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

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

Deceptive signals of phase transitions in small magnetic clusters

We present an analysis of the thermodynamic properties of small transition metal clusters and show how the commonly used indicators of phase transitions like peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see http://www.smallsystems.d

The Origins of Phase Transitions in Small Systems

The identification and classification of phases in small systems, e.g. nuclei, social and financial networks, clusters, and biological systems, where the traditional definitions of phase transitions are not applicable, is important to obtain a deeper understanding of the phenomena observed in such systems. Within a simple statistical model we investigate the validity and applicability of different classification schemes for phase transtions in small systems. We show that the whole complex temperature plane contains necessary information in order to give a distinct classification.Comment: 3 pages, 4 figures, revtex 4 beta 5, for further information see http://www.smallsystems.d

Biotechniques

The Bisulfite Sequencing Data Presentation and Compilation (BDPC) web interface for compilation and presentation of data from bisulfite sequencing DNA methylation studies has been improved by adding a new module. This module allows visualization of the whole data set in form of a heatmap of DNA methylation levels and clustering and comparison of tissue methylation patterns. It can also be used for data not processed by BDPC. In addition, several functions of the existing BDPC compilation module have been improved

DNA methylation analysis by bisulfite conversion, cloning, and sequencing of individual clones.

DNA methylation is an essential epigenetic modification in the human genome. For the investigation of DNA methylation patterns, bisulfite conversion and DNA sequencing is a method of choice, because it provides detailed information on the methylation pattern of individual DNA molecules at single CG site resolution. The method is based on the deamination of cytosine residues to uracils in the presence of NaOH and sodium bisulfite. Since methylcytosine is not converted under these conditions, the original methylation state of the DNA can be analyzed by sequencing of the converted DNA. After the conversion reaction, the DNA sequence under investigation is amplified by polymerase chain reaction (PCR) with primers specific for one strand of the bisulfite-converted DNA. The PCR product is cloned and individual clones are sequenced. Here, we describe an advanced protocol for bisulfite conversion, protocols for cloning, and tools for primer design (Methprimer, Bisearch). In addition, we present tools for the web display of primary data and data analysis (BiQ Analyzer, BDPC) and describe the setup of a sequencing and analysis pipeline for medium to high throughput