Finite Form of the Quintuple Product Identity

The celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula.Comment: 1 pag

Minimal Permutations and 2-Regular Skew Tableaux

Bouvel and Pergola introduced the notion of minimal permutations in the study of the whole genome duplication-random loss model for genome rearrangements. Let $\mathcal{F}_d(n)$ denote the set of minimal permutations of length $n$ with $d$ descents, and let $f_d(n)= |\mathcal{F}_d(n)|$. They derived that $f_{n-2}(n)=2^{n}-(n-1)n-2$ and $f_n(2n)=C_n$, where $C_n$ is the $n$-th Catalan number. Mansour and Yan proved that $f_{n+1}(2n+1)=2^{n-2}nC_{n+1}$. In this paper, we consider the problem of counting minimal permutations in $\mathcal{F}_d(n)$ with a prescribed set of ascents. We show that such structures are in one-to-one correspondence with a class of skew Young tableaux, which we call $2$-regular skew tableaux. Using the determinantal formula for the number of skew Young tableaux of a given shape, we find an explicit formula for $f_{n-3}(n)$. Furthermore, by using the Knuth equivalence, we give a combinatorial interpretation of a formula for a refinement of the number $f_{n+1}(2n+1)$.Comment: 19 page

Photodegradation modeling based on laboratory accelerated test data and predictions under outdoor weathering for polymeric materials

Photodegradation, driven primarily by ultraviolet (UV) radiation, is the primary cause of failure for organic paints and coatings, as well as many other products made from polymeric materials exposed to sunlight. Traditional methods of service life prediction involve the use of outdoor exposure in harsh UV environments (e.g., Florida and Arizona). Such tests, however, require too much time (generally many years) to do an evaluation. To overcome the shortcomings of traditional methods, scientists at the U.S. National Institute of Standards and Technology (NIST) conducted a multiyear research program to collect necessary data via scientifically-based laboratory accelerated tests. This paper presents the statistical modeling and analysis of the photodegradation data collected at NIST, and predictions of degradation for outdoor specimens that are subjected to weathering. The analysis involves identifying a physics/chemistry-motivated model that will adequately describe photodegradation paths. The model incorporates the effects of explanatory variables which are UV spectrum, UV intensity, temperature, and relative humidity. We use a nonlinear mixed-effects model to describe the sample paths. We extend the model to allow for dynamic covariates and compare predictions with specimens that were exposed in an outdoor environment where the explanatory variables are uncontrolled but recorded. We also discuss the findings from the analysis of the NIST data and some areas for future research

Conservation of a microRNA cluster in parasitic nematodes and profiling of miRNAs in excretory-secretory products and microvesicles of Haemonchus contortus

microRNAs are small non-coding RNAs that are important regulators of gene expression in a range of animals, including nematodes. We have analysed a cluster of four miRNAs from the pathogenic nematode species Haemonchus contortus that are closely linked in the genome. We find that the cluster is conserved only in clade V parasitic nematodes and in some ascarids, but not in other clade III species nor in clade V free-living nematodes. Members of the cluster are present in parasite excretory-secretory products and can be detected in the abomasum and draining lymph nodes of infected sheep, indicating their release in vitro and in vivo. As observed for other parasitic nematodes, H. contortus adult worms release extracellular vesicles (EV). Small RNA libraries were prepared from vesicle-enriched and vesicle-depleted supernatants from both adult worms and L4 stage larvae. Comparison of the miRNA species in the different fractions indicated that specific miRNAs are packaged within vesicles, while others are more abundant in vesicle-depleted supernatant. Hierarchical clustering analysis indicated that the gut is the likely source of vesicle-associated miRNAs in the L4 stage, but not in the adult worm. These findings add to the growing body of work demonstrating that miRNAs released from parasitic helminths may play an important role in host-parasite interactions

Risk for Post-Spinal Surgery Complications Associated with Pre-Operative Blood Transfusions

Introduction: The frequency of spinal surgeries has increased dramatically in the United States over the past decade and, as with all surgeries, spinal procedures carry inherent risks for complications after the operation. Recently, it has been recognized that procedures in which intra-operative/post-operative blood transfusions are administered carry a higher risk of postoperative morbidity and increased length of hospital stay (Seisean et al.). Despite this, there is little literature, currently, analyzing post-operative complications associated with blood transfusions taking place 72 hours prior to spinal operations. The aim of this study was to investigate the prevalence of pre-operative blood transfusions in spinal surgeries and elucidate the associations that exist between those transfusions and post-operative complications. Materials & Methods: We retrospectively analyzed cases of spinal surgeries between 2005 and 2014 from the American College of Surgeons National Surgical Quality Improvement Program (ACS-NSQIP) database with the exception of 2009 due to incomplete data. A total of 37,201 patients who had undergone spinal procedures were studied. Patients receiving pre-operative blood transfusions within 72 hours of surgery were documented. Demographic factors, including sex and age, were noted. Comorbidities included in this analysis include body mass index (BMI) and American Society of Anesthesiologists (ASA) score. Post-operative complications were stratified into major and minor categories. Chi-squared test, Fisher\u27s exact test, and ANOVA were used to perform univariate testing where appropriate, while multivariate analyses were performed to determine independent risk factors for complications. Results:With the exception of pneumonia (p=0.096), blood transfusions prior to spinal surgeries were associated with increased risk for all major and minor complication criteria analyzed, with major complications including myocardial infarction (MI), deep venous thrombosis (DVT), pulmonary embolism (PE), stroke, peripheral nerve injury, deep wound infection, organ cavity infection, sepsis, and death (p Discussion: Overall, patients receiving blood transfusions within 72 hours prior to undergoing spinal procedures had increased rates of several post-operative complications. Among these complications, the most notable include superficial and deep wound infections, MI, pneumonia, DVT, stroke, and even death. Armed with this knowledge, surgeons would better be able to predict, and therefore mitigate, such post-operative complications in these patients. Future research in this area, directed toward stratification of risk based on the patient’s need for pre-operative blood transfusion and procedure type, would provide further insight into preventing post-operative complications after spinal surgeries

Retrieval of mass and sizes of particles in sandstorms using two MODIS IR bands: A case study of april 7 2001 sandstorm in China

A thermal infrared remote sensing retrieval method developed by Wen and Rose [1994], which retrieves particle sizes, optical depth, and total masses of silicate particles in the volcanic cloud, was applied to an April 07, 2001 sandstorm over northern China, using MODIS. Results indicate that the area of the dust cloud observed was 1.34 million km2, the mean particle radius of the dust was 1.44 μm, and the mean optical depth at 11 μm was 0.79. The mean burden of dust was approximately 4.8 tons/km2 and the main portion of the dust storm on April 07, 2001 contained 6.5 million tons of dust. The results are supported by both independent remote sensing data (TOMS) and in-situ data for a similar event in 1998. This paper demonstrates that Wen and Rose’s retrieval method could be successfully applied to past and future sandstorm events using IR channels of AVHRR, GOES or MODIS