Cross-language Information Retrieval

Two key assumptions shape the usual view of ranked retrieval: (1) that the searcher can choose words for their query that might appear in the documents that they wish to see, and (2) that ranking retrieved documents will suffice because the searcher will be able to recognize those which they wished to find. When the documents to be searched are in a language not known by the searcher, neither assumption is true. In such cases, Cross-Language Information Retrieval (CLIR) is needed. This chapter reviews the state of the art for CLIR and outlines some open research questions.Comment: 49 pages, 0 figure

LIA@CLEF 2018: Mining events opinion argumentation from raw unlabeled Twitter data using convolutional neural network

International audienceSocial networks on the Internet are becoming increasingly important in our society. In recent years, this type of media, through communication platforms such as Twitter, has brought new research issues due to the massive size of data exchanged and the important number of ever-increasing users. In this context, the CLEF 2018 Mining opinion argumentation task aims to retrieve, for a specific event (festival name or topic), the most diverse argumentative microblogs from a large collection of tweets about festivals in different languages. In this paper, we propose a four-step approach for extracting argumentative microblogs related to a specific query (or event) while no reference data is provided

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

Effective Math-Aware Ad-Hoc Retrieval based on Structure Search and Semantic Similarities

Despite the prevalence of digital scientific and educational contents on the Internet, only a few search engines are capable to retrieve them efficiently and effectively. The main challenge in freely searching scientific literature arises from the presence of structured math formulas and their heterogeneous and contextually important surrounding words. This thesis introduces an effective math-aware, ad-hoc retrieval model that incorporates structure search and semantic similarities. Transformer-based neural retrievers have been adopted to capture additional semantics using domain-adapted supervised retrieval. To enable structure search, I suggest an unsupervised retrieval model that can filter potential mathematical formulas based on structure similarity. This similarity is determined by measuring the largest common substructure(s) in a formula tree representation, known as the Operator Tree (OPT). The structure matching is approximated by employing maximum matching of path-based structure features. The proposed structure similarity measurement can be tailored based on the desired effectiveness and efficiency trade-offs. It may consider various node types, such as operators and operands, and accommodate different numbers of common subtrees with varying weights. In addition to structure similarity, this unsupervised model also captures symbol substitutions through a greedy matching algorithm applied to the matched substructure(s). To achieve efficient structure search, I introduce a dynamic pruning algorithm to the problem of structure retrieval. The proposed retrieval algorithm efficiently identifies the maximum common subtree among formula candidates and safely eliminates potential structure matches that exceed a dynamic threshold. To accomplish this, three rank-safe pruning strategies are suggested and compared against exhaustive search baselines. Additionally, more aggressive thresholding policies are proposed to balance effectiveness with further speed improvements. A novel hierarchical inverted index has been implemented. This index is designed to be compatible with traditional information retrieval (IR) infrastructure and optimization techniques. To capture other semantic similarities, I have incorporated neural retrievers into a hybrid setting with structure search. This approach has achieved the state-of-the-art effectiveness in recent math information retrieval tasks. In comparison to strict and unsupervised matching, I have found that supervised neural retrievers are able to capture additional semantic similarities in a highly complementary manner. In order to learn effective representations in heterogeneous math contents, I have proposed a novel pretraining architecture that can improve the contextual awareness between math and its surrounding texts. This pretraining scheme generates effective downstream single-vector representations, eliminating the efficiency bottleneck from using multi-vector dense representations. In the end, the thesis examines future directions, specifically the integration of recent advancements in language modeling. This includes incorporating ongoing exciting developments of large language models for improved math information retrieval. A preliminary evaluation has been conducted to assess the impact of these advancements

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

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

General Course Catalog [July-December 2020]

Undergraduate Course Catalog, July-December 2020https://repository.stcloudstate.edu/undergencat/1132/thumbnail.jp

General Course Catalog [January-June 2019]

Undergraduate Course Catalog, January-June 2019https://repository.stcloudstate.edu/undergencat/1129/thumbnail.jp