Proof of the Umbral Moonshine Conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.Comment: 56 pages, to appear in Research in the Mathematical Science

Ultrafast slow-light: Raman-induced delay of THz-bandwidth pulses

We propose and experimentally demonstrate a scheme to generate optically-controlled delays based on off-resonant Raman absorption. Dispersion in a transparency window between two neighboring, optically-activated Raman absorption lines is used to reduce the group velocity of broadband 765 nm pulses. We implement this approach in a potassium titanyl phosphate (KTP) waveguide at room temperature, and demonstrate Raman-induced delays of up to 140 fs for a 650-fs duration, 1.8-THz bandwidth, signal pulse; the available delay-bandwidth product is $\approx1$. Our approach is applicable to single photon signals, offers wavelength tunability, and is a step toward processing ultrafast photons.Comment: 5+4 pages, 4+2 figure

The Effect of Sodium Bicarbonate Ingestion on Back Squat and Bench Press Exercise to Failure

This study examined the acute effects of NaHCO3 ingestion on repetitions to failure and rating of perceived exertion in the back squat and bench press in trained men. Eight resistance-trained men took part in this double-blind, randomized crossover experimental study whereby they ingested NaHCO3 (0.3 g[middle dot]kg-1 body mass) or placebo (sodium chloride NaCl: 0.045 g[middle dot]kg-1 body mass) solution 60 minutes before completing a bout of resistance exercise (3 sets of bench press and back squat exercise to failure at an intensity of 80% 1 repetition maximum). Experimental conditions were separated by at least 48 hours. Participants completed more repetitions to failure in the back squat after NaHCO3 ingestion (p = 0.04) but not for bench press (p = 0.679). Mean +/- SD of total repetitions was 31.3 +/- 15.3 and 24.6 +/- 16.2 for back squat and 28.7 +/- 12.2 and 26.7 +/- 10.2 for bench press in NaHCO3 and placebo conditions, respectively. Repetitions to failure decreased as set increased for the back squat and bench press (p = 0.001, both). Rating of perceived exertion significantly increased with set for the back squat and bench press (p = 0.002, both). There was no significant change in blood lactate across time or between conditions. There were however treatment x time interactions for blood pH (p = 0.014) and blood HCO3 concentration (p = 0.001). After ingestion, blood pH and HCO3 (p = 0.008) concentrations were greater for the NaHCO3 condition compared with the placebo condition (p \u3c 0.001). The results of this study suggest that sodium bicarbonate ingestion can enhance resistance exercise performance using a repetition to failure protocol in the first exercise in a resistance exercise session

Functional Movement Is Negatively Associated with Weight Status and Positively Associated with Physical Activity in British Primary School Children

Although prior studies have suggested that overweight and obesity in childhood are associated with poorer functional movement performance, no study appears to have examined this issue in a pediatric population. The relations between BMI, ambulatory physical activity and functional movement screen (FMS) performance were compared in 58, 10-11-year-old children. Total FMS score was significantly, negatively correlated with BMI (P = .0001) and positively related to PA (P = .029). Normal weight children scored significantly better for total FMS score compared to children classified as overweight/obese (P = .0001). Mean ± S.D. of FMS scores were 15.5 ± 2.2 and 10.6 ± 2.1 in normal weight and overweight/obese children, respectively. BMI and PA were also significant predictors of functional movement (P = .0001, Adjusted R2 = .602) with BMI and PA predicting 52.9% and 7.3% of the variance in total FMS score, respectively. The results of this study highlight that ambulatory physical activity and weight status are significant predictors of functional movement in British children. Scientists and practitioners therefore need to consider interventions which develop functional movement skills alongside physical activity and weight management strategies in children in order to reduce the risks of orthopaedic abnormality arising from suboptimal movement patterns in later life