Evaluation of binomial double sums involving absolute values

We show that double sums of the form $$\sum_{i,j=-n} ^{n} |i^sj^t(i^k-j^k)^\beta| \binom {2n} {n+i} \binom {2n} {n+j}$$ can always be expressed in terms of a linear combination of just four functions, namely $\binom {4n}{2n}$, ${\binom {2n}n}^2$, $4^n\binom {2n}n$, and $16^n$, with coefficients that are rational in $n$. We provide two different proofs: one is algorithmic and uses the second author's computer algebra package Sigma; the second is based on complex contour integrals. In many instances, these results are extended to double sums of the above form where $\binom {2n}{n+j}$ is replaced by $\binom {2m}{m+j}$ with independent parameter $m$.Comment: AmS-LaTeX, 42 pages; substantial revision: several additional and more general results, see Proposition 11 and Theorems 15-1

The inter-rater reliability of the diagnosis of surgical site infection in the context of a clinical trial.

ObjectivesThe diagnosis of surgical site infection following endoprosthetic reconstruction for bone tumours is frequently a subjective diagnosis. Large clinical trials use blinded Central Adjudication Committees (CACs) to minimise the variability and bias associated with assessing a clinical outcome. The aim of this study was to determine the level of inter-rater and intra-rater agreement in the diagnosis of surgical site infection in the context of a clinical trial.Materials and methodsThe Prophylactic Antibiotic Regimens in Tumour Surgery (PARITY) trial CAC adjudicated 29 non-PARITY cases of lower extremity endoprosthetic reconstruction. The CAC members classified each case according to the Centers for Disease Control (CDC) criteria for surgical site infection (superficial, deep, or organ space). Combinatorial analysis was used to calculate the smallest CAC panel size required to maximise agreement. A final meeting was held to establish a consensus.ResultsFull or near consensus was reached in 20 of the 29 cases. The Fleiss kappa value was calculated as 0.44 (95% confidence interval (CI) 0.35 to 0.53), or moderate agreement. The greatest statistical agreement was observed in the outcome of no infection, 0.61 (95% CI 0.49 to 0.72, substantial agreement). Panelists reached a full consensus in 12 of 29 cases and near consensus in five of 29 cases when CDC criteria were used (superficial, deep or organ space). A stable maximum Fleiss kappa of 0.46 (95% CI 0.50 to 0.35) at CAC sizes greater than three members was obtained.ConclusionsThere is substantial agreement among the members of the PARITY CAC regarding the presence or absence of surgical site infection. Agreement on the level of infection, however, is more challenging. Additional clinical information routinely collected by the prospective PARITY trial may improve the discriminatory capacity of the CAC in the parent study for the diagnosis of infection.Cite this article: J. Nuttall, N. Evaniew, P. Thornley, A. Griffin, B. Deheshi, T. O'Shea, J. Wunder, P. Ferguson, R. L. Randall, R. Turcotte, P. Schneider, P. McKay, M. Bhandari, M. Ghert. The inter-rater reliability of the diagnosis of surgical site infection in the context of a clinical trial. Bone Joint Res 2016;5:347-352. DOI: 10.1302/2046-3758.58.BJR-2016-0036.R1

Searching (the) FIRST radio arcs near ACO clusters

Gravitational lensing (GL) of distant radio sources by galaxy clusters should produce radio arc(let)s. We extracted radio sources from the FIRST survey near Abell cluster cores and found their radio position angles to be uniformly distributed with respect to the cluster centres. This result holds even when we restrict the sample to the richest or most centrally condensed clusters, and to sources with high S/N and large axial ratio. Our failure to detect GL with statistical methods may be due to poor cluster centre positions. We did not find convincing candidates for arcs either. Our result agrees with theoretical estimates predicting that surveys much deeper than FIRST are required to detect the effect. This is in apparent conflict with the detection of such an effect claimed by Bagchi & Kapahi (1995).Comment: 6 pages; 8 figures and 1 style file are included; to appear in Proc. "Observational Cosmology with the New Radio Surveys", eds. M. Bremer, N. Jackson & I. Perez-Fournon, Kluwer Acad. Pres

Exoplanet Catalogues

One of the most exciting developments in the field of exoplanets has been the progression from 'stamp-collecting' to demography, from discovery to characterisation, from exoplanets to comparative exoplanetology. There is an exhilaration when a prediction is confirmed, a trend is observed, or a new population appears. This transition has been driven by the rise in the sheer number of known exoplanets, which has been rising exponentially for two decades (Mamajek 2016). However, the careful collection, scrutiny and organisation of these exoplanets is necessary for drawing robust, scientific conclusions that are sensitive to the biases and caveats that have gone into their discovery. The purpose of this chapter is to discuss and demonstrate important considerations to keep in mind when examining or constructing a catalogue of exoplanets. First, we introduce the value of exoplanetary catalogues. There are a handful of large, online databases that aggregate the available exoplanet literature and render it digestible and navigable - an ever more complex task with the growing number and diversity of exoplanet discoveries. We compare and contrast three of the most up-to-date general catalogues, including the data and tools that are available. We then describe exoplanet catalogues that were constructed to address specific science questions or exoplanet discovery space. Although we do not attempt to list or summarise all the published lists of exoplanets in the literature in this chapter, we explore the case study of the NASA Kepler mission planet catalogues in some detail. Finally, we lay out some of the best practices to adopt when constructing or utilising an exoplanet catalogue.Comment: 14 pages, 6 figures. Invited review chapter, to appear in "Handbook of Exoplanets", edited by H.J. Deeg and J.A. Belmonte, section editor N. Batalh

One-shot genitalia are not an evolutionary dead end - Regained male polygamy in a sperm limited spider species

<p>Abstract</p> <p>Background</p> <p>Monogynous mating systems with extremely low male mating rates have several independent evolutionary origins and are associated with drastic adaptations involving self-sacrifice, one-shot genitalia, genital damage, and termination of spermatogenesis immediately after maturation. The combination of such extreme traits likely restricts evolutionary potential perhaps up to the point of making low male mating rates irreversible and hence may constitute an evolutionary dead end. Here, we explore the case of a reversion to multiple mating from monogynous ancestry in golden orb-web spiders, <it>Nephila senegalensis</it>.</p> <p>Results</p> <p>Male multiple mating is regained by the loss of genital damage and sexual cannibalism but spermatogenesis is terminated with maturation, restricting males to a single loading of their secondary mating organs and a fixed supply of sperm. However, males re-use their mating organs and by experimentally mating males to many females, we show that the sperm supply is divided between copulations without reloading the pedipalps.</p> <p>Conclusion</p> <p>By portioning their precious sperm supply, males achieve an average mating rate of four females which effectively doubles the maximal mating rate of their ancestors. A heritage of one-shot genitalia does not completely restrict the potential to increase mating rates in <it>Nephila </it>although an upper limit is defined by the available sperm load. Future studies should now investigate how males use this potential in the field and identify selection pressures responsible for a reversal from monogynous to polygynous mating strategies.</p

Honey bee foraging distance depends on month and forage type

To investigate the distances at which honey bee foragers collect nectar and pollen, we analysed 5,484 decoded waggle dances made to natural forage sites to determine monthly foraging distance for each forage type. Firstly, we found significantly fewer overall dances made for pollen (16.8 %) than for non-pollen, presumably nectar (83.2 %; P < 2.2 × 10−23). When we analysed distance against month and forage type, there was a significant interaction between the two factors, which demonstrates that in some months, one forage type is collected at farther distances, but this would reverse in other months. Overall, these data suggest that distance, as a proxy for forage availability, is not significantly and consistently driven by need for one type of forage over the other

State of the California current 2013-14: El niño looming

In 2013, the California current was dominated by strong coastal upwelling and high productivity. Indices of total cumulative upwelling for particular coastal locations reached some of the highest values on record. Chlorophyll a levels were high throughout spring and summer. Catches of upwelling-related fish species were also high. After a moderate drop in upwelling during fall 2013, the California current system underwent a major change in phase. Three major basin-scale indicators, the PDO, the NPGO, and the ENSO-MEI, all changed phase at some point during the winter of 2013/14. The PDO changed to positive values, indicative of warmer waters in the North Pacific; the NPGO to negative values, indicative of lower productivity along the coast; and the MEI to positive values, indicative of an oncoming El Niño. Whereas the majority of the California Current system appears to have transitioned to an El Niño state by August 2014, based on decreases in upwelling and chlorophyll a concentration, and increases in SST, there still remained pockets of moderate upwelling, cold water, and high chlorophyll a biomass at various central coast locations, unlike patterns seen during the more major El Niños (e.g., the 97-98 event). Catches of rockfish, market squid, euphausiids, and juvenile sanddab remained high along the central coast, whereas catches of sardine and anchovy were low throughout the CCS. 2014 appears to be heading towards a moderate El Niño state, with some remaining patchy regions of upwellingdriven productivity along the coast. Superimposed on this pattern, three major regions have experienced possibly non-El Niño-related warming since winter: the Bering Sea, the Gulf of Alaska, and offshore of southern California. It is unclear how this warming may interact with the predicted El Niño, but the result will likely be reduced growth or reproduction for many key fisheries species

In-reach specialist nursing teams for residential care homes : uptake of services, impact on care provision and cost-effectiveness

Background: A joint NHS-Local Authority initiative in England designed to provide a dedicated nursing and physiotherapy in-reach team (IRT) to four residential care homes has been evaluated.The IRT supported 131 residents and maintained 15 'virtual' beds for specialist nursing in these care homes. Methods: Data captured prospectively (July 2005 to June 2007) included: numbers of referrals; reason for referral; outcome (e.g. admission to IRT bed, short-term IRT support); length of stay in IRT; prevented hospital admissions; early hospital discharges; avoided nursing home transfers; and detection of unrecognised illnesses. An economic analysis was undertaken. Results: 733 referrals were made during the 2 years (range 0.5 to 13.0 per resident per annum)resulting in a total of 6,528 visits. Two thirds of referrals aimed at maintaining the resident's independence in the care home. According to expert panel assessment, 197 hospital admissions were averted over the period; 20 early discharges facilitated; and 28 resident transfers to a nursing home prevented. Detection of previously unrecognised illnesses accounted for a high number of visits. Investment in IRT equalled £44.38 per resident per week. Savings through reduced hospital admissions, early discharges, delayed transfers to nursing homes, and identification of previously unrecognised illnesses are conservatively estimated to produce a final reduction in care cost of £6.33 per resident per week. A sensitivity analysis indicates this figure might range from a weekly overall saving of £36.90 per resident to a 'worst case' estimate of £2.70 extra expenditure per resident per week. Evaluation early in implementation may underestimate some cost-saving activities and greater savings may emerge over a longer time period. Similarly, IRT costs may reduce over time due to the potential for refinement of team without major loss in effectiveness. Conclusion: Introduction of a specialist nursing in-reach team for residential homes is at least cost neutral and, in all probability, cost saving. Further benefits include development of new skills in the care home workforce and enhanced quality of care. Residents are enabled to stay in familiar surroundings rather than unnecessarily spending time in hospital or being transferred to a higher dependency nursing home setting

NMR and molecular modelling studies on the interaction of fluconazole with β-cyclodextrin

<p>Abstract</p> <p>Background</p> <p>Fluconazole (FLZ) is a synthetic, bistriazole antifungal agent, effective in treating superficial and systemic infections caused by <it>Candida </it>species. Major challenges in formulating this drug for clinical applications include solubility enhancement and improving stability in biological systems. Cyclodextrins (CDs) are chiral, truncated cone shaped macrocyles, and can easily encapsulate fluconazole inside their hydrophobic cavity. NMR spectroscopy has been recognized as an important tool for the interaction study of cyclodextrin and pharmaceutical compounds in solution state.</p> <p>Results</p> <p>Inclusion complex of fluconazole with β-cyclodextrins (β-CD) were investigated by applying NMR and molecular modelling methods. The 1:1 stoichiometry of FLZ:β-CD complex was determined by continuous variation (Job's plot) method and the overall association constant was determined by using Scott's method. The association constant was determined to be 68.7 M^-1which is consistent with efficient FLZ:β-CD complexation. The shielding of cavity protons of β-CD and deshielding of aromatic protons of FLZ in various¹H-NMR experiments show complexation between β-CD and FLZ. Based on spectral data obtained from 2D ROESY, a reasonable geometry for the complex could be proposed implicating the insertion of the <it>m</it>-difluorophenyl ring of FLZ into the wide end of the torus cavity of β-CD. Molecular modelling studies were conducted to further interpret the NMR data. Indeed the best docked complex in terms of binding free energy supports the model proposed from NMR experiments and the <it>m</it>-difluorophenyl ring of FLZ is observed to enter into the torus cavity of β-CD from the wider end.</p> <p>Conclusion</p> <p>Various NMR spectroscopic studies of FLZ in the presence of β-CD in D₂O at room temperature confirmed the formation of a 1:1 (FLZ:β-CD) inclusion complex in which <it>m</it>-difluorophenyl ring acts as guest. The induced shift changes as well as splitting of most of the signals of FLZ in the presence of β-CD suggest some chiral differentiation of guest by β-CD.</p