First-return maps of Birkhoff sections of the geodesic flow

This paper compares different pseudo-Anosov maps coming from different Birkhoff sections of a given flow. More precisely, given a hyperbolic surface and a collection of periodic geodesics on it, we study those Birkhoff sections for the geodesic flow on the unit bundle to the surface bounded by the collection. We show that there is a canonical identification of all those surfaces, and that the first-return maps induced by the flow can all be expressed as a composition of negative Dehn twists along the same family of curves: only the order depends on the choice of a particular surface

Oriented Birkhoff sections of Anosov flows

This paper gives 3 different proofs (independently obtained by the 3 authors) of the following fact: given an Anosov flow on an oriented 3 manifold, the existence of a positive Birkhoff section is equivalent to the fact that the flow is $\mathbb{R}$-covered positively twisted.Comment: 40 pages, 6 figure

Trends in Fatal Poisoning Among Drug Users in France From 2011 to 2021

Importance The DRAMES (Décès en Relation avec l’Abus de Médicaments Et de Substances) register is a database of drug-related deaths with the aim of identifying the psychoactive substances associated with and estimating the trends in these deaths. Our novel approach is based on the collection of data on all deaths for which toxicology experts have performed analyses. Objective To describe drug-related deaths in France and report trends over an 11-year period. Design, Setting, and Participants This case series used a national register to assess 4460 drug-related deaths that occurred from 2011 to 2021 in France. Data analyses were performed from January 1, 2012, to December 31, 2022. Main Outcomes and Measures Demographic characteristics; medical and substance abuse history; forensic autopsy findings; and toxicology reports. Results Among the 4460 deceased individuals (mean [SD] age, 37.8 [10.5] years), the mortality rate was highest among men (sex ratio, 4.4:1). Of the deaths involving a single or predominant drug, the legal substitution product, methadone, was the leading cause of death during the entire study period, ahead of heroin—44.7% and 35.9% for methadone vs 15.8% and 21.8% for heroin in 2011 and 2021, respectively. Between 2011 and 2021, most of the drug-related deaths shifted from licit to illicit drugs, and statistically significant variations were found for buprenorphine, cocaine, heroin, methadone, and other licit opioids. Deaths related to polydrug use increased from 23.2% in 2011 to 30.6% in 2021. In this context, opioids remained associated with most deaths, with at least 1 opioid being involved in approximately 9 of 10 cases (85.9%) in 2021. However, the main trend was the dramatic increase in drug combinations with cocaine, from less than one-third of cases in 2011 (30.8%) to more than half in 2021 (57.8%). Conclusions and Relevance This case series assessment of 4460 drug-related deaths found that opioids used alone or in combination were the main contributor to drug-related deaths, despite having a lower prevalence than other drugs. This finding is similar to that of other countries; however, in France licit methadone was the leading cause of opioid-related deaths (ahead of heroin) during the study period. Deaths associated with use of cannabis, new psychoactive substances, and stimulants (including amphetamine-type stimulants and cocaine, especially in combination) have increased and should be closely monitored

Impact on disease mortality of clinical, biological, and virological characteristics at hospital admission and overtime in COVID‐19 patients

International audienc