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

Paradoxical Magnetic Cooling in a Structural Transition Model

In contrast to the experimentally widely used isentropic demagnetization process for cooling to ultra-low temperatures we examine a particular classical model system that does not cool, but rather heats up with isentropic demagnetization. This system consists of several magnetite particles in a colloidal suspension, and shows the uncommon behavior of disordering structurally while ordering magnetically in an increasing magnetic field. For a six-particle system, we report an uncommon structural transition from a ring to a chain as a function of magnetic field and temperature.Comment: 3 pages, 2 figures. For recent information on physics of small systems see http://www.smallsystems.d

First order phase transitions: equivalence between bimodalities and the Yang-Lee theorem

First order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one to one correspondence with the Yang Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.Comment: 10 pages, no figure

Bisulfite sequencing Data Presentation and Compilation (BDPC) web server—a useful tool for DNA methylation analysis

During bisulfite genomic sequencing projects large amount of data are generated. The Bisulfite sequencing Data Presentation and Compilation (BDPC) web interface (http://biochem.jacobs-university.de/BDPC/) automatically analyzes bisulfite datasets prepared using the BiQ Analyzer. BDPC provides the following output: (i) MS-Excel compatible files compiling for each PCR product (a) the average methylation level, the number of clones analyzed and the percentage of CG sites analyzed (which is an indicator of data quality), (b) the methylation level observed at each CG site and (c) the methylation level of each clone. (ii) A methylation overview table compiling the methylation of all amplicons in all tissues. (iii) Publication grade figures in PNG format showing the methylation pattern for each PCR product embedded in an HMTL file summarizing the methylation data, the DNA sequence and some basic statistics. (iv) A summary file compiling the methylation pattern of different tissues, which is linked to the individual HTML result files, and can be directly used for presentation of the data in the internet. (v) A condensed file, containing all primary data in simplified format for further downstream data analysis and (vi) a custom track file for display of the results in the UCSC genome browser

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

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

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

Phase Transition in Small System

Everybody knows that when a liquid is heated, its temperature increases until the moment when it starts to boil. The increase in temperature then stops, all heat being used to transform the liquid into vapor. What is the microscopic origin of such a strange behavior? Does a liquid drop containing only few molecules behave the same? Recent experimental and theoretical developments seem to indicate that at the elementary level of very small systems, this anomaly appears in an even more astonishing way: during the change of state - for example from liquid to gas - the system cools whereas it is heated, i.e. its temperature decreases while its energy increases. This paper presents a review of our understanding of the negative specific heat phenomenon