For any abelian group $A$, we prove an asymptotic formula for the number of $A$-extensions $K/\mathbb {Q}$ of bounded discriminant such that the associated norm one torus $R_{K/\mathbb {Q}}^1 \mathbb {G}_m$ satisfies weak approximation. We are also able to produce new results on the Hasse norm principle and to provide new explicit values for the leading constant in some instances of Malle's conjecture.

Glucagon-like peptide-1 receptor agonists are effective for treating obesity, but the high cost of these medications endangers the financial viability of our health care system. To ensure that these drugs are available to Medicare beneficiaries, pharmaceutical manufacturers must lower their prices.

The ASACUSA (atomic spectroscopy and collisions using slow antiprotons) Cusp experiment requires the production of dense positron plasmas with a high repetition rate to produce a beam of antihydrogen. In this work, details of the positron production apparatus used for the first observation of the antihydrogen beam, and subsequent measurements, are described in detail. This apparatus replaced the previous compact trap design resulting in an improvement in the positron accumulation rate by a factor of $52\pm 3$.

Recently, Congress has focused on reforms to address pharmacy benefit managers’ (PBMs) role in high drug prices for patients. Congress must not excessively restrict PBMs’ ability to negotiate with manufacturers; alternatively, reforms could be paired with other policies that address the high prices of brand-name drugs.

Thanks to the isomorphism between the drift-Poisson and Euler equations, inviscid two-dimensional fluid experiments can be performed in magnetized, single-component plasmas in Penning–Malmberg traps. Within this analogy, a trapped electron plasma column is equivalent to a two-dimensional vortex. Here, we focus our attention on the generation of V-states, i.e. $l$-fold symmetric rotating vorticity patches where the deformation with respect to the circular cross-section has reached the nonlinear regime. We detail a linear theoretical analysis and devise an experimental routine to generate V-states through the precise excitation of single Kelvin–Helmholtz perturbations in a magnetized electron plasma. This technique makes use of suitable multipolar rotating electric fields, which are shown to be able to select the desired wavemode. In particular, with rotating fields, a hardware limitation in the highest accessible mode is removed and nonlinear Kelvin–Helmholtz waves of generic order $l$ can be attained, which pave the way for further investigations on the evolution and stability properties of V-states. Systematic experimental results for the selective mode growth in the linear and nonlinear regimes up to saturation and collapse are discussed.

Methods for reducing the radius, temperature and space charge of a non-neutral plasma are usually reported for conditions which approximate an ideal Penning Malmberg trap. Here, we show that (i) similar methods are still effective under surprisingly adverse circumstances: we perform strong drive regime (SDR) compression and SDREVC in a strong magnetic mirror field using only 3 out of 4 rotating wall petals. In addition, we demonstrate (ii) an alternative to SDREVC, using e-kick instead of evaporative cooling (EVC) and (iii) an upper limit for how much plasma can be cooled to $T<20\ \mathrm {K}$ using EVC. This limit depends on the space charge, not on the number of particles or the plasma density.

The European Commission’s proposal to address antimicrobial resistance using transferable exclusivity vouchers (TEVs) is fundamentally flawed. European policymakers and regulators should consider alternatives, such as better funding for basic and clinical research, use of advance market commitments funded by a pay-or-play tax, or enacting an EU Fund for Antibiotic Development.

Interventional cardiology plays a key role in the diagnosis and management of patients with functionally univentricular physiology after the various stages of surgical palliation. The interventions performed are widely variable in type, including angioplasty of stenotic vessels and implantation of stents in stenotic vessels; closure of defects such as collaterals, leaks in baffles, and fenestrations; creation of fenestration; and more. In the setting of venous hypertension associated with stenosis at the Fontan baffle, conduit, or pulmonary arteries, stent implantation is often preferred, as the aim is to eliminate completely the narrowing, given that relatively mild stenosis can have a significant detrimental hemodynamic effect in patients with functionally univentricular circulation. The procedure is highly successful. In patients who fail after Fontan procedure, creation of a fenestration is often performed, with variable technique depending on the underlying anatomic substrate. To increase chances of patency of the fenestration, implantation of a stent is often required, particularly in the setting of an extracardiac conduit. For those patients with cyanosis and favorable Fontan hemodynamics, closure of the fenestration is performed using atrial septal occluder devices with high success rate. Coils compatible with magnetic resonance imaging are used widely to treat collateral vessels, although on occasion other specific embolization tools are required, such as particles or vascular plugs. Postoperative arch obstruction is successfully managed with angioplasty at a younger age, while implantation of a stent in the aorta is reserved for older patients. Specifics of these interventional procedures as applied to the population of patients with functionally univentricular hearts are described in this manuscript.