Health consequences that persist beyond the acute infection phase of COVID-19, termed post-COVID-19 condition (also commonly known as long COVID), vary widely and represent a growing global health... Show moreHealth consequences that persist beyond the acute infection phase of COVID-19, termed post-COVID-19 condition (also commonly known as long COVID), vary widely and represent a growing global health challenge. Research on post-COVID-19 condition is expanding but, at present, no agreement exists on the health outcomes that should be measured in people living with the condition. To address this gap, we conducted an international consensus study, which included a comprehensive literature review and classification of outcomes for post-COVID-19 condition that informed a two-round online modified Delphi process followed by an online consensus meeting to finalise the core outcome set (COS). 1535 participants from 71 countries were involved, with 1148 individuals participating in both Delphi rounds. Eleven outcomes achieved consensus for inclusion in the final COS: fatigue; pain; post-exertion symptoms; work or occupational and study changes; survival; and functioning, symptoms, and conditions for each of cardiovascular, respiratory, nervous system, cognitive, mental health, and physical outcomes. Recovery was included a priori because it was a relevant outcome that was part of a previously published COS on COVID-19. The next step in this COS development exercise will be to establish the instruments that are most appropriate to measure these core outcomes. This international consensus-based COS should provide a framework for standardised assessment of adults with post-COVID-19 condition, aimed at facilitating clinical care and research worldwide. Show less
Background A substantial portion of people with COVID-19 subsequently experience lasting symptoms including fatigue, shortness of breath, and neurological complaints such as cognitive dysfunction... Show moreBackground A substantial portion of people with COVID-19 subsequently experience lasting symptoms including fatigue, shortness of breath, and neurological complaints such as cognitive dysfunction many months after acute infection. Emerging evidence suggests that this condition, commonly referred to as long COVID but also known as post-acute sequelae of SARS-CoV-2 infection (PASC) or post-COVID-19 condition, could become a significant global health burden. Main text While the number of studies investigating the post-COVID-19 condition is increasing, there is no agreement on how this new disease should be defined and diagnosed in clinical practice and what relevant outcomes to measure. There is an urgent need to optimise and standardise outcome measures for this important patient group both for clinical services and for research and to allow comparing and pooling of data. Conclusions A Core Outcome Set for post-COVID-19 condition should be developed in the shortest time frame possible, for improvement in data quality, harmonisation, and comparability between different geographical locations. We call for a global initiative, involving all relevant partners, including, but not limited to, healthcare professionals, researchers, methodologists, patients, and caregivers. We urge coordinated actions aiming to develop a Core Outcome Set (COS) for post-COVID-19 condition in both the adult and paediatric populations. Show less
We prove that a formula for the 'pluricanonical' double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a cycle... Show moreWe prove that a formula for the 'pluricanonical' double ramification cycle proposed by Janda, Pandharipande, Pixton, Zvonkine, and the second-named author is in fact the class of a cycle constructed geometrically by the first-named author. Our proof proceeds by a detailed explicit analysis of the deformation theory of the double ramification cycle, both to first and to higher order. Show less
