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Recognition and Retrieval of Mathematical Expressions
 INTERNATIONAL JOURNAL ON DOCUMENT ANALYSIS AND RECOGNITION
"... Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased ..."
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Document recognition and retrieval technologies complement one another, providing improved access to increasingly large document collections. While recognition and retrieval of textual information is fairly mature, with widespread availability of Optical Character Recognition (OCR) and textbased search engines, recognition and retrieval of graphics such as images, figures, tables, diagrams, and mathematical expressions are in comparatively early stages of research. This paper surveys the state of the art in recognition and retrieval of mathematical expressions, organized around four key problems in math retrieval (query construction, normalization, indexing, and relevance feedback), and four key problems in math recognition (detecting expressions, detecting and classifying symbols, analyzing symbol layout, and constructing a representation of meaning). Of special interest is the machine learning problem of jointly optimizing the component algorithms in a math recognition system, and developing effective indexing, retrieval and relevance feedback algorithms for math retrieval. Another important open problem is developing user interfaces that seamlessly integrate recognition and retrieval. Activity in these important research areas is increasing, in part because math notation provides an excellent domain for studying problems common to many document and graphics recognition and retrieval applications, and also because mature applications will likely provide substantial benefits for education, research, and mathematical literacy.
Bootstrapping a semantic wiki application for learning mathematics
 In Sure and Schaffert
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Extending full text search engine for mathematical content
 Towards Digital Mathematics Library. Birmingham, United Kingdom, July
, 2008
"... Abstract. The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in ..."
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Abstract. The WWW became the main resource of mathematical knowledge. Currently available full text search engines can be used on these documents but they are deficient in almost all cases. By applying axioms, equal transformations, and by using different notation each formula can be expressed in numerous ways. Most of these documents do not contain semantic information; therefore, precise mathematical interpretation is impossible. On the other hand, semantic information can help to give more precise information. In this work we address these issues and present a new technique how to search for mathematical formulae in realworld mathematical documents, but still offering an extensible level of mathematical awareness. It exploits the advantages of full text search engine and stores each formula not only once but in several generalised representations. Because it is designed as an extension, any full text search engine can adopt it. Based on the proposed theory we developed EgoMath—new mathematical search engine. Experiments with EgoMath over two document sets, containing semantic information, showed that this technique can be used to build a fullyfledged mathematical search engine. Key words: mathematical discourse, language processing, mathematical searching, full text search engine, indexing 1
MathWebSearch 0.4: A semantic search engine for mathematics. (unpublished manuscript
, 2008
"... Abstract. We present a search engine for mathematical formulae. The MathWebSearch system harvests the web for content representations of formulae and indexes them with substitution tree indexing. In version 0.4 we have parallelized and distributed the search server and augmented the web interface wi ..."
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Abstract. We present a search engine for mathematical formulae. The MathWebSearch system harvests the web for content representations of formulae and indexes them with substitution tree indexing. In version 0.4 we have parallelized and distributed the search server and augmented the web interface with a new JavaScriptbased visual editor for content math formulae. Furthermore, we have extended the query language by generalization, variants, unification, and text search facilities, which can also be mixed. Our experiments show that this architecture results in a scalable application. 1
Knowledge Archives in Theorema: A LogicInternal Approach
"... Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to ..."
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Archives are implemented as an extension of Theorema for representing mathematical repositories in a natural way. An archive can be conceived as one large formula in a language consisting of higherorder predicate logic together with a few constructs for structuring knowledge: attaching labels to subhierarchies, disambiguating symbols by the use of namespaces, importing symbols from other namespaces and specifying the domains of categories and functors as namespaces with variable operations. All these constructs are logicinternal in the sense that they have a natural translation to higherorder logic so that certain aspects of Mathematical Knowledge Management can be realized in the object logic itself. There are a variety of operations on archives, though in this paper we can only sketch a few of them: knowledge retrieval and theory exploration, merging and splitting, insertion and translation to predicate logic.
Algorithm, Performance
"... We report on the user requirements study and preliminary implementation phases in creating a digital library that indexes and retrieves educational materials on math. We first review the current approaches and resources for math retrieval, then report on the interviews of a small group of potential ..."
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We report on the user requirements study and preliminary implementation phases in creating a digital library that indexes and retrieves educational materials on math. We first review the current approaches and resources for math retrieval, then report on the interviews of a small group of potential users to properly ascertain their needs. While preliminary, the results suggest that metasearch and resource categorization are two basic requirements for a math search engine. In addition, we implement a prototype categorization system and show that the generic features work well in identifying the math contents from the webpage but perform less well at categorizing them. We discuss our long term goals, where we plan to investigate how math expressions and text search may be best integrated.
T.: Integrated Semantic Math I/O in ActiveMath: an Evaluation
 in Proceedings of the 2007 Mathematical UserInterface Workshop
, 2007
"... The ActiveMath system is a webbased learning environment that integrates static mathematical content and interactive exercises with evaluated mathematical input from learners. Mathematical formulæ in ActiveMath are encoded in OpenMath and presented with regional notations. Users can input formul ..."
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The ActiveMath system is a webbased learning environment that integrates static mathematical content and interactive exercises with evaluated mathematical input from learners. Mathematical formulæ in ActiveMath are encoded in OpenMath and presented with regional notations. Users can input formulæ using the same notations via a formula editor or using plaintext input. Input to the editor is assisted by allowing users to copy formulæ from other parts of ActiveMath. In this paper we will describe how all these components are integrated and work within the system. We will then discuss recent evaluations of the formulæ input methods run within the LeActiveMath project in Malaga and Edinburgh. The results indicate that, even though the assisted input methods provided by the Formula Editor and copyandpaste are appreciated by users the most popular input method remains the plain text input fields. Proposals are made for how direct input of text can be facilitated and assisted in future formulæ input systems.
Discovering How to Write Semantic Math with new Symbols
"... The ActiveMath learning environment is based on semantic mathematical formulæ encoded using OpenMath1. This gives it a chance to render formulæ on a variety of platforms, using culturaldependent adaptations, and with addedvalue services that may help the learners in reading the formulæ. The pri ..."
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The ActiveMath learning environment is based on semantic mathematical formulæ encoded using OpenMath1. This gives it a chance to render formulæ on a variety of platforms, using culturaldependent adaptations, and with addedvalue services that may help the learners in reading the formulæ. The price to pay at authoring, however, is high since it requires encoding the meaning and not only the graphical presentation of the formulæ. Examples of challenges include the input of K[x1,..., xn] which is well known to represent the ring of polynomials on n variables but which does not enjoy, yet, the support of official Content Dictionaries for the symbols. In this paper, we explain methods we propose to discover the symbols needed to encode expressions, the typical expressions, and the ways to input this within the ActiveMath learning environment with jEditOQMath and to have it rendered. En passant, we describe requirements on the browsing and search methods for the presentations of OpenMath Content Dictionaries. symbol: from Latin symbolum token, sign, symbol, from Greek symbolon, literally, token of identity verified by comparing its other half, from symballein to throw together, compare, from syn + ballein: to throw MerriamWebster dictionary One of the foundations of the manipulations of formulæ in the ActiveMath learning environment is that they are expressed semantically in OpenMath; that is their representation encodes their meaning. This is a strong requirement compared to the long tradition of encoding mathematical formulæ to obtain their typeset form. It brings along several features (such as a mathematical search, a rendering which may help the learner, or the facility to copyandpaste)
Gap Detection in Webbased Adaptive Educational Systems
"... Abstract. Content development for adaptive educational systems is known to be an errorprone task. Gaps can occur when the content is created, modified or when the context of its usage changes. This paper aims at improving the existing practises of learning content quality control in adaptive educa ..."
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Abstract. Content development for adaptive educational systems is known to be an errorprone task. Gaps can occur when the content is created, modified or when the context of its usage changes. This paper aims at improving the existing practises of learning content quality control in adaptive educational systems by automating detection and management of gaps. Several categories of gaps are identified to account for structural, linguistic, and semantic content inconsistencies in learning content collections. An effective filtering mechanism have been implemented in order to slice the collected gap data into categories that are relevant for the current authoring context. Evaluation of the developed tool demonstrates its utility. 1