Two-divisibility of the coefficients of certain weakly holomorphic modular forms

We study a canonical basis for spaces of weakly holomorphic modular forms of weights 12, 16, 18, 20, 22, and 26 on the full modular group. We prove a relation between the Fourier coefficients of modular forms in this canonical basis and a generalized Ramanujan tau-function, and use this to prove that these Fourier coefficients are often highly divisible by 2.Comment: Corrected typos. To appear in the Ramanujan Journa

TIC 378898110: A bright, short-period AM CVn binary in TESS

AM CVn-type systems are ultracompact, helium-accreting binary systems which are evolutionarily linked to the progenitors of thermonuclear supernovae and are expected to be strong Galactic sources of gravitational waves detectable to upcoming space-based interferometers. AM CVn binaries with orbital periods ≲ 20–23 min exist in a constant high state with a permanently ionised accretion disc. We present the discovery of TIC 378898110, a bright (G = 14.3 mag), nearby (309.3 ± 1.8 pc), high-state AM CVn binary discovered in TESS two-minute-cadence photometry. At optical wavelengths this is the third-brightest AM CVn binary known. The photometry of the system shows a 23.07172(6) min periodicity, which is likely to be the ‘superhump’ period and implies an orbital period in the range 22–23 min. There is no detectable spectroscopic variability. The system underwent an unusual, year-long brightening event during which the dominant photometric period changed to a shorter period (constrained to 20.5 ± 2.0 min), which we suggest may be evidence for the onset of disc-edge eclipses. The estimated mass transfer rate, log(M˙ /M⊙yr−1 ) = −6.8±1.0, is unusually high and may suggest a high-mass or thermally inflated donor. The binary is detected as an X-ray source, with a flux of 9.2+4.2 −1.8 ×10−13 erg cm−2s−1 in the 0.3–10 keV range. TIC 378898110 is the shortest-period binary system discovered with TESS, and its large predicted gravitational-wave amplitude makes it a compelling verification binary for future space-based gravitational wave detectors

Effects of antibiotic resistance, drug target attainment, bacterial pathogenicity and virulence, and antibiotic access and affordability on outcomes in neonatal sepsis: an international microbiology and drug evaluation prospective substudy (BARNARDS)

Background Sepsis is a major contributor to neonatal mortality, particularly in low-income and middle-income countries (LMICs). WHO advocates ampicillin–gentamicin as first-line therapy for the management of neonatal sepsis. In the BARNARDS observational cohort study of neonatal sepsis and antimicrobial resistance in LMICs, common sepsis pathogens were characterised via whole genome sequencing (WGS) and antimicrobial resistance profiles. In this substudy of BARNARDS, we aimed to assess the use and efficacy of empirical antibiotic therapies commonly used in LMICs for neonatal sepsis. Methods In BARNARDS, consenting mother–neonates aged 0–60 days dyads were enrolled on delivery or neonatal presentation with suspected sepsis at 12 BARNARDS clinical sites in Bangladesh, Ethiopia, India, Pakistan, Nigeria, Rwanda, and South Africa. Stillborn babies were excluded from the study. Blood samples were collected from neonates presenting with clinical signs of sepsis, and WGS and minimum inhibitory concentrations for antibiotic treatment were determined for bacterial isolates from culture-confirmed sepsis. Neonatal outcome data were collected following enrolment until 60 days of life. Antibiotic usage and neonatal outcome data were assessed. Survival analyses were adjusted to take into account potential clinical confounding variables related to the birth and pathogen. Additionally, resistance profiles, pharmacokinetic–pharmacodynamic probability of target attainment, and frequency of resistance (ie, resistance defined by in-vitro growth of isolates when challenged by antibiotics) were assessed. Questionnaires on health structures and antibiotic costs evaluated accessibility and affordability. Findings Between Nov 12, 2015, and Feb 1, 2018, 36 285 neonates were enrolled into the main BARNARDS study, of whom 9874 had clinically diagnosed sepsis and 5749 had available antibiotic data. The four most commonly prescribed antibiotic combinations given to 4451 neonates (77·42%) of 5749 were ampicillin–gentamicin, ceftazidime–amikacin, piperacillin–tazobactam–amikacin, and amoxicillin clavulanate–amikacin. This dataset assessed 476 prescriptions for 442 neonates treated with one of these antibiotic combinations with WGS data (all BARNARDS countries were represented in this subset except India). Multiple pathogens were isolated, totalling 457 isolates. Reported mortality was lower for neonates treated with ceftazidime–amikacin than for neonates treated with ampicillin–gentamicin (hazard ratio [adjusted for clinical variables considered potential confounders to outcomes] 0·32, 95% CI 0·14–0·72; p=0·0060). Of 390 Gram-negative isolates, 379 (97·2%) were resistant to ampicillin and 274 (70·3%) were resistant to gentamicin. Susceptibility of Gram-negative isolates to at least one antibiotic in a treatment combination was noted in 111 (28·5%) to ampicillin–gentamicin; 286 (73·3%) to amoxicillin clavulanate–amikacin; 301 (77·2%) to ceftazidime–amikacin; and 312 (80·0%) to piperacillin–tazobactam–amikacin. A probability of target attainment of 80% or more was noted in 26 neonates (33·7% [SD 0·59]) of 78 with ampicillin–gentamicin; 15 (68·0% [3·84]) of 27 with amoxicillin clavulanate–amikacin; 93 (92·7% [0·24]) of 109 with ceftazidime–amikacin; and 70 (85·3% [0·47]) of 76 with piperacillin–tazobactam–amikacin. However, antibiotic and country effects could not be distinguished. Frequency of resistance was recorded most frequently with fosfomycin (in 78 isolates [68·4%] of 114), followed by colistin (55 isolates [57·3%] of 96), and gentamicin (62 isolates [53·0%] of 117). Sites in six of the seven countries (excluding South Africa) stated that the cost of antibiotics would influence treatment of neonatal sepsis