Strategies for Parallel Markup

Cross-referenced parallel markup for mathematics allows the combination of both presentation and content representations while associating the components of each. Interesting applications are enabled by such an arrangement, such as interaction with parts of the presentation to manipulate and querying the corresponding content, and enhanced search indexing. Although the idea of such markup is hardly new, effective techniques for creating and manipulating it are more difficult than it appears. Since the structures and tokens in the two formats often do not correspond one-to-one, decisions and heuristics must be developed to determine in which way each component refers to and is referred to by components of the other representation. Conversion between fine and coarse grained parallel markup complicates ID assignments. In this paper, we will describe the techniques developed for \LaTeXML, a \TeX/\LaTeX to XML converter, to create cross-referenced parallel MathML. While we do not yet consider \LaTeXML's content MathML to be useful, the current effort is a step towards that continuing goal

VMEXT: A Visualization Tool for Mathematical Expression Trees

Mathematical expressions can be represented as a tree consisting of terminal symbols, such as identifiers or numbers (leaf nodes), and functions or operators (non-leaf nodes). Expression trees are an important mechanism for storing and processing mathematical expressions as well as the most frequently used visualization of the structure of mathematical expressions. Typically, researchers and practitioners manually visualize expression trees using general-purpose tools. This approach is laborious, redundant, and error-prone. Manual visualizations represent a user's notion of what the markup of an expression should be, but not necessarily what the actual markup is. This paper presents VMEXT - a free and open source tool to directly visualize expression trees from parallel MathML. VMEXT simultaneously visualizes the presentation elements and the semantic structure of mathematical expressions to enable users to quickly spot deficiencies in the Content MathML markup that does not affect the presentation of the expression. Identifying such discrepancies previously required reading the verbose and complex MathML markup. VMEXT also allows one to visualize similar and identical elements of two expressions. Visualizing expression similarity can support support developers in designing retrieval approaches and enable improved interaction concepts for users of mathematical information retrieval systems. We demonstrate VMEXT's visualizations in two web-based applications. The first application presents the visualizations alone. The second application shows a possible integration of the visualizations in systems for mathematical knowledge management and mathematical information retrieval. The application converts LaTeX input to parallel MathML, computes basic similarity measures for mathematical expressions, and visualizes the results using VMEXT.Comment: 15 pages, 4 figures, Intelligent Computer Mathematics - 10th International Conference CICM 2017, Edinburgh, UK, July 17-21, 2017, Proceeding

Isabelle/PIDE as Platform for Educational Tools

The Isabelle/PIDE platform addresses the question whether proof assistants of the LCF family are suitable as technological basis for educational tools. The traditionally strong logical foundations of systems like HOL, Coq, or Isabelle have so far been counter-balanced by somewhat inaccessible interaction via the TTY (or minor variations like the well-known Proof General / Emacs interface). Thus the fundamental question of math education tools with fully-formal background theories has often been answered negatively due to accidental weaknesses of existing proof engines. The idea of "PIDE" (which means "Prover IDE") is to integrate existing provers like Isabelle into a larger environment, that facilitates access by end-users and other tools. We use Scala to expose the proof engine in ML to the JVM world, where many user-interfaces, editor frameworks, and educational tools already exist. This shall ultimately lead to combined mathematical assistants, where the logical engine is in the background, without obstructing the view on applications of formal methods, formalized mathematics, and math education in particular.Comment: In Proceedings THedu'11, arXiv:1202.453

Which one is better: presentation-based or content-based math search?

Mathematical content is a valuable information source and retrieving this content has become an important issue. This paper compares two searching strategies for math expressions: presentation-based and content-based approaches. Presentation-based search uses state-of-the-art math search system while content-based search uses semantic enrichment of math expressions to convert math expressions into their content forms and searching is done using these content-based expressions. By considering the meaning of math expressions, the quality of search system is improved over presentation-based systems

Vertical Distribution, Parallel Trade, and Price Divergence in Integrated Markets

We develop a model of vertical pricing in which an original manufacturer sets wholesale prices in two markets that are integrated at the distributor level by parallel imports (PI). The manufacturing firm needs to set these two prices to balance three competing interests: restricting competition in the PI-recipient market, avoiding resource wastes due to actual trade, and reducing the double-markup problem in the PI-source nation. These trade-offs imply the counterintuitive result that both wholesale and retail prices could diverge as a result of declining trading costs, even as the volume of PI increases. Thus, in some circumstances it may be misleading to think of PI as an unambiguous force for price integration.Vertical Restraints; Parallel Imports; Market Integration

An effective data placement strategy for XML documents

As XML is increasingly being used in Web applications, new technologies need to be investigated for processing XML documents with high performance. Parallelism is a promising solution for structured document processing and data placement is a major factor for system performance improvement in parallel processing. This paper describes an effective XML document data placement strategy. The new strategy is based on a multilevel graph partitioning algorithm with the consideration of the unique features of XML documents and query distributions. A new algorithm, which is based on XML query schemas to derive the weighted graph from the labelled directed graph presentation of XML documents, is also proposed. Performance analysis on the algorithm presented in the paper shows that the new data placement strategy exhibits low workload skew and a high degree of parallelism

Understanding Strategic Bidding in Restructured Electricity Markets: A Case Study of ERCOT

We examine the bidding behavior of firms competing on ERCOT, the hourly electricity balancing market in Texas. We characterize an equilibrium model of bidding into this uniform-price divisible-good auction market. Using detailed firm-level data on bids and marginal costs of generation, we find that firms with large stakes in the market performed close to theoretical benchmarks of static, profit-maximizing bidding derived from our model. However, several smaller firms utilized excessively steep bid schedules that deviated significantly from our theoretical benchmarks, in a manner that could not be empirically accounted for by the presence of technological adjustment costs, transmission constraints, or collusive behavior. Our results suggest that payoff scale matters in firms' willingness and ability to participate in complex, strategic market environments. Finally, although smaller firms moved closer to theoretical bidding benchmarks over time, their bidding patterns contributed to productive inefficiency in this newly restructured market, along with efficiency losses due to the close-to optimal exercise of market power by larger firms.

Measuring the Global Research Environment: Information Science Challenges for the 21st Century

“What does the global research environment look like?” This paper presents a summary look at the results of efforts to address this question using available indicators on global research production. It was surprising how little information is available, how difficult some of it is to access and how flawed the data are. The three most useful data sources were UNESCO (United Nations Educational, Scientific and Cultural Organization) Research and Development data (1996-2002), the Institute of Scientific Information publications listings for January 1998 through March 2003, and the World of Learning 2002 reference volume. The data showed that it is difficult to easily get a good overview of the global research situation from existing sources. Furthermore, inequalities between countries in research capacity are marked and challenging. Information science offers strategies for responding to both of these challenges. In both cases improvements are likely if access to information can be facilitated and the process of integrating information from different sources can be simplified, allowing transformation into effective action. The global research environment thus serves as a case study for the focus of this paper – the exploration of information science responses to challenges in the management, exchange and implementation of knowledge globally

Design issues in the production of hyper‐books and visual‐books

This paper describes an ongoing research project in the area of electronic books. After a brief overview of the state of the art in this field, two new forms of electronic book are presented: hyper‐books and visual‐books. A flexible environment allows them to be produced in a semi‐automatic way starting from different sources: electronic texts (as input for hyper‐books) and paper books (as input for visual‐books). The translation process is driven by the philosophy of preserving the book metaphor in order to guarantee that electronic information is presented in a familiar way. Another important feature of our research is that hyper‐books and visual‐books are conceived not as isolated objects but as entities within an electronic library, which inherits most of the features of a paper‐based library but introduces a number of new properties resulting from its non‐physical nature