In this paper, we prove: (1) for any closed contact three-manifold with a $C^\infty$-generic contact form, the union of periodic Reeb orbits is dense; (2) for any closed surface with a $C^\infty$-generic Riemannian metric, the union of closed geodesics is dense. The key observation is a $C^\infty$-closing lemma for three-dimensional Reeb flows, which follows from the fact that the embedded contact homology (ECH) spectral invariants recover the volume.

Since December 2019, a novel coronavirus (severe acute respiratory syndrome‐coronavirus 2 (SARS‐CoV‐2)) infection has been rapidly spreading worldwide and causing the respiratory illness, coronavirus disease 2019 (COVID‐19). The antiretroviral drug favipiravir (FPV) has been experimentally used for COVID‐19 treatment since March 2020 in Japan. However, the pharmacokinetics of FPV in critically ill patients is unknown. We measured the serum concentration of FPV using high‐performance liquid chromatography in patients with severe COVID‐19 who were admitted to the intensive care unit and placed on mechanical ventilation. The patients were administered 1,600 mg of FPV twice daily on day 1, followed by 600 mg twice daily from day 2 to day 5 (or more if needed). Suspensions of FPV tablets were administered through a nasogastric tube. Seven patients were enrolled in this study. Forty‐nine blood samples were obtained from the eligible patients to evaluate FPV concentration. The FPV trough (after 8–12 hours) concentrations of most samples were lower than the lower limit of quantification (1 µg/mL) and half‐maximal effective concentration (9.7 µg/mL) against SARS‐CoV‐2 previously tested in vitro. FPV trough concentration in critically ill patients was much lower than that of healthy subjects in a previous clinical trial, which is a cause for great concern. Further study is required to determine the optimal strategy for treatment of patients with severe COVID‐19.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books

The antiretroviral drug favipiravir (FPV) inhibits RNA‐dependent RNA polymerase. It has been developed for the treatment of the novel coronavirus (severe acute respiratory syndrome coronavirus 2) infection disease, coronavirus disease 2019 (COVID‐19). However, its pharmacokinetics in patients with COVID‐19 is poorly understood. In this study, we measured FPV serum concentration by liquid chromatography–tandem mass spectrometry and conducted population pharmacokinetic analysis. A total of 39 patients were enrolled in the study: 33 were administered FPV 1600 mg twice daily (b.i.d.) on the first day followed by 600 mg b.i.d., and 6 were administered FPV 1800 mg b.i.d. on the first day followed by 800 mg or 600 mg b.i.d. The median age was 68 years (range, 27–89 years), 31 (79.5%) patients were men, median body surface area (BSA) was 1.72 m² (range, 1.11–2.2 m²), and 10 (25.6%) patients required invasive mechanical ventilation (IMV) at the start of FPV. A total of 204 serum concentrations were available for pharmacokinetic analysis. A one‐compartment model with first‐order elimination was used to describe the pharmacokinetics. The estimated mean clearance/bioavailability (CL/F) and distribution volume/bioavailability (V/F) were 5.11 L/h and 41.6 L, respectively. Covariate analysis revealed that CL/F was significantly related to dosage, IMV use, and BSA. A simulation study showed that the 1600 mg/600 mg b.i.d. regimen was insufficient for the treatment of COVID‐19 targeting the 50% effective concentration (9.7 µg/mL), especially in patients with larger BSA and/or IMV. A higher FPV dosage is required for COVID‐19, but dose‐dependent nonlinear pharmacokinetics may cause an unexpected significant pharmacokinetic change and drug toxicity. Further studies are warranted to explore the optimal FPV regimen.

The aim of this article is to define a chain level refinement of the Batalin–Vilkovisky (BV) algebra structure on the homology of the free loop space of a closed, oriented |$C^\infty$|-manifold. For this purpose, we define a (nonsymmetric) cyclic dg operad which consists of “de Rham chains” of free loops with marked points. A notion of de Rham chains, which is a certain hybrid of the notions of singular chains and differential forms, is a key ingredient in our construction. Combined with a generalization of cyclic Deligne’s conjecture, this dg operad produces a chain model of the free loop space which admits an action of a chain model of the framed little disks operad, recovering the string topology BV algebra structure on the homology level.

International Press of Boston - publishers of scholarly mathematical and scientific journals and books