Generalized polynomials and hyperplane functions in (Z/pkZ)n(\mathbb{Z}/p^k\mathbb{Z})^n

For $p$ prime, let $\mathcal{H}^n$ be the linear span of characteristic functions of hyperplanes in $(\mathbb{Z}/p^k\mathbb{Z})^n$. We establish new upper bounds on the dimension of $\mathcal{H}^n$ over $\mathbb{Z}/p\mathbb{Z}$, or equivalently, on the rank of point-hyperplane incidence matrices in $(\mathbb{Z}/p^k\mathbb{Z})^n$ over $\mathbb{Z}/p\mathbb{Z}$. Our proof is based on a variant of the polynomial method using binomial coefficients in $\mathbb{Z}/p^k\mathbb{Z}$ as generalized polynomials. We also establish additional necessary conditions for a function on $(\mathbb{Z}/p^k\mathbb{Z})^n$ to be an element of $\mathcal{H}^n$.Comment: 33 page

New Bird Records for Nusa Tenggara Islands: Sumbawa, Moyo, Sumba, Flores, Pulau Besar and Timor

We present a total of 59 new island records comprising more than 100 independent site records of 52 species for selected Nusa Tenggara islands: Sumbawa (21) and its satellite Moyo (18); Sumba (4); Flores (3) and its satellite islands including Pulau Besar (12); and Timor (3). Records were gathered between 1994 and 2001 during surveys by BirdLife international Indonesia Programme, Dames and Moore Pry Ltd (especially within the Batu Hijau Project Area), and an extended bird watching visit. Records of particular note include those of the globally vulnerable Flores Green Pigeon Treron Jloris and two near-threatened species: Beach Thick-knee Esacus neglectus and Great-billed Heron Ardea sumatrana. A Superb Fruit-dove Ptilinopus superbus on Sumba represents the first record for Nusa Tenggara. Significant records of Palearctic migrants are accumulating for the region. We document the first two Nusa Tenggara records of the migrant Grey-streaked Flycatcher Muscicapa griseisticta and numerous records of Chinese Sparrowhawk Accipiter soloensis and Japanese Sparrowhawk A. gularis

Adjunctive rifampicin for Staphylococcus aureus bacteraemia (ARREST): a multicentre, randomised, double-blind, placebo-controlled trial.

BACKGROUND: Staphylococcus aureus bacteraemia is a common cause of severe community-acquired and hospital-acquired infection worldwide. We tested the hypothesis that adjunctive rifampicin would reduce bacteriologically confirmed treatment failure or disease recurrence, or death, by enhancing early S aureus killing, sterilising infected foci and blood faster, and reducing risks of dissemination and metastatic infection. METHODS: In this multicentre, randomised, double-blind, placebo-controlled trial, adults (≥18 years) with S aureus bacteraemia who had received ≤96 h of active antibiotic therapy were recruited from 29 UK hospitals. Patients were randomly assigned (1:1) via a computer-generated sequential randomisation list to receive 2 weeks of adjunctive rifampicin (600 mg or 900 mg per day according to weight, oral or intravenous) versus identical placebo, together with standard antibiotic therapy. Randomisation was stratified by centre. Patients, investigators, and those caring for the patients were masked to group allocation. The primary outcome was time to bacteriologically confirmed treatment failure or disease recurrence, or death (all-cause), from randomisation to 12 weeks, adjudicated by an independent review committee masked to the treatment. Analysis was intention to treat. This trial was registered, number ISRCTN37666216, and is closed to new participants. FINDINGS: Between Dec 10, 2012, and Oct 25, 2016, 758 eligible participants were randomly assigned: 370 to rifampicin and 388 to placebo. 485 (64%) participants had community-acquired S aureus infections, and 132 (17%) had nosocomial S aureus infections. 47 (6%) had meticillin-resistant infections. 301 (40%) participants had an initial deep infection focus. Standard antibiotics were given for 29 (IQR 18-45) days; 619 (82%) participants received flucloxacillin. By week 12, 62 (17%) of participants who received rifampicin versus 71 (18%) who received placebo experienced treatment failure or disease recurrence, or died (absolute risk difference -1·4%, 95% CI -7·0 to 4·3; hazard ratio 0·96, 0·68-1·35, p=0·81). From randomisation to 12 weeks, no evidence of differences in serious (p=0·17) or grade 3-4 (p=0·36) adverse events were observed; however, 63 (17%) participants in the rifampicin group versus 39 (10%) in the placebo group had antibiotic or trial drug-modifying adverse events (p=0·004), and 24 (6%) versus six (2%) had drug interactions (p=0·0005). INTERPRETATION: Adjunctive rifampicin provided no overall benefit over standard antibiotic therapy in adults with S aureus bacteraemia. FUNDING: UK National Institute for Health Research Health Technology Assessment

Multilinear restriction estimates on fractal sets

In harmonic analysis there is a rich history of restriction theory for measures supported on smooth manifolds, and recently much focus has turned to restriction for measures supported on fractal sets. On the other hand, the use of multilinear restriction estimates has propelled most current progress on classical restriction theory. In this thesis we discuss the existing literature on both of these main interests in restriction theory, and then consider their combination. We analyze the existence of multilinear restriction estimates for a collection of singular measures, particularly measures supported on Cantor sets. We generalize a linear restriction estimate of Chen to a multilinear setting and provide a class of Cantor sets to which this result applies. Furthermore, we give necessary conditions for the existence of multilinear restriction for singular measures. We are hopeful that the success of multilinear restriction estimates in furthering classical restriction theory may be reproduced in our context.Science, Faculty ofMathematics, Department ofGraduat

Dynamic changes in brain aromatase activity following sexual interactions in males: Where, when and why?

peer reviewedIt is increasingly recognized that estrogens produce rapid and transient effects at many neural sites ultimately impacting physiological and behavioral endpoints. The ability of estrogens to acutely regulate cellular processes implies that their concentration should also be rapidly fine-tuned. Accordingly, rapid changes in the catalytic activity of aromatase, the limiting enzyme for estrogen synthesis, have been identified that could serve as a regulatory mechanism of local estrogen concentrations. However, the precise anatomical localization, time-course, triggering stimuli and functional significance of these enzymatic changes in vivo are not well understood. To address these issues as to where, when and why aromatase activity (AA) rapidly changes after sexual interactions, AA was assayed in six populations of aromatase-expressing cells microdissected from the brain of male quail that experienced varying durations of visual exposure to or copulation with a female. Sexual interactions resulted in a rapid AA inhibition. This inhibition occurred in specific brain regions (including the medial preoptic nucleus), in a context-dependent fashion and time-scale suggestive of post-translational modifications of the enzyme. Interestingly, the enzymatic fluctuations occurring in the preoptic area followed rather than preceded copulation and were tied specifically to the female's presence. This pattern of enzymatic changes suggests that rapid estrogen effects are important during the motivational phase of the behavior to trigger physiological events essential to activate mate search and copulation.UL