A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Controlled vocabularies and semantics in systems biology

The use of computational modeling to describe and analyze biological systems is at the heart of systems biology. Model structures, simulation descriptions and numerical results can be encoded in structured formats, but there is an increasing need to provide an additional semantic layer. Semantic information adds meaning to components of structured descriptions to help identify and interpret them unambiguously. Ontologies are one of the tools frequently used for this purpose. We describe here three ontologies created specifically to address the needs of the systems biology community. The Systems Biology Ontology (SBO) provides semantic information about the model components. The Kinetic Simulation Algorithm Ontology (KiSAO) supplies information about existing algorithms available for the simulation of systems biology models, their characterization and interrelationships. The Terminology for the Description of Dynamics (TEDDY) categorizes dynamical features of the simulation results and general systems behavior. The provision of semantic information extends a model's longevity and facilitates its reuse. It provides useful insight into the biology of modeled processes, and may be used to make informed decisions on subsequent simulation experiments

Deep Understanding of Technical Documents : Automated Generation of Pseudocode from Digital Diagrams & Analysis/Synthesis of Mathematical Formulas

The technical document is an entity that consists of several essential and interconnected parts, often referred to as modalities. Despite the extensive attention that certain parts have already received, per say the textual information, there are several aspects that severely under researched. Two such modalities are the utility of diagram images and the deep automated understanding of mathematical formulas. Inspired by existing holistic approaches to the deep understanding of technical documents, we develop a novel formal scheme for the modelling of digital diagram images. This extends to a generative framework that allows for the creation of artificial images and their annotation. We contribute on the field with the creation of a novel synthetic dataset and its generation mechanism. We propose the conversion of the pseudocode generation problem to an image captioning task and provide a family of techniques based on adaptive image partitioning. We address the mathematical formulas’ semantic understanding by conducting an evaluating survey on the field, published in May 2021. We then propose a formal synthesis framework that utilized formula graphs as metadata, reaching for novel valuable formulas. The synthesis framework is validated by a deep geometric learning mechanism, that outsources formula data to simulate the missing a priori knowledge. We close with the proof of concept, the description of the overall pipeline and our future aims

Navegador ontológico matemático-NOMAT

The query algorithms in search engines use indexing, contextual analysis and ontologies, among other techniques, for text search. However, they do not use equations due to their writing complexity. NOMAT is a prototype of mathematical expression search engine that seeks information both in thesaurus and internet, using ontological tool for filtering and contextualizing information and LaTeX editor for the symbols in these expressions. This search engine was created to support mathematical research. Compared to other Internet search engines, NOMAT does not require prior knowledge of LaTeX, because has an editing tool which enables writing directly the symbols that make up the mathematical expression of interest. The results obtained were accurate and contextualized, compared to other commercial and no-commercial search engines.Los algoritmos de consulta de los motores de búsqueda utilizan indexación, análisis contextual y ontologías, entre otras técnicas, para la búsqueda de texto. Sin embargo, no utilizan ecuaciones debido a su complejidad de escritura. Nomat es un prototipo de motor de búsqueda de expresión matemática que busca información tanto en tesauro como en Internet, utilizando la Herramienta ontológica para filtrar y contextualizar información y editor de látex para los símbolos de estas expresiones. Este buscador fue creado para apoyar la investigación matemática. En comparación con otros motores de búsqueda de Internet, Nomat no requiere conocimientos previos de látex, ya que cuenta con una herramienta de edición que permite escribir directamente los símbolos que componen la expresión matemática de interés. Los resultados obtenidos fueron precisos y contextualizados, en comparación con otros motores de búsqueda comerciales y no comerciales

Context classification for improved semantic understanding of mathematical formulae

The correct semantic interpretation of mathematical formulae in electronic mathematical documents is an important prerequisite for advanced tasks such as search, accessibility or computational processing. Especially in advanced maths, the meaning of characters and symbols is highly domain dependent, and only limited information can be gained from considering individual formulae and their structures. Although many approaches have been proposed for semantic interpretation of mathematical formulae, most of them rely on the limited semantics from maths representation languages whereas very few use maths context as a source of information. This thesis presents a novel approach for principal extraction of semantic information of mathematical formulae from their context in documents. We utilised different supervised machine learning (SML) techniques (i.e. Linear-Chain Conditional Random Fields (CRF), Maximum Entropy (MaxEnt) and Maximum Entropy Markov Models (MEMM) combined with Rprop- and Rprop+ optimisation algorithms) to detect definitions of simple and compound mathematical expressions, thereby deriving their meaning. The learning algorithms demand annotated corpus which its development considered as one of this thesis contributions. The corpus has been developed utilising a novel approach to extract desired maths expressions and sub-formulae and manually annotated by two independent annotators employing a standard measure for inter-annotation agreement. The thesis further developed a new approach to feature representation depending on the definitions' templates that extracted from maths documents to defeat the restraint of conventional window-based features. All contributions were evaluated by various techniques including employing the common metrics recall, precision, and harmonic F-measure

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

数学情報アクセスのための数式表現の検索と曖昧性解消

学位の種別: 課程博士審査委員会委員 : （主査）東京大学准教授 渋谷 哲朗, 東京大学教授 萩谷 昌己, 東京大学准教授 蓮尾 一郎, 東京大学准教授 鶴岡 慶雅, 東京工業大学准教授 藤井 敦University of Tokyo(東京大学

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

Representing Mathematical Concepts Associated With Formulas Using Math Entity Cards

We introduce Math Entity Cards, a modified version of existing Entity Cards specifically tailored for Math Information Retrieval. Math Entity Cards help connect formulas to titles and description and make the navigation between formulas and text related to formulas, seamless. These cards are populated from a new knowledge base, created by extracting and combining formulas, titles and descriptions from three different sources, Wikidata, Wiktionary & ProofWiki. We demonstrate a novel approach of using entity cards for auto-complete by integrating our cards into a Math-Aware Search Interface: MathSeer. This helps create a new ecosystem for consuming information during formula editing and search. We design and conduct a human experiment, in a math information retrieval setting and find statistical evidence for the usefulness of individual card components