Cayley graphs of order kp are hamiltonian for k < 48

We provide a computer-assisted proof that if G is any finite group of order kp, where k < 48 and p is prime, then every connected Cayley graph on G is hamiltonian (unless kp = 2). As part of the proof, it is verified that every connected Cayley graph of order less than 48 is either hamiltonian connected or hamiltonian laceable (or has valence less than three).Comment: 16 pages. GAP source code is available in the ancillary file

Fifteen new risk loci for coronary artery disease highlight arterial-wall-specific mechanisms

Coronary artery disease (CAD) is a leading cause of morbidity and mortality worldwide. Although 58 genomic regions have been associated with CAD thus far, most of the heritability is unexplained, indicating that additional susceptibility loci await identification. An efficient discovery strategy may be larger-scale evaluation of promising associations suggested by genome-wide association studies (GWAS). Hence, we genotyped 56,309 participants using a targeted gene array derived from earlier GWAS results and performed meta-analysis of results with 194,427 participants previously genotyped, totaling 88,192 CAD cases and 162,544 controls. We identified 25 new SNP-CAD associations (P &lt; 5 × 10(-8), in fixed-effects meta-analysis) from 15 genomic regions, including SNPs in or near genes involved in cellular adhesion, leukocyte migration and atherosclerosis (PECAM1, rs1867624), coagulation and inflammation (PROCR, rs867186 (p.Ser219Gly)) and vascular smooth muscle cell differentiation (LMOD1, rs2820315). Correlation of these regions with cell-type-specific gene expression and plasma protein levels sheds light on potential disease mechanisms

Temperature Effects Explain Continental Scale Distribution of Cyanobacterial Toxins

Insight into how environmental change determines the production and distribution of cyanobacterial toxins is necessary for risk assessment. Management guidelines currently focus on hepatotoxins (microcystins). Increasing attention is given to other classes, such as neurotoxins (e.g., anatoxin-a) and cytotoxins (e.g., cylindrospermopsin) due to their potency. Most studies examine the relationship between individual toxin variants and environmental factors, such as nutrients, temperature and light. In summer 2015, we collected samples across Europe to investigate the effect of nutrient and temperature gradients on the variability of toxin production at a continental scale. Direct and indirect effects of temperature were the main drivers of the spatial distribution in the toxins produced by the cyanobacterial community, the toxin concentrations and toxin quota. Generalized linear models showed that a Toxin Diversity Index (TDI) increased with latitude, while it decreased with water stability. Increases in TDI were explained through a significant increase in toxin variants such as MC-YR, anatoxin and cylindrospermopsin, accompanied by a decreasing presence of MC-LR. While global warming continues, the direct and indirect effects of increased lake temperatures will drive changes in the distribution of cyanobacterial toxins in Europe, potentially promoting selection of a few highly toxic species or strains.Peer reviewe

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms

Sharper bounds for Chebyshev's θ(x)\theta(x) function

In 1792, Gauss conjectured that the primes occur with a density of $\frac{1}{log x}$ around $x$. Therefore, when developing explicit results relating to the Prime Number Theorem, it is useful to study Chebyshevâ à ôs $\theta(x)$ function, given by $$\sum_{p \le x} \log p .$$ Over summer 2017, I worked on a joint project supported by NSERC USRA to develop an effective version of the Prime Number Theorem. In this talk, I present our results which are the current best results for the prime counting function $\theta(x)$ for various ranges of x. We developed these results by first surveying existing explicit results from the past 60 years on prime counting functions. Our results are based on a recent zero density result for the zeroes of the Riemann Zeta function (due to H. Kadiri, A. Lumley, and N. Ng).Non UBCUnreviewedAuthor affiliation: University of LethbridgeUndergraduat

Stratification strength and light climate explain variation in chlorophyll a at the continental scale in a European multilake survey in a heatwave summer

To determine the drivers of phytoplankton biomass, we collected standardized morphometric, physical, and biological data in 230 lakes across the Mediterranean, Continental, and Boreal climatic zones of the European continent. Multilinear regression models tested on this snapshot of mostly eutrophic lakes (median total phosphorus [TP] = 0.06 and total nitrogen [TN] = 0.7 mg L-1), and its subsets (2 depth types and 3 climatic zones), show that light climate and stratification strength were the most significant explanatory variables for chlorophyll a (Chl a) variance. TN was a significant predictor for phytoplankton biomass for shallow and continental lakes, while TP never appeared as an explanatory variable, suggesting that under high TP, light, which partially controls stratification strength, becomes limiting for phytoplankton development. Mediterranean lakes were the warmest yet most weakly stratified and had significantly less Chl a than Boreal lakes, where the temperature anomaly from the long-term average, during a summer heatwave was the highest (+4 degrees C) and showed a significant, exponential relationship with stratification strength. This European survey represents a summer snapshot of phytoplankton biomass and its drivers, and lends support that light and stratification metrics, which are both affected by climate change, are better predictors for phytoplankton biomass in nutrient-rich lakes than nutrient concentrations and surface temperature.Peer reviewe