, to our knowledge, the first study on analyzing mathematical expressions to detect academic plagiarism. We make the following contributions. First, we investigate confirmed cases of plagiarism to categorize the similarities of mathematical content commonly found in plagiarized publications. From this investigation, we derive possible feature selection and feature comparison strategies for developing math-based detection approaches and a ground truth for our experiments. Second, we create a test collection by embedding confirmed cases of plagiarism into the NTCIR-11 MathIR Task dataset, which contains approx. 60 million mathematical expressions in 105,120 documents from arXiv.org. Third, we develop a first math-based detection approach by implementing and evaluating different feature comparison approaches using an open source parallel data processing pipeline built using the Apache Flink framework. The best performing approach identifies all but two of our real-world test cases at the top rank and achieves a mean reciprocal rank of 0.86. The results show that mathematical expressions are promising text-independent features to identify academic plagiarism in large collections. To facilitate future research on math-based plagiarism detection, we make our source code and data available.

We present Citolytics - a novel link-based recommendation system for Wikipedia articles. In a preliminary study, Citolytics achieved promising results compared to the widely used text-based approach of Apache Lucene's MoreLikeThis (MLT). In this demo paper, we describe how we plan to integrate Citolytics into the Wikipedia infrastructure by using Elasticsearch and Apache Flink to serve recommendations for Wikipedia articles. Additionally, we propose a large-scale online evaluation design using the Wikipedia Android app. Working with Wikipedia data has several unique advantages. First, the availability of a very large user sample contributes to statistically significant results. Second, the openness of Wikipedia's architecture allows making our source code and evaluation data public, thus benefiting other researchers. If link-based recommendations show promise in our online evaluation, a deployment of the presented system within Wikipedia would have a far-reaching impact on Wikipedia's more than 30 million users.

Mathematical formulae are essential in science, but face challenges of ambiguity, due to the use of a small number of identifiers to represent an immense number of concepts. Corresponding to word sense disambiguation in Natural Language Processing, we disambiguate mathematical identifiers. By regarding formulae and natural text as one monolithic information source, we are able to extract the semantics of identifiers in a process we term Mathematical Language Processing (MLP). As scientific communities tend to establish standard (identifier) notations, we use the document domain to infer the actual meaning of an identifier. Therefore, we adapt the software development concept of namespaces to mathematical notation. Thus, we learn namespace definitions by clustering the MLP results and mapping those clusters to subject classification schemata. In addition, this gives fundamental insights into the usage of mathematical notations in science, technology, engineering and mathematics. Our gold standard based evaluation shows that MLP extracts relevant identifier-definitions. Moreover, we discover that identifier namespaces improve the performance of automated identifier-definition extraction, and elevate it to a level that cannot be achieved within the document context alone.

Mathematical Information Retrieval concerns retrieving information related to a particular mathematical concept. The NTCIR-11 Math Task develops an evaluation test collection for document sections retrieval of scientific articles based on human generated topics. Those topics involve a combination of formula patterns and keywords. In addition, the optional Wikipedia Task provides a test collection for retrieval of individual mathematical formula from Wikipedia based on search topics that contain exactly one formula pattern. We developed a framework for automatic query generation and immediate evaluation. This paper discusses our dataset preparation, topic generation and evaluation methods, and summarizes the results of the participants, with a special focus on the Wikipedia Task.