Generalised Elliptic Functions

We consider multiply periodic functions, sometimes called Abelian functions, defined with respect to the period matrices associated with classes of algebraic curves. We realise them as generalisations of the Weierstras P-function using two different approaches. These functions arise naturally as solutions to some of the important equations of mathematical physics and their differential equations, addition formulae, and applications have all been recent topics of study. The first approach discussed sees the functions defined as logarithmic derivatives of the sigma-function, a modified Riemann theta-function. We can make use of known properties of the sigma function to derive power series expansions and in turn the properties mentioned above. This approach has been extended to a wide range of non hyperelliptic and higher genus curves and an overview of recent results is given. The second approach defines the functions algebraically, after first modifying the curve into its equivariant form. This approach allows the use of representation theory to derive a range of results at lower computational cost. We discuss the development of this theory for hyperelliptic curves and how it may be extended in the future.Comment: 16 page

Dimeric FcγR ectodomains detect pathogenic anti-platelet factor 4-heparin antibodies in heparin-induced thromobocytopenia

Background Heparin‐induced thrombocytopenia (HIT) is a major and potentially fatal consequence of antibodies produced against platelet factor 4 (PF4)–heparin complexes following heparin exposure. Not all anti‐PF4–heparin antibodies are pathogenic, so overdiagnosis can occur, with resulting inappropriate use of alternative anticoagulation therapies that have associated risks of bleeding. However, definitive platelet functional assays are not widely available for routine analysis. Objectives To assess the utility of dimeric recombinant soluble FcγRIIa (rsFcγRIIa) ectodomains for detecting HIT antibodies. Patients/Methods Plasma from 27 suspected HIT patients were tested for pathogenic anti‐PF4–heparin antibodies by binding of a novel dimeric FcγRIIa ectodomain probe. Plasmas were also tested by the use of PF4–heparin IgG ELISA, the HemosIL AcuStar HIT IgG‐specific assay, and a serotonin release assay (SRA). Results The dimeric rsFcγRIIa test produced no false positives and excluded four samples that were positive by IgG ELISA. In this small patient cohort, the novel assay correctly assigned 93% of the suspected HIT patients, with two of the HIT patients being scored as false negatives. The improved discrimination of the novel assay over the IgG ELISA, which scored four false positives, supports the mechanistic interpretation that binding of dimeric rsFcγRIIa detects pairs of closely spaced IgG antibodies in PF4–heparin immune complexes. Conclusions This study found the cell‐free, function‐based dimeric rsFcγRIIa assay to be convenient, simple, and potentially predictive of HIT. The assay had improved specificity over the IgG ELISA, and correlated strongly with the AcuStar HIT IgG‐specific assay, warranting further evaluation of its potential to identify HIT in larger patient cohorts

Ecological speciation in sympatric palms: 2. Pre- and post-zygotic isolation

We evaluated reproductive isolation in two species of palms (Howea) that have evolved sympatrically on Lord Howe Island (LHI, Australia). We estimated the strength of some pre- and post-zygotic mechanisms in maintaining current species boundaries. We found that flowering time displacement between species is consistent across in and ex situ common gardens and is thus partly genetically determined. On LHI, pre-zygotic isolation due solely to flowering displacement was 97% for Howea belmoreana and 80% for H. forsteriana; this asymmetry results from H. forsteriana flowering earlier than H. belmoreana and being protandrous. As expected, only a few hybrids (here confirmed by genotyping) at both juvenile and adult stages could be detected in two sites on LHI, in which the two species grow intermingled (the Far Flats) or adjacently (Transit Hill). Yet, the distribution of hybrids was different between sites. At Transit Hill, we found no hybrid adult trees, but 13.5% of younger palms examined there were of late hybrid classes. In contrast, we found four hybrid adult trees, mostly of late hybrid classes, and only one juvenile F1 hybrid in the Far Flats. This pattern indicates that selection acts against hybrids between the juvenile and adult stages. An in situ reciprocal seed transplant between volcanic and calcareous soils also shows that early fitness components (up to 36 months) were affected by species and soil. These results are indicative of divergent selection in reproductive isolation, although it does not solely explain the current distribution of the two species on LHI

Synaptophysin sustains presynaptic performance by preserving vesicular synaptobrevin-II levels

The two most abundant molecules on synaptic vesicles (SVs) are synaptophysin and synaptobrevin-II (sybII). SybII is essential for SV fusion, whereas synaptophysin is proposed to control the trafficking of sybII after SV fusion and its retrieval during endocytosis. Despite controlling key aspects of sybII packaging into SVs, the absence of synaptophysin results in negligible effects on neurotransmission. We hypothesised that this apparent absence of effect may be because of the abundance of sybII on SVs, with the impact of inefficient sybII retrieval only revealed during periods of repeated SV turnover. To test this hypothesis, we subjected primary cultures of synaptophysin knockout neurons to repeated trains of neuronal activity, while monitoring SV fusion events and levels of vesicular sybII. We identified a significant decrease in both the number of SV fusion events (monitored using the genetically encoded reporter vesicular glutamate transporter-pHluorin) and vesicular sybII levels (via both immunofluorescence and Western blotting) using this protocol. This revealed that synaptophysin is essential to sustain both parameters during periods of repetitive SV turnover. This was confirmed by the rescue of presynaptic performance by the expression of exogenous synaptophysin. Importantly, the expression of exogenous sybII also fully restored SV fusion events in synaptophysin knockout neurons. The ability of additional copies of sybII to fully rescue presynaptic performance in these knockout neurons suggests that the principal role of synaptophysin is to mediate the efficient retrieval of sybII to sustain neurotransmitter release

An international comparison of surface texture parameters quantification on polymer artefacts using optical instruments

An international comparison of optical instruments measuring polymer surfaces with arithmetic mean height values in the sub-micrometre range has been carried out. The comparison involved sixteen optical surface texture instruments (focus variation instruments, confocal microscopes and coherent scanning interferometers) from thirteen research laboratories worldwide. Results demonstrated that: (i) Agreement among different instruments could be achieved to a limited extent; (ii) standardised guidelines for uncertainty evaluation of areal surface parameters are needed for users; (iii) it is essential that the performance characteristics (and especially the spatial frequency response) of an instrument is understood prior to a measurement

Ecological speciation in sympatric palms: 1. Gene expression, selection and pleiotropy

Ecological speciation requires divergent selection, reproductive isolation and a genetic mechanism to link the two. We examined the role of gene expression and coding sequence evolution in this process using two species of Howea palms that have diverged sympatrically on Lord Howe Island, Australia. These palms are associated with distinct soil types and have displaced flowering times, representing an ideal candidate for ecological speciation. We generated large amounts of RNA-Seq data from multiple individuals and tissue types collected on the island from each of the two species. We found that differentially expressed loci as well as those with divergent coding sequences between Howea species were associated with known ecological and phenotypic differences, including response to salinity, drought, pH and flowering time. From these loci, we identified potential 'ecological speciation genes' and further validate their effect on flowering time by knocking out orthologous loci in a model plant species. Finally, we put forward six plausible ecological speciation loci, providing support for the hypothesis that pleiotropy could help to overcome the antagonism between selection and recombination during speciation with gene flow

Hard Instances of the Constrained Discrete Logarithm Problem

The discrete logarithm problem (DLP) generalizes to the constrained DLP, where the secret exponent $x$ belongs to a set known to the attacker. The complexity of generic algorithms for solving the constrained DLP depends on the choice of the set. Motivated by cryptographic applications, we study sets with succinct representation for which the constrained DLP is hard. We draw on earlier results due to Erd\"os et al. and Schnorr, develop geometric tools such as generalized Menelaus' theorem for proving lower bounds on the complexity of the constrained DLP, and construct sets with succinct representation with provable non-trivial lower bounds

Gender inequities in dental research publications: findings from 20 years

Background: The first steps towards gender equity in science are measuring the magnitude of inequity and increasing awareness of the problem. Objectives: To describe trends in gender disparities in first and last authorship in the most cited dental publications and general dental literature over a 20-year period. Methods: Articles and bibliometric data were retrieved from the Scopus database for the period 1996 to 2015. Two groups of 1000 articles each were retrieved: a random sample and another sample of top-cited articles for each year. The gender of the first and last author of each publication was manually identified. When this was not possible, we used an online software platform (https://genderize.io/). Descriptive analyses identified the proportion of women first and last authors in both samples, stratifying by dental discipline and geographic region. Trends were ascertained by frequency metrics across years. Gender disparity was observed in both first and last authorship, with a larger gap being observed in the top-cited sample. Results: Women led 28.4% and 20.3% of articles in the random and top-cited samples, respectively. A similar pattern was observed for the last authorship group (22.1% and 16.1%, respectively). An increasing trend in the proportion of articles led by women over time was observed in both samples. This increase was larger in the top-cited sample (from 15.0% in 1996–2000 to 25.1% in 2015) than in the random sample (from 26.3% in 1996–2000 to 33.2% in 2011). Conclusions: Clear gender disparities in dental research publications in the last 20 years were identified in both general and top-cited manuscripts, across dental disciplines, across countries, across first and last authorship, and over time. It is paramount that actions are taken to attract, retain and promote women in science, as well as to monitor and ensure progress towards gender equity