The Katz-Klemm-Vafa conjecture for K3 surfaces

We prove the KKV conjecture expressing Gromov–Witten invariants of K3 surfaces in terms of modular forms. Our results apply in every genus and for every curve class. The proof uses the Gromov–Witten/Pairs correspondence for K3-fibered hypersurfaces of dimension 3 to reduce the KKV conjecture to statements about stable pairs on (thickenings of) K3 surfaces. Using degeneration arguments and new multiple cover results for stable pairs, we reduce the KKV conjecture further to the known primitive cases. Our results yield a new proof of the full Yau–Zaslow formula, establish new Gromov–Witten multiple cover formulas, and express the fiberwise Gromov–Witten partition functions of K3-fibered 3-folds in terms of explicit modular forms

Sheaf counting on local K3 surfaces

There are two natural ways to count stable pairs or Joyce–Song pairs on X=K3×C; one via weighted Euler characteristic and the other by virtual localisation of the reduced virtual class. Since X is noncompact these need not be the same. We show their generating series are related by an exponential. As applications we prove two conjectures of Toda, and a conjecture of Tanaka–Thomas defining Vafa–Witten invariants in the semistable case

Uveitis presenting with iris bombe in a patient with HIV: the importance of multi-disciplinary management — a case study

This case study concerns a 53-year-old female presenting to an eye-hospital in London with uveitis, on a background of well-controlled HIV. After investigation, no cause for the uveitis was found other than the HIV itself, and the patient was treated with immunosuppressants. Because of the nature of her underlying HIV infection, help was sought from HIV specialists, who gave advice on the management, including alteration of corticosteroid dosing due to the risk of drug-interactions between her uveitis and HIV treatments. Of particular concern was the risk of cytochrome P450 3A inhibition by cobicistat and the potential for iatrogenic Cushing syndrome through elevated steroid doses. This case is used as an example to highlight the importance of the multi-disciplinary team in the management ofcomplex conditions, as well as to add to the literature in support of the HIV virus itself as a cause of uveitis

Effects of river water and salinity on the toxicity of deltamethrin to freshwater shrimp, cladoceran, and fish

Deltamethrin is a pyrethroid insecticide used extensively to control invertebrate pests on cotton and other crops. It is acutely toxic to nontarget aquatic organisms, but existing toxicity data are mostly from toxicity tests using purified laboratory water that differs greatly from the turbid, high-conductivity rivers in the cotton-growing regions of Australia. The aim of this study was to determine whether the water quality variables conductivity, suspended particles, and dissolved organic matter alter the toxicity of deltamethrin to freshwater crustaceans and a fish. We tested three Australian native species: a cladoceran (Ceriodaphnia cf. dubia), a freshwater shrimp (Paratya australiensis), and larvae of the eastern rainbow fish (Melanotaenia duboulayi). Conductivity of the test solutions ranged from 200 to 750 μS/cm, but such changes did not modify the toxicity of deltamethrin to any of the test species. However, the toxicity of deltamethrin to C. cf. dubia and P. australiensis in river water was significantly decreased (1.8-fold to 6.3-fold reduction) compared to that in laboratory water. Variability in the toxicity data limited our ability to detect differences between laboratory and river water for M. duboulayi. Despite reductions in toxicity in natural waters, deltamethrin remained highly toxic [all L(E)C50 values <0.26 μg/L] to all organisms tested; thus, further investigation of the hazard of deltamethrin is warranted. © 2008 Springer Science+Business Media, LLC

Socioeconomic inequalities in food outlet access through an online food delivery service in England: A cross-sectional descriptive analysis.

Online food delivery services facilitate 'online' access to food outlets selling food prepared away-from-home. Online food outlet access has not previously been investigated in England or across an entire country. Systematic differences in online food outlet access could exacerbate existing health inequalities, which is a public health concern. However, this is not known. Across postcode districts in England (n = 2118), we identified and described the number of food outlets and unique cuisine types accessible online from the market leader (Just Eat). We investigated associations with area-level deprivation using adjusted negative binomial regression models. We also compared the number of food outlets accessible online with the number physically accessible in the neighbourhood (1600m Euclidean buffers of postcode district geographic centroids) and investigated associations with deprivation using an adjusted general linear model. For each outcome, we predicted means and 95% confidence intervals. In November 2019, 29,232 food outlets were registered to accept orders online. Overall, the median number of food outlets accessible online per postcode district was 63.5 (IQR; 16.0-156.0). For the number of food outlets accessible online as a percentage of the number accessible within the neighbourhood, the median was 63.4% (IQR; 35.6-96.5). Analysis using negative binomial regression showed that online food outlet access was highest in the most deprived postcode districts (n = 106.1; 95% CI: 91.9, 120.3). The number of food outlets accessible online as a percentage of those accessible within the neighbourhood was highest in the least deprived postcode districts (n = 86.2%; 95% CI: 78.6, 93.7). In England, online food outlet access is socioeconomically patterned. Further research is required to understand how online food outlet access is related to using online food delivery services

VIRTUAL SIGNED EULER CHARACTERISTICS

Roughly speaking, to any space $M$ with perfect obstruction theory we associate a space $N$ with symmetric perfect obstruction theory. It is a cone over $M$ given by the dual of the obstruction sheaf of $M$ and contains $M$ as its zero section. It is locally the critical locus of a function. More precisely, in the language of derived algebraic geometry, to any quasi-smooth space $M$ we associate its $(\!-\!1)$-shifted cotangent bundle $N$. By localising from $N$ to its $\mathbb{C}^*$-fixed locus $M$ this gives five notions of a virtual signed Euler characteristic of $M$: The Ciocan-Fontanine-Kapranov/Fantechi-Göttsche signed virtual Euler characteristic of $M$ defined using its own obstruction theory, Graber-Pandharipande's virtual Atiyah-Bott localisation of the virtual cycle of $N$ to $M$, Behrend's Kai-weighted Euler characteristic localisation of the virtual cycle of $N$ to $M$, Kiem-Li's cosection localisation of the virtual cycle of $N$ to $M$, $(-1)^{\textrm {vd}}$ times by the topological Euler characteristic of $M$. Our main result is that (1)=(2) and (3)=(4)=(5). The first two are deformation invariant while the last three are not

Maxillary sinus textiloma: a case report

<p>Abstract</p> <p>Introduction</p> <p>Textilomas have been reported in many locations. We report the first case of textiloma located in the maxillary sinus that mimicked a sinus cyst recurrence on computed tomography images.</p> <p>Case presentation</p> <p>A 60-year-old Caucasian man was referred for persistent infection of the right maxillary sinus. A maxillary sinus benign cyst had been removed three months before. Computed tomography showed a sinus opacity evoking a cyst recurrence. A new operation was planned to remove the cyst by a Caldwell-Luc approach. After excision of very thick fibrous tissue, a compress was discovered in the maxillary sinus. The patient did not present with any sinus infection after the operation.</p> <p>Conclusion</p> <p>The surgeon should always take into account the possibility of textilomas in a patient with a history of sinus surgery.</p

Size and emotion or depth and emotion? Evidence, using Matryoshka (Russian) dolls, of children using physical depth as a proxy for emotional charge

Background: The size and emotion effect is the tendency for children to draw people and other objects with a positive emotional charge larger than those with a negative or neutral charge. Here we explored the novel idea that drawing size might be acting as a proxy for depth (proximity).Methods: Forty-two children (aged 3-11 years) chose, from 2 sets of Matryoshka (Russian) dolls, a doll to represent a person with positive, negative or neutral charge, which they placed in front of themselves on a sheet of A3 paper. Results: We found that the children used proximity and doll size, to indicate emotional charge. Conclusions: These findings are consistent with the notion that in drawings, children are using size as a proxy for physical closeness (proximity), as they attempt with varying success to put positive charged items closer to, or negative and neutral charge items further away from, themselves

The SYZ conjecture via homological mirror symmetry

These are expository notes based on a talk given at the Superschool on derived categories and D-branes at University of Alberta in July of 2016. The goal of these notes is to give a motivated introduction to the Strominger-Yau-Zaslow (SYZ) conjecture from the point of view of homological mirror symmetry.Comment: Contribution to the proceedings of the Superschool on derived categories and D-brane