Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

The ExoMolOP Database: Cross-sections and k-tables for Molecules of Interest in High-Temperature Exoplanet Atmospheres

A publicly available database of opacities for molecules of astrophysical interest, ExoMolOP, has been compiled for over 80 species, based on the latest line list data from the ExoMol, HITEMP and MoLLIST databases. These data are generally suitable for characterising high temperature exoplanet or cool stellar/substellar atmospheres, and have been computed at a variety of pressures and temperatures, with a few molecules included at room-temperature only from the HITRAN database. The data are formatted in different ways for four different exoplanet atmosphere retrieval codes; ARCiS, TauREx, NEMESIS and petitRADTRANS, and include both cross-sections (at R~=~λΔλ~=~15,000) and k-tables (at R~=~λΔλ~=~1000) for the 0.3~-~50μm wavelength region. Opacity files can be downloaded and used directly for these codes. Atomic data for alkali metals Na and K are also included, using data from the NIST database and the latest line shapes for the resonance lines. Broadening parameters have been taken from the literature where available, or from those for a known molecule with similar molecular properties where no broadening data are available

A July Spike in Fatal Medication Errors: A Possible Effect of New Medical Residents

residencies and acquire increased responsibility for patient care. Many have suggested that these new medical residents may produce errors and worsen patient outcomes—the so-called “July Effect; ” however, we have found no U.S. evidence documenting this effect. OBJECTIVE: Determine whether fatal medication errors spike in July

Detection of Chlamydia trachomatis mRNA using digital PCR as a more accurate marker of viable organism

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. Spontaneous resolution of urogenital Chlamydia trachomatis (CT) without treatment has previously been described, but a limitation of these reports is that DNA or RNA-based amplification tests used do not differentiate between viable infection and non-viable DNA. We modified a previously published CT mRNA detection (omp2) method to differentiate between viable infection and non-viable DNA in a sample of CT DNA PCR positive women. We modified a CT mRNA detection (omp2) method from reverse transcriptase qPCR (RTqPCR) to digital PCR (dPCR) and evaluated it in samples from CT DNA positive women. Firstly, CT infected McCoy B cells treated with azithromycin in vitro identified detectable mRNA levels disappeared <2 days, while DNA persisted up to 6 days. We used 55 self-collected vaginal swabs from a cohort of women diagnosed as DNA positive for chlamydia obtained pre- and 7 days of post-azithromycin treatment. Concordance with DNA results was higher for dPCR than RTqPCR (74.5% versus 65.5%). At visit 1, there was a strong linear relationship between DNA and mRNA (r = 0.9, p < 0.000); 24 samples had both mRNA and DNA detected (82.8%) and 5 had only DNA detected with a potential false positive proportion of 17.2% (95%CI: 5.8, 35.8). At visit 2, there was poor correlation between DNA and mRNA (r = 0.14, p = 0.55); eight specimens had only DNA detected (42.1%; 95%CI: 20.25, 66.50) and one had mRNA detected. DNA detection methods alone may detect non-viable DNA. Consideration should be given to further develop mRNA assays as ancillary tests to improve detection of viable chlamydia

Identifying predictable foraging habitats for a wide-ranging marine predator using ensemble ecological niche models

Aim: Ecological niche modelling can provide valuable insight into species' environmental preferences and aid the identification of key habitats for populations of conservation concern. Here, we integrate biologging, satellite remote-sensing and ensemble ecological niche models (EENMs) to identify predictable foraging habitats for a globally important population of the grey-headed albatross (GHA) Thalassarche chrysostoma. Location: Bird Island, South Georgia; Southern Atlantic Ocean. Methods: GPS and geolocation-immersion loggers were used to track at-sea movements and activity patterns of GHA over two breeding seasons (n = 55; brood-guard). Immersion frequency (landings per 10-min interval) was used to define foraging events. EENM combining Generalized Additive Models (GAM), MaxEnt, Random Forest (RF) and Boosted Regression Trees (BRT) identified the biophysical conditions characterizing the locations of foraging events, using time-matched oceanographic predictors (Sea Surface Temperature, SST; chlorophyll a, chl-a; thermal front frequency, TFreq; depth). Model performance was assessed through iterative cross-validation and extrapolative performance through cross-validation among years. Results: Predictable foraging habitats identified by EENM spanned neritic ( 0.5 mg m−3) and frequent manifestation of mesoscale thermal fronts. Our results confirm previous indications that GHA exploit enhanced foraging opportunities associated with frontal systems and objectively identify the APFZ as a region of high foraging habitat suitability. Moreover, at the spatial and temporal scales investigated here, the performance of multi-model ensembles was superior to that of single-algorithm models, and cross-validation among years indicated reasonable extrapolative performance. Main conclusions: EENM techniques are useful for integrating the predictions of several single-algorithm models, reducing potential bias and increasing confidence in predictions. Our analysis highlights the value of EENM for use with movement data in identifying at-sea habitats of wide-ranging marine predators, with clear implications for conservation and management

The US stock market leads the Federal funds rate and Treasury bond yields

Using a recently introduced method to quantify the time varying lead-lag dependencies between pairs of economic time series (the thermal optimal path method), we test two fundamental tenets of the theory of fixed income: (i) the stock market variations and the yield changes should be anti-correlated; (ii) the change in central bank rates, as a proxy of the monetary policy of the central bank, should be a predictor of the future stock market direction. Using both monthly and weekly data, we found very similar lead-lag dependence between the S&P500 stock market index and the yields of bonds inside two groups: bond yields of short-term maturities (Federal funds rate (FFR), 3M, 6M, 1Y, 2Y, and 3Y) and bond yields of long-term maturities (5Y, 7Y, 10Y, and 20Y). In all cases, we observe the opposite of (i) and (ii). First, the stock market and yields move in the same direction. Second, the stock market leads the yields, including and especially the FFR. Moreover, we find that the short-term yields in the first group lead the long-term yields in the second group before the financial crisis that started mid-2007 and the inverse relationship holds afterwards. These results suggest that the Federal Reserve is increasingly mindful of the stock market behavior, seen at key to the recovery and health of the economy. Long-term investors seem also to have been more reactive and mindful of the signals provided by the financial stock markets than the Federal Reserve itself after the start of the financial crisis. The lead of the S&P500 stock market index over the bond yields of all maturities is confirmed by the traditional lagged cross-correlation analysis.Comment: 12 pages, 7 figures, 1 tabl

Effect of parasympathetic stimulation on brain activity during appraisal of fearful expressions

Autonomic nervous system activity is an important component of human emotion. Mental processes influence bodily physiology, which in turn feeds back to influence thoughts and feelings. Afferent cardiovascular signals from arterial baroreceptors in the carotid sinuses are processed within the brain and contribute to this two-way communication with the body. These carotid baroreceptors can be stimulated non-invasively by externally applying focal negative pressure bilaterally to the neck. In an experiment combining functional neuroimaging (fMRI) with carotid stimulation in healthy participants, we tested the hypothesis that manipulating afferent cardiovascular signals alters the central processing of emotional information (fearful and neutral facial expressions). Carotid stimulation, compared with sham stimulation, broadly attenuated activity across cortical and brainstem regions. Modulation of emotional processing was apparent as a significant expression-by-stimulation interaction within left amygdala, where responses during appraisal of fearful faces were selectively reduced by carotid stimulation. Moreover, activity reductions within insula, amygdala, and hippocampus correlated with the degree of stimulation-evoked change in the explicit emotional ratings of fearful faces. Across participants, individual differences in autonomic state (heart rate variability, a proxy measure of autonomic balance toward parasympathetic activity) predicted the extent to which carotid stimulation influenced neural (amygdala) responses during appraisal and subjective rating of fearful faces. Together our results provide mechanistic insight into the visceral component of emotion by identifying the neural substrates mediating cardiovascular influences on the processing of fear signals, potentially implicating central baroreflex mechanisms for anxiolytic treatment targets

Fingerprint Recognition with Identical Twin Fingerprints

Fingerprint recognition with identical twins is a challenging task due to the closest genetics-based relationship existing in the identical twins. Several pioneers have analyzed the similarity between twins' fingerprints. In this work we continue to investigate the topic of the similarity of identical twin fingerprints. Our study was tested based on a large identical twin fingerprint database that contains 83 twin pairs, 4 fingers per individual and six impressions per finger: 3984 (83*2*4*6) images. Compared to the previous work, our contributions are summarized as follows: (1) Two state-of-the-art fingerprint identification methods: P071 and VeriFinger 6.1 were used, rather than one fingerprint identification method in previous studies. (2) Six impressions per finger were captured, rather than just one impression, which makes the genuine distribution of matching scores more realistic. (3) A larger sample (83 pairs) was collected. (4) A novel statistical analysis, which aims at showing the probability distribution of the fingerprint types for the corresponding fingers of identical twins which have same fingerprint type, has been conducted. (5) A novel analysis, which aims at showing which finger from identical twins has higher probability of having same fingerprint type, has been conducted. Our results showed that: (a) A state-of-the-art automatic fingerprint verification system can distinguish identical twins without drastic degradation in performance. (b) The chance that the fingerprints have the same type from identical twins is 0.7440, comparing to 0.3215 from non-identical twins. (c) For the corresponding fingers of identical twins which have same fingerprint type, the probability distribution of five major fingerprint types is similar to the probability distribution for all the fingers' fingerprint type. (d) For each of four fingers of identical twins, the probability of having same fingerprint type is similar

Grifonin-1: A Small HIV-1 Entry Inhibitor Derived from the Algal Lectin, Griffithsin

Background: Griffithsin, a 121-residue protein isolated from a red algal Griffithsia sp., binds high mannose N-linked glycans of virus surface glycoproteins with extremely high affinity, a property that allows it to prevent the entry of primary isolates and laboratory strains of T- and M-tropic HIV-1. We used the sequence of a portion of griffithsin's sequence as a design template to create smaller peptides with antiviral and carbohydrate-binding properties. Methodology/Results: The new peptides derived from a trio of homologous β-sheet repeats that comprise the motifs responsible for its biological activity. Our most active antiviral peptide, grifonin-1 (GRFN-1), had an EC50 of 190.8±11.0 nM in in vitro TZM-bl assays and an EC50 of 546.6±66.1 nM in p24gag antigen release assays. GRFN-1 showed considerable structural plasticity, assuming different conformations in solvents that differed in polarity and hydrophobicity. Higher concentrations of GRFN-1 formed oligomers, based on intermolecular β-sheet interactions. Like its parent protein, GRFN-1 bound viral glycoproteins gp41 and gp120 via the N-linked glycans on their surface. Conclusion: Its substantial antiviral activity and low toxicity in vitro suggest that GRFN-1 and/or its derivatives may have therapeutic potential as topical and/or systemic agents directed against HIV-1