Characterizing Van Kampen Squares via Descent Data

Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science. Usually, exactness is expressed in terms of properties of the pullback functor associated with the cocone. Even in the case of non-exactness, researchers in model semantics and rewriting theory inquire an elementary characterization of the image of this functor. In this paper we will investigate this question in the special case where the cocone is a cospan, i.e. part of a Van Kampen square. The use of Descent Data as the dominant categorical tool yields two main results: A simple condition which characterizes the reachable part of the above mentioned functor in terms of liftings of involved equivalence relations and (as a consequence) a necessary and sufficient condition for a pushout to be a Van Kampen square formulated in a purely algebraic manner.Comment: In Proceedings ACCAT 2012, arXiv:1208.430

The Drosophila genome nexus: a population genomic resource of 623 Drosophila melanogaster genomes, including 197 from a single ancestral range population.

Hundreds of wild-derived Drosophila melanogaster genomes have been published, but rigorous comparisons across data sets are precluded by differences in alignment methodology. The most common approach to reference-based genome assembly is a single round of alignment followed by quality filtering and variant detection. We evaluated variations and extensions of this approach and settled on an assembly strategy that utilizes two alignment programs and incorporates both substitutions and short indels to construct an updated reference for a second round of mapping prior to final variant detection. Utilizing this approach, we reassembled published D. melanogaster population genomic data sets and added unpublished genomes from several sub-Saharan populations. Most notably, we present aligned data from phase 3 of the Drosophila Population Genomics Project (DPGP3), which provides 197 genomes from a single ancestral range population of D. melanogaster (from Zambia). The large sample size, high genetic diversity, and potentially simpler demographic history of the DPGP3 sample will make this a highly valuable resource for fundamental population genetic research. The complete set of assemblies described here, termed the Drosophila Genome Nexus, presently comprises 623 consistently aligned genomes and is publicly available in multiple formats with supporting documentation and bioinformatic tools. This resource will greatly facilitate population genomic analysis in this model species by reducing the methodological differences between data sets

Generalised Compositional Theories and Diagrammatic Reasoning

This chapter provides an introduction to the use of diagrammatic language, or perhaps more accurately, diagrammatic calculus, in quantum information and quantum foundations. We illustrate the use of diagrammatic calculus in one particular case, namely the study of complementarity and non-locality, two fundamental concepts of quantum theory whose relationship we explore in later part of this chapter. The diagrammatic calculus that we are concerned with here is not merely an illustrative tool, but it has both (i) a conceptual physical backbone, which allows it to act as a foundation for diverse physical theories, and (ii) a genuine mathematical underpinning, permitting one to relate it to standard mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G. Chirabella, R. Spekken

Arctic shipping emissions inventories and future scenarios

This paper presents 5 km×5 km Arctic emissions inventories of important greenhouse gases, black carbon and other pollutants under existing and future (2050) scenarios that account for growth of shipping in the region, potential diversion traffic through emerging routes, and possible emissions control measures. These high-resolution, geospatial emissions inventories for shipping can be used to evaluate Arctic climate sensitivity to black carbon (a short-lived climate forcing pollutant especially effective in accelerating the melting of ice and snow), aerosols, and gaseous emissions including carbon dioxide. We quantify ship emissions scenarios which are expected to increase as declining sea ice coverage due to climate change allows for increased shipping activity in the Arctic. A first-order calculation of global warming potential due to 2030 emissions in the high-growth scenario suggests that short-lived forcing of ~4.5 gigagrams of black carbon from Arctic shipping may increase global warming potential due to Arctic ships' CO<sub>2</sub> emissions (~42 000 gigagrams) by some 17% to 78%. The paper also presents maximum feasible reduction scenarios for black carbon in particular. These emissions reduction scenarios will enable scientists and policymakers to evaluate the efficacy and benefits of technological controls for black carbon, and other pollutants from ships

Three qubit entanglement within graphical Z/X-calculus

The compositional techniques of categorical quantum mechanics are applied to analyse 3-qubit quantum entanglement. In particular the graphical calculus of complementary observables and corresponding phases due to Duncan and one of the authors is used to construct representative members of the two genuinely tripartite SLOCC classes of 3-qubit entangled states, GHZ and W. This nicely illustrates the respectively pairwise and global tripartite entanglement found in the W- and GHZ-class states. A new concept of supplementarity allows us to characterise inhabitants of the W class within the abstract diagrammatic calculus; these method extends to more general multipartite qubit states.Comment: In Proceedings HPC 2010, arXiv:1103.226

Nets, relations and linking diagrams

In recent work, the author and others have studied compositional algebras of Petri nets. Here we consider mathematical aspects of the pure linking algebras that underly them. We characterise composition of nets without places as the composition of spans over appropriate categories of relations, and study the underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in Computer Science (CALCO), Warsaw, Poland, 3-6 September 201

Can sexual selection drive female life histories? A comparative study on Galliform birds

Sexual selection is an important driver of many of the most spectacular morphological traits that we find in the animal kingdom (for example see Andersson, 1994). As such, sexual selection is most often emphasized as

The Serre spectral sequence of a noncommutative fibration for de Rham cohomology

For differential calculi on noncommutative algebras, we construct a twisted de Rham cohomology using flat connections on modules. This has properties similar, in some respects, to sheaf cohomology on topological spaces. We also discuss generalised mapping properties of these theories, and relations of these properties to corings. Using this, we give conditions for the Serre spectral sequence to hold for a noncommutative fibration. This might be better read as giving the definition of a fibration in noncommutative differential geometry. We also study the multiplicative structure of such spectral sequences. Finally we show that some noncommutative homogeneous spaces satisfy the conditions to be such a fibration, and in the process clarify the differential structure on these homogeneous spaces. We also give two explicit examples of differential fibrations: these are built on the quantum Hopf fibration with two different differential structures.Comment: LaTeX, 33 page

Correctness, completeness and termination of pattern-based model-to-model transformation

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-03741-2_26Proceedings of Third International Conference, CALCO 2009, Udine, Italy, September 7-10, 2009.Model-to-model (M2M) transformation consists in trans- forming models from a source to a target language. Many transformation languages exist, but few of them combine a declarative and relational style with a formal underpinning able to show properties of the transformation. Pattern-based transformation is an algebraic, bidirectional, and relational approach to M2M transformation. Specifications are made of patterns stating the allowed or forbidden relations between source and target models, and then compiled into low level operational mechanisms to perform source-to-target or target-to-source transformations. In this paper, we study the compilation into operational triple graph grammar rules and show: (i) correctness of the compilation of a specification without negative patterns; (ii) termination of the rules, and (iii) completeness, in the sense that every model considered relevant can be built by the rules.Work supported by the Spanish Ministry of Science and Innovation, projects METEORIC (TIN2008-02081), MODUWEB (TIN2006-09678) and FORMALISM (TIN2007-66523). Moreover, part of this work was done during a sabbatical leave of the first author at TU Berlin, with financial support from the Spanish Ministry of Science and Innovation (grant ref. PR2008-0185). We thank the referees for their useful comment