Calculating the pp-canonical basis of Hecke algebras

We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke category inside a semisimple category to build a "model" for indecomposable objects and bases of their morphism spaces. Inside this semisimple category, objects are sequences of Coxeter group elements, and morphisms are (sparse) matrices over a fraction field, making it quite amenable to computations. This strategy works for the full Hecke category over any base field, but in the antispherical case we must instead work over $\mathbb{Z}_{(p)}$ and use an idempotent lifting argument to deduce the result for a field of characteristic $p > 0$. We also describe a less sophisticated algorithm which is much more suited to the case of finite groups. We provide complete implementations of both algorithms in the MAGMA computer algebra system.Comment: 21 page

Michelle Nunn’s midterm result shows that Georgia’s demographics may be shifting to favor the Democrats

In Georgia’s Senate race Republican David Purdue defeated Democrat Michelle Nunn by nearly eight points, despite polling that had shown a much closer contest. Jamie L. Carson, Joel Sievert, and Ryan D. Williamson reflect on Georgia’s midterm election results, writing that in gaining more than 40 percent of the vote, Nunn outperformed many previous Democratic candidates in the state. They argue that if the Democratic Party continues to field good candidates in Georgia, shifting demographics may mean that they will be able to take statewide races within a few election cycles

Starspots and relativity: Applied Doppler imaging for the Gravity Probe B mission

We present Doppler images and surface differential rotation measurements for the primary of the RS CVn binary IM Pegasi, the guide star for the Gravity Probe B experiment. The data used is a subset of that taken during optical support of the mission and was obtained almost nightly over a near three year period from the Automatic Spectroscopic Telescope operated by Tennessee State University. Using the technique of least-squares deconvolution to increase the signal-to-noise ratio of the data, we have reconstructed 31 maximum entropy Doppler images of the star. The images show that the spot features are relatively stable for over a year (and possibly longer) with both a polar spot and lower latitude features. The most intense features are located on the side facing the secondary. In addition, we have incorporated a solar-like differential rotation law into the imaging process to determine the level of surface differential rotation for IM Peg for 22 epochs. A weighted least-squares average of the measurements gives a surface shear of 0.0142 ± 0.0007 rad/d, meaning that the equator takes ∼440 ± 20 days to lap the poles. Although the level of surface differential rotation was shown to vary over the period of the observations, this may indicate an underestimate in the errors of the method rather than any temporal evolution in the differential rotation

Health and fitness benefits using a heart rate intensity-based group fitness exercise regimen

Inactivity leads to morbidity and mortality, while novel and engaging approaches to fitness improve health outcomes. The current study examined an 8-week commercial group exercise regimen for high intensity interval training (HIIT) in order to examine comprehensive metrics of health and fitness. Aerobic fitness, body composition, resting metabolic rate, blood cholesterol and glucose, in addition to resting blood pressure were quantified in a laboratory setting independent of the training facilities. Exercise training utilized multimodal HIIT-based exercises and work intensity was gauged by real-time heart rate feedback. All participants completed the required two sessions per week. Pre-Post analyses indicate aerobic fitness (Pre VO2max = 36.8 ml•kg-1•min-1; Post VO2max = 40.8 ml•kg-1•min-1), % fat (Pre = 28.1%; Post = 27.0%), resting metabolic rate (Pre = 1557 kcals; Post = 1664 kcals), resting blood pressure (Pre = 128.8/78.1 mmHg; Post = 116.7/75.4 mmHg), and circulating triacylglycerol (Pre = 100.0 mg/dl; Post = 78.7 mg/dl) were significantly altered. This study quantified improvements in aerobic fitness, body composition, resting metabolic rate, resting blood pressure, and triacylglycerol after an 8-week HIIT regimen. The implications of heart rate (HR) monitoring within franchised group exercise with wearable technology serves as an unexplored scientific approach to understand novel exercise prescriptions on health-fitness outcomes. Future research should investigate sociological aspects of program adherence, while biological applications should examine the adaptive stimuli of HIIT training on health and fitness improvements.This work was supported by the Ultimate Fitness Group, LLC dba Orange Theory Fitness

Extraction-scintillation medium and method of use

An extraction-scintillation medium of substantially free-flowing, porous, solid particulate matter having one or more fluors retained within the particulate matter and an extraction agent adsorbed on or bound to the surface of the particulate matter. The medium is capable of extracting one of a selected radionuclide from an aqueous stream and permits transmission of light therethrough, which light is emitted from the one or more fluors in response to radiation absorbed thereby from the selected radionuclide. A sensor system using the extraction-scintillation medium for real-time or near real-time detection of the selected radionuclide is also disclosed

Mutations in the voltage-gated sodium channel gene associated with deltamethrin resistance in commercially sourced Phytoseiulus persimilis

The implementation of Integrated Pest Management (IPM) in current agricultural practice is a convenient and very effective strategy to maintain pest populations under control. The use of biological control agents, like Phytoseiulus persimilis, is key for the success of such an approach. This predatory mite is widely used since it is very effective for controlling Tetranychus urticae, one of the most devastating crop pests. Here we identify several mutations located in the Voltage Gated Sodium Channel (VGSC) of commercially sourced P. persimilis that correlate with a reduced susceptibility to the pyrethroid deltamethrin. We found that the mites sourced from two different biocontrol product companies have intrinsic genotypic differences that correlate with their phenotype when tested with different concentrations of deltamethrin. Mites from Syngenta Bioline, carrying the mutations M918L and A1536T, were able to survive deltamethrin concentrations of up to 10 ppm, while the mites from Koppert Biological Systems, with the combination M918L, L925V and S1539T, survived treatment with 40 ppm. All of the point mutations identified in the predatory mite samples are located in a particular region of the VGSC, previously proposed as the binding site for this family of pesticides and identified as a 'hot spot' for resistance