Balanced growth for solutions of nonautonomous partial differential equations

We show balanced growth for solutions of some nonautonomous partial differential equations which in certain cases also describe the dynamics of structured populations

On the net reproduction rate of continuous structured populations with distributed states at birth

We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral properties of a parametrized family of unbounded operators. The alternative approach, on which we focus here, is based on the reformulation of the problem as an integral equation. In this context we introduce a density dependent net reproduction rate and discuss its relationship to a biologically meaningful quantity. Finally, we briefly discuss a third approach, which is based on the finite rank approximation of the recruitment operator.Comment: To appear in Computers and Mathematics with Application

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Global behavior of solutions to the static spherically symmetric EYM equations

The set of all possible spherically symmetric magnetic static Einstein-Yang-Mills field equations for an arbitrary compact semi-simple gauge group $G$ was classified in two previous papers. Local analytic solutions near the center and a black hole horizon as well as those that are analytic and bounded near infinity were shown to exist. Some globally bounded solutions are also known to exist because they can be obtained by embedding solutions for the $G=SU(2)$ case which is well understood. Here we derive some asymptotic properties of an arbitrary global solution, namely one that exists locally near a radial value $r_{0}$, has positive mass $m(r)$ at $r_{0}$ and develops no horizon for all $r>r_{0}$. The set of asymptotic values of the Yang-Mills potential (in a suitable well defined gauge) is shown to be finite in the so-called regular case, but may form a more complicated real variety for models obtained from irregular rotation group actions.Comment: 43 page

Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§

We employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model. Using the regularity properties of the governing semigroup, we are able to formulate a general stability condition which permits an intuitively clear interpretation in a special case of model ingredients. Moreover, we derive a comprehensive instability criterion that reduces to an elegant instability condition for the classical Daphnia population model in terms of the inherent net reproduction rate of Daphnia individuals

Torino: A Tangible Programming Language Inclusive of Children with Visual Disabilities

© 2018, Copyright © 2018 Taylor & Francis Group, LLC. Across the world, policy initiatives are being developed to engage children with computer programming and computational thinking. Diversity and inclusion has been a strong force in this agenda, but children with disabilities have largely been omitted from the conversation. Currently, there are no age appropriate tools for teaching programming concepts and computational thinking to primary school children with visual disabilities. We address this gap through presenting the design and implementation of Torino, a tangible programming language for teaching programming concepts to children age 7–11 regardless of level of vision. In this paper, we: (1) describe the design process done in conjunction with children with visual disabilities; (2) articulate the design decisions made; and (3) report insights generated from an evaluation with 10 children with mixed visual abilities that considers how children are able to trace (read) and create (write) programs with Torino. We discuss key design trade-offs: (1) readability versus extensibility; and (2) size versus liveness. We conclude by reflecting upon how an inclusive design approach shaped the final result

Coseismic fault lubrication by viscous deformation

Despite the hazard posed by earthquakes, we still lack fundamental understanding of the processes that control fault lubrication behind a propagating rupture front and enhance ground acceleration. Laboratory experiments show that fault materials dramatically weaken when sheared at seismic velocities (>0.1 m s−1). Several mechanisms, triggered by shear heating, have been proposed to explain the coseismic weakening of faults, but none of these mechanisms can account for experimental and seismological evidence of weakening. Here we show that, in laboratory experiments, weakening correlates with local temperatures attained during seismic slip in simulated faults for diverse rock-forming minerals. The fault strength evolves according to a simple, material-dependent Arrhenius-type law. Microstructures support this observation by showing the development of a principal slip zone with textures typical of sub-solidus viscous flow. We show evidence that viscous deformation (at either sub- or super-solidus temperatures) is an important, widespread and quantifiable coseismic lubrication process. The operation of these highly effective fault lubrication processes means that more energy is then available for rupture propagation and the radiation of hazardous seismic waves

Sensing and adhesion are adaptive functions in the plant pathogenic xanthomonads

<p>Abstract</p> <p>Background</p> <p>Bacterial plant pathogens belonging to the <it>Xanthomonas </it>genus are tightly adapted to their host plants and are not known to colonise other environments. The host range of each strain is usually restricted to a few host plant species. Bacterial strains responsible for the same type of symptoms on the same host range cluster in a pathovar. The phyllosphere is a highly stressful environment, but it provides a selective habitat and a source of substrates for these bacteria. Xanthomonads colonise host phylloplane before entering leaf tissues and engaging in an invasive pathogenic phase. Hence, these bacteria are likely to have evolved strategies to adapt to life in this environment. We hypothesised that determinants responsible for bacterial host adaptation are expressed starting from the establishment of chemotactic attraction and adhesion on host tissue.</p> <p>Results</p> <p>We established the distribution of 70 genes coding sensors and adhesins in a large collection of xanthomonad strains. These 173 strains belong to different pathovars of <it>Xanthomonas </it>spp and display different host ranges. Candidate genes are involved in chemotactic attraction (25 genes), chemical environment sensing (35 genes), and adhesion (10 genes). Our study revealed that candidate gene repertoires comprised core and variable gene suites that likely have distinct roles in host adaptation. Most pathovars were characterized by unique repertoires of candidate genes, highlighting a correspondence between pathovar clustering and repertoires of sensors and adhesins. To further challenge our hypothesis, we tested for molecular signatures of selection on candidate genes extracted from sequenced genomes of strains belonging to different pathovars. We found strong evidence of adaptive divergence acting on most candidate genes.</p> <p>Conclusions</p> <p>These data provide insight into the potential role played by sensors and adhesins in the adaptation of xanthomonads to their host plants. The correspondence between repertoires of sensor and adhesin genes and pathovars and the rapid evolution of sensors and adhesins shows that, for plant pathogenic xanthomonads, events leading to host specificity may occur as early as chemotactic attraction by host and adhesion to tissues.</p