Kingston Maurward College

We study the Wasserstein gradient flow of semi-discrete energies in the space of probability measures, that is functionals depending on two measures-one being an absolutely continuous density and the other an atomic measure. These energies appear naturally in the field of urban planning. This is done via the celebrated JKO scheme, for which we prove convergence to a limiting system composed of a parabolic PDE with singular advection coupled with an ODE, also presenting singular dynamics. This is first done under more general assumptions using classical tools, and in a second moment convergence is proven to hold in $L^2_tH^1_x$ for the cases of linear and Porous-Medium type diffusions. We then pass to the study of some qualitative properties of this system, such as the convergence of the atoms towards the baricenters of their corresponding Laguerre cells. We finish this work with extensive numerical simulations that aid in formulating conjectures for the qualitative behavior of this system; in the case of linear diffusion, for instance, we observe a dynamic crystallization phenomenon.

This work addresses the issue of the convergence of an $N$-player game towards a limit model involving a continuum of players, as the number of agents $N$ goes to infinity. More precisely, we investigate the convergence of Nash equilibria to a Cournot--Nash equilibrium of the limit model. When the cost function of the players is the first variation of some potential function, equilibria can be characterized by a stationarity condition, satisfied in particular by the minimizers of the potential. We demonstrate such a characterization under low regularity assumptions. Then we focus on the case where the players interact in a pairwise fashion; in this case we show that the original sequence of $N$-player games also admit a potential structure and prove that their corresponding potential functions converge in the sense of $Γ$-convergence to the potential function of the limit game.

Abstract Roads are an important way to transport people and goods, but they sometimes have negative impacts on wildlife. One of the leading causes of mortality for several species is identified as road strikes, and the most significant remains bird-vehicle collisions. This study aimed to investigate what species of birds are most affected, and what other factors impact in their susceptibility in road collisions, such as age, sex, season, and type of transports. A total of N=5413 records, and 140 bird species were documented by BTO ringers. For analysis four Bayesian Hierarchical Models were used, with random effects results showing that Barn owls were most affected by collisions. Road mortality presents the highest cause of mortality among species when contrasted with rail mortality. Age and sexual bias was detected across all species, however juveniles and males did appear to be prominent in relation to other age classes. Winter and early spring were the months with most reported casualties and 2016 had lower abundance of mortality across the 10-year period. 75% of birds were found within a week, which may indicate some bias interference from scavenging animals, as true figures could be up to 16 times more. This study discusses some mitigation measures found in current research, that could dramatically reduce numbers of birds affected each year by road mortality.

I welcome the discussion on the relationship between vets and organic farming, but would like to comment on some remarks in Josh Loeb’s editorial ( VR , 23 March 2019, vol 184, p 361). He states that ‘organic farming can impinge on veterinary decision making’. The Soil Association vaccine standards are used as an example, apparently restricting the use of clostridial vaccines in sheep. The current standards are as follows:1 10.9.11 You may only use vaccines: • in consultation with your vet, and • when there is a known disease risk which you cannot control …

Teaching numeric disciplines to higher education students in many life sciences disciplines is highly challenging. In this study, we test whether an approach linking field observations with predictive models can be useful in allowing students to understand basic numeracy and probability, as well as developing skills in modelling, understanding species interactions and even community/ecosystem-service interactions. We presented a field-based lecture in a morning session (on rocky shore ecology), followed by an afternoon session parameterising a belief network using a simple, user-friendly interface. The study was conducted with students during their second week of a foundation degree, hence having little prior knowledge of these systems or models. All students could create realistic predictive models of competition, predation and grazing, although most initially failed to account for trophic cascade effects in parameterising their models of the rocky shore they had previously seen. The belief network was then modified to account for a marine ecosystem management approach, where fishing effort and economic benefit of fishing were linked to population abundance of different species, and management goals were included. Students had little difficultly in applying conceptual links between species and ecosystem services in the same manner as between species. Students evaluated their understanding of a range of variables from rocky shore knowledge to marine management as increasing over the session, but the role of the predictive modelling task was indicated as a major source of learning, even for topics we thought may be better learned in the field. The study adds evidence to the theories that students benefit from exposure to numeric topics, even very early in their degree programmes, but students grasp concepts better when applied to real world situations which they have experience of, or perceive as important.

The 155 km long Dorset and East Devon Coast World Heritage Site is recognized for its 250 million years of earth history, including internationally renowned coastal geomorphological landforms and processes. It is a naturally active coast ranging from vertical ‘hard’ cliffs to very active landslides, protected by both national and international conservation designations. The primary conservation focus of the Site is geoconservation, but its cliff ecosystems also provide outstanding examples of natural resilience to rapid change as well as preserving very important communities. One of the key features of the Site is that its dynamics allow a constant renewal of the visible geology and exposures of fossils, Erosion is accepted as normal. It is a heavily used tourist location with cliff-top paths in use all year and there are concerns about safety, especially for visitors beneath cliffs and crossing mudslides. Management of the Site deals with such issues as fossil collecting and conservation, access, education, coast protection and through a management plan.

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