A note on a curious formula for Euler's constant

In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite series due to Flajolet, Gourdon, and Dumas.Comment: 4 page

Spanning tree generating functions and Mahler measures

We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when differentiated. By making use of known results for logarithmic Mahler measures of certain Laurent polynomials, and proving new results, we express the STGFs as hypergeometric functions for all regular two and three dimensional lattices (and one higher-dimensional lattice). This gives closed form expressions for the spanning tree constants for all such lattices, which were previously largely unknown in all but one three-dimensional case. We show for all lattices that these can also be represented as Dirichlet $L$-series. Making the connection between spanning tree generating functions and lattice Green functions produces integral identities and hypergeometric connections, some of which appear to be new.Comment: 26 pages. Dedicated to F Y Wu on the occasion of his 80th birthday. This version has additional references, additional calculations, and minor correction

Developments in HF Propagation Predictions to Support Communications with Aircraft on Trans-polar Routes

Commercial airlines began operations over polar routes in 1999 with a small number of proving flights. By 2014 the number had increased to in excess of 12,000 flights per year, and further increases are expected. For safe operations, the aircraft have to be able to communicate with air traffic control centres at all times. This is achieved by VHF links whilst within range of the widespread network of ground stations, and by HF radio in remote areas such as the Polar regions, the North Atlantic and Pacific where VHF ground infrastructure does not exist. Furthermore, the Russian side of the pole only has HF capability. This has created a demand for improved HF nowcasting and forecasting procedures to support the polar operations, which are the subject of this paper

Molecular and cellular mechanisms underlying the evolution of form and function in the amniote jaw.

The amniote jaw complex is a remarkable amalgamation of derivatives from distinct embryonic cell lineages. During development, the cells in these lineages experience concerted movements, migrations, and signaling interactions that take them from their initial origins to their final destinations and imbue their derivatives with aspects of form including their axial orientation, anatomical identity, size, and shape. Perturbations along the way can produce defects and disease, but also generate the variation necessary for jaw evolution and adaptation. We focus on molecular and cellular mechanisms that regulate form in the amniote jaw complex, and that enable structural and functional integration. Special emphasis is placed on the role of cranial neural crest mesenchyme (NCM) during the species-specific patterning of bone, cartilage, tendon, muscle, and other jaw tissues. We also address the effects of biomechanical forces during jaw development and discuss ways in which certain molecular and cellular responses add adaptive and evolutionary plasticity to jaw morphology. Overall, we highlight how variation in molecular and cellular programs can promote the phenomenal diversity and functional morphology achieved during amniote jaw evolution or lead to the range of jaw defects and disease that affect the human condition

Micromechanical Properties of Injection-Molded Starch–Wood Particle Composites

The micromechanical properties of injection molded starch–wood particle composites were investigated as a function of particle content and humidity conditions. The composite materials were characterized by scanning electron microscopy and X-ray diffraction methods. The microhardness of the composites was shown to increase notably with the concentration of the wood particles. In addition,creep behavior under the indenter and temperature dependence were evaluated in terms of the independent contribution of the starch matrix and the wood microparticles to the hardness value. The influence of drying time on the density and weight uptake of the injection-molded composites was highlighted. The results revealed the role of the mechanism of water evaporation, showing that the dependence of water uptake and temperature was greater for the starch–wood composites than for the pure starch sample. Experiments performed during the drying process at 70°C indicated that the wood in the starch composites did not prevent water loss from the samples.Peer reviewe

Multiple novel prostate cancer susceptibility signals identified by fine-mapping of known risk loci among Europeans

Genome-wide association studies (GWAS) have identified numerous common prostate cancer (PrCa) susceptibility loci. We have fine-mapped 64 GWAS regions known at the conclusion of the iCOGS study using large-scale genotyping and imputation in 25 723 PrCa cases and 26 274 controls of European ancestry. We detected evidence for multiple independent signals at 16 regions, 12 of which contained additional newly identified significant associations. A single signal comprising a spectrum of correlated variation was observed at 39 regions; 35 of which are now described by a novel more significantly associated lead SNP, while the originally reported variant remained as the lead SNP only in 4 regions. We also confirmed two association signals in Europeans that had been previously reported only in East-Asian GWAS. Based on statistical evidence and linkage disequilibrium (LD) structure, we have curated and narrowed down the list of the most likely candidate causal variants for each region. Functional annotation using data from ENCODE filtered for PrCa cell lines and eQTL analysis demonstrated significant enrichment for overlap with bio-features within this set. By incorporating the novel risk variants identified here alongside the refined data for existing association signals, we estimate that these loci now explain ∼38.9% of the familial relative risk of PrCa, an 8.9% improvement over the previously reported GWAS tag SNPs. This suggests that a significant fraction of the heritability of PrCa may have been hidden during the discovery phase of GWAS, in particular due to the presence of multiple independent signals within the same regio

Diabetes self-management arrangements in Europe: a realist review to facilitate a project implemented in six countries

Background: Self-management of long term conditions can promote quality of life whilst delivering benefits to the financing of health care systems. However, rarely are the meso-level influences, likely to be of direct relevance to these desired outcomes, systematically explored. No specific international guidelines exist suggesting the features of the most appropriate structure and organisation of health care systems within which to situate self-management approaches and practices. This review aimed to identify the quantitative literature with regard to diabetes self-management arrangements currently in place within the health care systems of six countries (The United Kingdom, The Netherlands, Norway, Spain, Bulgaria, and Greece) and explore how these are integrated into the broader health care and welfare systems in each country. Methods: The methodology for a realist review was followed. Publications of interest dating from 2000 to 2013 were identified through appropriate MeSH terms by a systematic search in six bibliographic databases. A search diary was maintained and the studies were assessed for their quality and risk of bias. Results: Following the multi-step search strategy, 56 studies were included in the final review (the majority from the UK) reporting design methods and findings on 21 interventions and programmes for diabetes and chronic disease self-management. Most (11/21, 52%) of the interventions were designed to fit within the context of primary care. The majority (11/21, 52%) highlighted behavioural change as an important goal. Finally, some (5/21, 24%) referred explicitly to Internet-based tools. Conclusions: This review is based on results which are derived from a total of at least 5,500 individuals residing in the six participating countries. It indicates a policy shift towards patient-centred self-management of diabetes in a primary care context. The professional role of diabetes specialist nurses, the need for multidisciplinary approaches and a focus on patient education emerge as fundamental principles in the design of relevant programmes. Socio-economic circumstances are relevant to the capacity to self-manage and suggest that any gains and progress will be hard to maintain during economic austerity. This realist review should be interpreted within the wider context of a whole systems approach regarding self-care support and chronic illness management

Prognostic model to predict postoperative acute kidney injury in patients undergoing major gastrointestinal surgery based on a national prospective observational cohort study.

Background: Acute illness, existing co-morbidities and surgical stress response can all contribute to postoperative acute kidney injury (AKI) in patients undergoing major gastrointestinal surgery. The aim of this study was prospectively to develop a pragmatic prognostic model to stratify patients according to risk of developing AKI after major gastrointestinal surgery. Methods: This prospective multicentre cohort study included consecutive adults undergoing elective or emergency gastrointestinal resection, liver resection or stoma reversal in 2-week blocks over a continuous 3-month period. The primary outcome was the rate of AKI within 7 days of surgery. Bootstrap stability was used to select clinically plausible risk factors into the model. Internal model validation was carried out by bootstrap validation. Results: A total of 4544 patients were included across 173 centres in the UK and Ireland. The overall rate of AKI was 14·2 per cent (646 of 4544) and the 30-day mortality rate was 1·8 per cent (84 of 4544). Stage 1 AKI was significantly associated with 30-day mortality (unadjusted odds ratio 7·61, 95 per cent c.i. 4·49 to 12·90; P < 0·001), with increasing odds of death with each AKI stage. Six variables were selected for inclusion in the prognostic model: age, sex, ASA grade, preoperative estimated glomerular filtration rate, planned open surgery and preoperative use of either an angiotensin-converting enzyme inhibitor or an angiotensin receptor blocker. Internal validation demonstrated good model discrimination (c-statistic 0·65). Discussion: Following major gastrointestinal surgery, AKI occurred in one in seven patients. This preoperative prognostic model identified patients at high risk of postoperative AKI. Validation in an independent data set is required to ensure generalizability