Dynamics of a structured slug population model in the absence of seasonal variation

We develop a novel, nonlinear structured population model for the slug Deroceras reticulatum, a highly significant agricultural pest of great economic impact, in both organic and non-organic settings. In the absence of seasonal variations, we numerically explore the effect of life history traits that are dependent on an individual's size and measures of population biomass. We conduct a systematic exploration of parameter space and highlight the main mechanisms and implications of model design. A major conclusion of this work is that strong size dependent predation significantly adjusts the competitive balance, leading to non-monotonic steady state solutions and slowly decaying transients consisting of distinct generational cycles. Furthermore, we demonstrate how a simple ratio of adult to juvenile biomass can act as a useful diagnostic to distinguish between predated and non-predated environments, and may be useful in agricultural settings

A categorification of Morelli's theorem

We prove a theorem relating torus-equivariant coherent sheaves on toric varieties to polyhedrally-constructible sheaves on a vector space. At the level of K-theory, the theorem recovers Morelli's description of the K-theory of a smooth projective toric variety. Specifically, let $X$ be a proper toric variety of dimension $n$ and let M_\bR = \mathrm{Lie}(T_\bR^\vee)\cong \bR^n be the Lie algebra of the compact dual (real) torus T_\bR^\vee\cong U(1)^n. Then there is a corresponding conical Lagrangian \Lambda \subset T^*M_\bR and an equivalence of triangulated dg categories \Perf_T(X) \cong \Sh_{cc}(M_\bR;\Lambda), where \Perf_T(X) is the triangulated dg category of perfect complexes of torus-equivariant coherent sheaves on $X$ and \Sh_{cc}(M_\bR;\Lambda) is the triangulated dg category of complex of sheaves on M_\bR with compactly supported, constructible cohomology whose singular support lies in $\Lambda$. This equivalence is monoidal---it intertwines the tensor product of coherent sheaves on $X$ with the convolution product of constructible sheaves on M_\bR.Comment: 20 pages. This is a strengthened version of the first half of arXiv:0811.1228v3, with new results; the second half becomes arXiv:0811.1228v

Feigned Consensus: Usurping the Law in Shaken Baby Syndrome/Abusive Head Trauma Prosecutions

Few medico-legal matters have generated as much controversy--both in the medical literature and in the courtroom--as Shaken Baby Syndrome (SBS), now known more broadly as Abusive Head Trauma (AHT). The controversies are of enormous significance in the law because child abuse pediatricians claim, on the basis of a few non-specific medical findings supported by a weak and methodologically flawed research base, to be able to “diagnose” child abuse, and thereby to provide all of the evidence necessary to satisfy all of the legal elements for criminal prosecution (or removal of children from their parents). It is a matter, therefore, in which medical opinion claims to fully occupy the legal field. As controversies flare up increasingly in the legal arena, child abuse pediatricians and prosecutors now respond by claiming both that there is actually no real controversy about SBS/AHT, and that it is a purely medical “diagnosis” and not a legal conclusion, so testimony in support of the SBS hypothesis should not be challenged in court. This article, coauthored by four law professors, two physicians, and a physicist, demonstrates that there is very much a live controversy about the SBS/AHT hypothesis and maintains that, under traditional principles of evidence law, physicians should not be permitted to “diagnose” abuse in court (as opposed to identifying specific symptoms or medical findings)

The environmental impacts of biomass crops: use by birds of miscanthus in summer and winter in southwestern England

We compared birds in a group of established and well-managed miscanthus (Miscanthus x giganteus) fields in Somerset and East Devon, southwestern England, with plots of short rotation coppice (SRC) willow, arable crops and grassland in two winters and one summer. Following early spring cutting, 19 miscanthus fields grew taller, initially produced greater cover and were less weedy than SRC. As stubble in May, the miscanthus contained broadly similar species at similar densities to arable and grassland comparison plots. By July, at 2-m-tall, miscanthus held higher densities of birds but of fewer species, most of them characteristic of woodland and scrub. SRC, previously identified as being a beneficial crop for many birds, always contained more species and individuals than miscanthus. Throughout each of two winters, 15 miscanthus plots remained unharvested and contained more wood/scrub species such as Blackbirds Turdus merula, tits, Reed Buntings Emberiza schoeniclus and Woodcock Scolopax rusticola than the comparison plots, which held more corvids and Skylarks Alauda arvensis amongst others. Similar overall mean densities of birds in the miscanthus and the comparison plots masked relatively low density variance in miscanthus and very high variance in the comparison plots. Unharvested miscanthus crops grown in place of habitat types supporting flocks of wintering birds would displace these flocks. Miscanthus plantations with open patches attracted more finches and waders in winter. The two previous studies of birds in miscanthus in the UK found more species and more individuals than we did in summer and winter. Both these studies documented high levels of weediness and patchy crop growth. In the context of this previous work our data suggest that bird use of miscanthus in summer and winter is likely to be variable, affected by region, weediness, crop structure and patchiness. While large-scale cropping of SRC in England is likely to have a positive overall impact on a suite of common farmland and woodland birds, our data suggest that miscanthus in the southwest of England may have an approximately neutral effect. However, some open farmland specialist species may be lost when planting either crop

Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds

We present a proof of the mirror conjecture of Aganagic-Vafa [arXiv:hep-th/0012041] and Aganagic-Klemm-Vafa [arXiv:hep-th/0105045] on disk enumeration in toric Calabi-Yau 3-folds for all smooth semi-projective toric Calabi-Yau 3-folds. We consider both inner and outer branes, at arbitrary framing. In particular, we recover previous results on the conjecture for (i) an inner brane at zero framing in the total space of the canonical line bundle of the projective plane (Graber-Zaslow [arXiv:hep-th/0109075]), (ii) an outer brane at arbitrary framing in the resolved conifold (Zhou [arXiv:1001.0447]), and (iii) an outer brane at zero framing in the total space of the canonical line bundle of the projective plane (Brini [arXiv:1102.0281, Section 5.3]).Comment: 39 pages, 11 figure

Modelling the production, profit, and greenhouse gas emissions of Irish sheep flocks divergent in genetic merit

peer-reviewedCONTEXTSheep production industries face the challenge of increasing farm production and profit while reducing environmental impacts. OBJECTIVESGenetic selection using multi-trait breeding indices can be used to improve flock productivity, profitability, and greenhouse gas (GHG) emissions intensities (kg CO2-eq /kg of product), however validation of the improved performance of animals ranked higher on breeding indices at a flock level is required. METHODSPhenotypic data from 387,580 production records of animals born between 2018 and 2020 of known genetic merit in commercial flocks were inputted to an established bio-economic model. Two contrasting flocks were compared, a flock of ewes ranked High (top 20%) on the Irish replacement Index bred with rams ranked High on the replacement and terminal indices, and a flock of ewes ranked Low (bottom 20%) on the Irish replacement Index bred with rams ranked Low on the replacement and terminal indices. The two flocks were then simulated using life cycle assessment to estimate the GHG emissions profile for both systems. RESULTS AND CONCLUSIONFlock weaning rates were 1.70 and 1.53 lambs weaned per ewe presented for breeding for the High and Low genetic merit flocks, respectively. The flock of High genetic merit ewes sold 0.17 more lambs per ewe, equating to 3.29 kg more lamb carcass per ewe, than the flock of Low genetic merit ewes; lambs from the High genetic merit flock were also sold at an earlier age. The greater production of the High genetic merit flocks resulted in an additional €18/ewe net profit than the Low genetic merit flock. Although total flock GHG emissions were higher for the High genetic merit flock, GHG emissions intensities were lower at 21.7 and 23.3 kg CO2-eq /kg lamb carcass sold for the High and Low genetic merit flocks, respectively. The lower emissions intensity of the High genetic merit flock was due to the dilution effect of higher lamb production and lambs being drafted for slaughter ealier. SIGNIFICANCEThe results suggest Irish sheep producers can make substantial profit gains through selection according to the national breeding indices while also reducing their environmental impact, and farmers should consider genetic merit when purchasing their rams, particularly sires of replacement ewe lambs

Automated Discovery of Food Webs from Ecological Data Using Logic-Based Machine Learning

Networks of trophic links (food webs) are used to describe and understand mechanistic routes for translocation of energy (biomass) between species. However, a relatively low proportion of ecosystems have been studied using food web approaches due to difficulties in making observations on large numbers of species. In this paper we demonstrate that Machine Learning of food webs, using a logic-based approach called A/ILP, can generate plausible and testable food webs from field sample data. Our example data come from a national-scale Vortis suction sampling of invertebrates from arable fields in Great Britain. We found that 45 invertebrate species or taxa, representing approximately 25% of the sample and about 74% of the invertebrate individuals included in the learning, were hypothesized to be linked. As might be expected, detritivore Collembola were consistently the most important prey. Generalist and omnivorous carabid beetles were hypothesized to be the dominant predators of the system. We were, however, surprised by the importance of carabid larvae suggested by the machine learning as predators of a wide variety of prey. High probability links were hypothesized for widespread, potentially destabilizing, intra-guild predation; predictions that could be experimentally tested. Many of the high probability links in the model have already been observed or suggested for this system, supporting our contention that A/ILP learning can produce plausible food webs from sample data, independent of our preconceptions about “who eats whom.” Well-characterised links in the literature correspond with links ascribed with high probability through A/ILP. We believe that this very general Machine Learning approach has great power and could be used to extend and test our current theories of agricultural ecosystem dynamics and function. In particular, we believe it could be used to support the development of a wider theory of ecosystem responses to environmental change

Mathematical stories: Why do more boys than girls choose to study mathematics at AS-level in England?

Copyright @ 2005 Taylor & FrancisIn this paper I address the question: How is it that people come to choose mathematics and in what ways is this process gendered? I draw on the findings of a qualitative research study involving interviews with 43 young people all studying mathematics in post-compulsory education in England. Working within a post-structuralist framework, I argue that gender is a project and one that is achieved in interaction with others. Through a detailed reading of Toni and Claudia’s stories I explore the tensions for young women who are engaging in mathematics, something that is discursively inscribed as masculine, while (understandably) being invested in producing themselves as female. I conclude by arguing that seeing ‘doing mathematics’ as ‘doing masculinity’ is a productive way of understanding why mathematics is so male dominated and by looking at the implications of this understanding for gender and mathematics reform work.This work is funded by the ESR

Modelling laser-atom interactions in the strong field regime

We consider the ionisation of atomic hydrogen by a strong infrared field. We extend and study in more depth an existing semi-analytical model. Starting from the time-dependent Schroedinger equation in momentum space and in the velocity gauge we substitute the kernel of the non-local Coulomb potential by a sum of N separable potentials, each of them supporting one hydrogen bound state. This leads to a set of N coupled one-dimensional linear Volterra integral equations to solve. We analyze the gauge problem for the model, the different ways of generating the separable potentials and establish a clear link with the strong field approximation which turns out to be a limiting case of the present model. We calculate electron energy spectra as well as the time evolution of electron wave packets in momentum space. We compare and discuss the results obtained with the model and with the strong field approximation and examine in this context, the role of excited states.Comment: 11 pages, 5 figure