Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

The epidemiology of traumatic brain injuries sustained by children under 10 years of age presenting to a tertiary hospital in Soweto, South Africa

Background. Traumatic brain injury (TBI) in the paediatric population is a significant contributor to death and disability worldwide. In sub-Saharan Africa, death and disability from TBI are still superseded by infectious disease. Mechanisms of injury differ by region and socioeconomics, but in general, falls, road traffic collisions (RTCs), being ‘struck by/against objects’ and non-accidental injuries (NAIs) are responsible for most cases.Objectives. To: (i) quantify the burden of TBI in terms of demographics, causes and severity; (ii) explore resource utilisation regarding length of stay, computed tomography (CT) brain scan use and multidisciplinary participation; (iii) interrogate possible temporal patterns of injury; and (iv) thus identify potential targets for community-based prevention strategies.Methods. In a 5-year retrospective review of all children aged <10 years admitted with TBI between September 2013 and August 2018, demographics, date of injury, mechanism of injury, severity of TBI based on the Glasgow Coma Scale, and requirement for a CT brain scan were collected for each patient. Outcomes were reported as discharge, transfer or death. Outcomes for children sustaining isolated TBI were compared with those for children sustaining TBI with polytrauma.Results. A total of 2 153 patients were included, with a mean (standard deviation) age of 4.6 (2.7) years and a male/female ratio of 1.7:1. RTCs were the most frequent cause of injury at 59% (80% of these were pedestrian-vehicle collisions), followed by falls at 24%. Mild TBIs accounted for 87% of admissions, moderate injuries for 6%, and severe injuries for 7%. Polytrauma was associated with increased severity of TBI. The cohort had a 2.3% mortality. NAIs accounted for 6% of injuries and carried a 4% mortality. The median (interquartile range) duration of hospitalisation was 1 (1 - 3) days, ranging from <24 hours to 132 days. CT scans were performed on 43% of admitted patients, and 48% of patients had consultations with another medical or allied medical discipline. Injuries were more frequent during the summer months and over weekends. Infants aged <1 year were identified as a group particularly vulnerable to injury, specifically NAI.Conclusions. Paediatric TBI was demonstrated to be a resource-intensive public health concern. From the results, we identified potential primary prevention targets that could perhaps be incorporated into broader community-based intervention programmes. We also identified a need to study long-term consequences of mild TBI further in our paediatric population

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

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

Picturing classical and quantum Bayesian inference

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators rather than probability distributions as representative of degrees of belief. The diagrammatic framework is stated in the graphical language of symmetric monoidal categories and of compact structures and Frobenius structures therein, in which Bayesian inversion boils down to transposition with respect to an appropriate compact structure. We characterize classical Bayesian inference in terms of a graphical property and demonstrate that our approach eliminates some purely conventional elements that appear in common representations thereof, such as whether degrees of belief are represented by probabilities or entropic quantities. We also introduce a quantum-like calculus wherein the Frobenius structure is noncommutative and show that it can accommodate Leifer's calculus of `conditional density operators'. The notion of conditional independence is also generalized to our graphical setting and we make some preliminary connections to the theory of Bayesian networks. Finally, we demonstrate how to construct a graphical Bayesian calculus within any dagger compact category.Comment: 38 pages, lots of picture

Extrapair paternity in two populations of the socially monogamous Thorn-tailed Rayadito Aphrastura spinicauda (Passeriformes: Furnariidae)

Studies on extrapair paternity (EPP) are key to understanding the ecological and evolutionary drivers of variation in avian mating strategies, but information is currently lacking for most tropical and subtropical taxa. We describe the occurrence of EPP in two populations of a South American socially monogamous bird, the Thorn-tailed Rayadito, based on data from 266 broods and 895 offspring that were sampled during six breeding seasons in north-central and southern Chile. In the northern population, 21% of the broods contained at least one extrapair young and 14% of all offspring were sired by an extrapair male, while in the southern population, we detected extrapair offspring (EPO) in 14% of the broods, and 6% of all offspring were EPO. Variation in the frequency of EPP could stem from population differences in the duration of the breeding season or the density of breeding individuals. Other factors such as differences in breeding synchrony and variation in food availability need to be evaluated. More reports on EPP rates are necessary to determine the patterns of taxonomic and geographic variation in mating strategies in Neotropical birds, and to better understand the differences in ecological dynamics between northern and southern hemisphere populations.Fil: Botero Delgadillo, Esteban. Max Plank Institute For Ornithology; Alemania. SELVA: Investigación para la Conservación en el Neotrópico; Colombia. Universidad de Chile; ChileFil: Quirici, Verónica. Universidad Andrés Bello; ChileFil: Poblete, Yanina. Universidad de Las Américas; ChileFil: Ippi, Silvina Graciela. Universidad Nacional del Comahue. Centro Regional Universitario Bariloche. Departamento de Ecología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; ArgentinaFil: Kempenaers, Bart. Max Plank Institute For Ornithology; AlemaniaFil: Vásquez, Rodrigo A.. Universidad de Chile; Chil

On the definition of parallel independence in the algebraic approaches to graph transformation

Parallel independence between transformation steps is a basic and well-understood notion of the algebraic approaches to graph transformation, and typically guarantees that the two steps can be applied in any order obtaining the same resulting graph, up to isomorphism. The concept has been redefined for several algebraic approaches as variations of a classical “algebraic” condition, requiring that each matching morphism factorizes through the context graphs of the other transformation step. However, looking at some classical papers on the double-pushout approach, one finds that the original definition of parallel independence was formulated in set-theoretical terms, requiring that the intersection of the images of the two left-hand sides in the host graph is contained in the intersection of the two interface graphs. The relationship between this definition and the standard algebraic one is discussed in this position paper, both in the case of left-linear and non-left-linear rules

The stress hormone corticosterone in a marine top predatorreflects short-term changes in food availability

-In many seabird studies, single annual proxies of prey abundance have been used to explain variability in breeding performance, but much more important is probably the timing of prey availability relative to the breeding season when energy demand is at a maximum. Until now, intraseasonal variation in prey availability has been difficult to quantify in seabirds. Using a state-of-the-art ocean drift model of larval cod Gadus morhua, an important constituent of the diet of common guillemots Uria aalge in the southwestern Barents Sea, we were able to show clear, short-term correlations between food availability and measurements of the stress hormone corticosterone (CORT) in parental guillemots over a 3-year period (2009–2011). The model allowed the extraction of abundance and size of cod larvae with very high spatial (4 km) and temporal resolutions (1 day) and showed that cod larvae from adjacent northern spawning grounds in Norway were always available near the guillemot breeding colony while those from more distant southerly spawning grounds were less frequent, but larger. The latter arrived in waves whose magnitude and timing, and thus overlap with the guillemot breeding season, varied between years. CORT levels in adult guillemots were lower in birds caught after a week with high frequencies of southern cod larvae. This pattern was restricted to the two years (2009 and 2010) in which southern larvae arrived before the end of the guillemot breeding season. Any such pattern was masked in 2011 by already exceptionally high numbers of cod larvae in the region throughout chick-rearing period. The findings suggest that CORT levels in breeding birds increase when the arrival of southern sizable larvae does not match the period of peak energy requirements during breeding. Common guillemot, CORT, food availability, seabird, Uria aalg