On an identity by Chaundy and Bullard. I

An identity by Chaundy and Bullard writes 1/(1-x)^n (n=1,2,...) as a sum of two truncated binomial series. This identity was rediscovered many times. Notably, a special case was rediscovered by I. Daubechies, while she was setting up the theory of wavelets of compact support. We discuss or survey many different proofs of the identity, and also its relationship with Gauss hypergeometric series. We also consider the extension to complex values of the two parameters which occur as summation bounds. The paper concludes with a discussion of a multivariable analogue of the identity, which was first given by Damjanovic, Klamkin and Ruehr. We give the relationship with Lauricella hypergeometric functions and corresponding PDE's. The paper ends with a new proof of the multivariable case by splitting up Dirichlet's multivariable beta integral.Comment: 20 pages; added in v3: more references to earlier occurrences of the identity and its multivariable analogue, combinatorial proof of the identity and extension to noninteger m,n, proof of multivariable identity by splitting up Dirichlet's multivariable beta integra

Efficacy of a T Cell-Biased Adenovirus Vector as a Zika Virus Vaccine

Zika virus (ZIKV) is a major public health concern due to the risk of congenital Zika syndrome in developing fetuses and Guillain-Barre syndrome in adults. Currently, there are no approved vaccines available to protect against infection. Adenoviruses are safe and highly immunogenic vaccine vectors capable of inducing lasting humoral and cellular immune responses. Here, we developed two Adenovirus (Ad) vectored Zika virus vaccines by inserting a ZIKV prM-E gene expression cassette into human Ad types 4 (Ad4-prM-E) and 5 (Ad5-prM-E). Immune correlates indicate that Ad5-prM-E vaccination induces both an anti-ZIKV antibody and T-cell responses whereas Ad4-prM-E vaccination only induces a T-cell response. In a highly lethal challenge in an interferon α/β receptor knockout mice, 80% of Ad5 vaccinated animals and 33% of Ad4 vaccinated animals survived a lethal ZIKV challenge, whereas no animals in the sham vaccinated group survived. In an infection model utilizing immunocompetent C57BL/6 mice that were immunized and then treated with a blocking anti-IFNAR-1 antibody immediately before ZIKV challenge, 100% of Ad4-prM-E and Ad5-prM-E vaccinated mice survived. This indicates that Ad4-prM-E vaccination is protective without the development of detectable anti-ZIKV antibodies. The protection seen in these highly lethal mouse models demonstrate the efficacy of Ad vectored vaccines for use against ZIKV

Directional Microwave Emission from Femtosecond-laser Illuminated Linear Arrays of Superconducting Rings

We examine the electromagnetic emission from two photo-illuminated linear arrays composed of inductively charged superconducting ring elements. The arrays are illuminated by an ultrafast infrared laser that triggers microwave broadband emission detected in the 1–26 GHz range. Based on constructive interference from the arrays a narrowing of the forward radiation lobe is observed with increasing element count and frequency demonstrating directed GHz emission. Results suggest that higher frequencies and a larger number of elements are achievable leading to a unique pulsed array emitter concept that can span frequencies from the microwave to the terahertz (THz) regime

Expressed sequence tags from Peromyscus testis and placenta tissue: Analysis, annotation, and utility for mapping

<p>Abstract</p> <p>Background</p> <p>Mice of the genus <it>Peromyscus </it>are found in nearly every habitat from Alaska to Central America and from the Atlantic to the Pacific. They provide an evolutionary outgroup to the <it>Mus/Rattus </it>lineage and serve as an intermediary between that lineage and humans. Although <it>Peromyscus </it>has been studied extensively under both field and laboratory conditions, research has been limited by the lack of molecular resources. Genes associated with reproduction typically evolve rapidly and thus are excellent sources of evolutionary information. In this study we describe the generation of two cDNA libraries, one from placenta and one from testis, characterize the resulting ESTs, and describe their utility for mapping the <it>Peromyscus </it>genome.</p> <p>Results</p> <p>The 5' ends of 1,510 placenta and 4,798 testis clones were sequenced. Low quality sequences were removed and after clustering and contig assembly, 904 unique placenta and 2,002 unique testis sequences remained. Average lengths of placenta and testis ESTs were 711 bp and 826 bp, respectively. Approximately 82% of all ESTs were identified using the BLASTX algorithm to <it>Mus </it>and <it>Rattus</it>, and 34 – 54% of all ESTs could be assigned to a biological process gene ontology category in either <it>Mus </it>or <it>Rattus</it>. Because the <it>Peromyscus </it>genome organization resembles the <it>Rattus </it>genome more closely than <it>Mus </it>we examined the distribution of the <it>Peromyscus </it>ESTs across the rat genome finding markers on all rat chromosomes except the Y. Approximately 40% of all ESTs were specific to only one location in the <it>Mus </it>genome and spanned introns of an appropriate size for sequencing and SNP detection. Of the primers that were tried 54% provided useful assays for genotyping on interspecific backcross and whole-genome radiation hybrid cell panels.</p> <p>Conclusion</p> <p>The 2,906 <it>Peromyscus </it>placenta and testis ESTs described here significantly expands the molecular resources available for the genus. These ESTs allow for specific PCR amplification and broad coverage across the genome, creating an excellent genetic marker resource for the generation of a medium-density genomic map. Thus, this resource will significantly aid research of a genus that is uniquely well-suited to both laboratory and field research.</p

Gapless spin-excitations in the superconducting state of a quasi-one-dimensional spin-triplet superconductor

Majorana zero modes form as intrinsic defects in an odd-orbital one-dimensional superconductor thus motivating the search for such materials in the pursuit of Majorana physics. Here, we present combined experimental results and first principles calculations which suggest that quasi-one-dimensional K$_2$Cr$_3$As$_3$ may be such a superconductor. Using inelastic neutron scattering we probe the dynamic spin-susceptibilities of K$_2$Cr$_3$As$_3$ and K$_2$Mo$_3$As$_3$ and show the presence of antiferromagnetic spin-fluctuations in both compounds. Below the superconducting transition, these fluctuations gap in K$_2$Mo$_3$As$_3$ but not in K$_2$Cr$_3$As$_3$. Using first principles calculations, we show that these fluctuations likely arise from nesting on one dimensional features of the Fermi surface. Considering these results we propose that while K$_2$Mo$_3$As$_3$ is a conventional superconductor, K$_2$Cr$_3$As$_3$ is likely a spin-triplet, and consequently, topological superconductor.Comment: 8 pages, 4 figure

High risk clinical characteristics for subarachnoid haemorrhage in patients with acute headache: prospective cohort study

Objective To identify high risk clinical characteristics for subarachnoid haemorrhage in neurologically intact patients with headache

Sensitivity of computed tomography performed within six hours of onset of headache for diagnosis of subarachnoid haemorrhage: prospective cohort study

Objective To measure the sensitivity of modern third generation computed tomography in emergency patients being evaluated for possible subarachnoid haemorrhage, especially when carried out within six hours of headache onset

Ursolic Acid Increases Skeletal Muscle and Brown Fat and Decreases Diet-Induced Obesity, Glucose Intolerance and Fatty Liver Disease

Skeletal muscle Akt activity stimulates muscle growth and imparts resistance to obesity, glucose intolerance and fatty liver disease. We recently found that ursolic acid increases skeletal muscle Akt activity and stimulates muscle growth in non-obese mice. Here, we tested the hypothesis that ursolic acid might increase skeletal muscle Akt activity in a mouse model of diet-induced obesity. We studied mice that consumed a high fat diet lacking or containing ursolic acid. In skeletal muscle, ursolic acid increased Akt activity, as well as downstream mRNAs that promote glucose utilization (hexokinase-II), blood vessel recruitment (Vegfa) and autocrine/paracrine IGF-I signaling (Igf1). As a result, ursolic acid increased skeletal muscle mass, fast and slow muscle fiber size, grip strength and exercise capacity. Interestingly, ursolic acid also increased brown fat, a tissue that shares developmental origins with skeletal muscle. Consistent with increased skeletal muscle and brown fat, ursolic acid increased energy expenditure, leading to reduced obesity, improved glucose tolerance and decreased hepatic steatosis. These data support a model in which ursolic acid reduces obesity, glucose intolerance and fatty liver disease by increasing skeletal muscle and brown fat, and suggest ursolic acid as a potential therapeutic approach for obesity and obesity-related illness