The Mean Value of L(12,χ)L(\tfrac{1}{2},\chi) in the Hyperelliptic Ensemble

We obtain an asymptotic formula for the first moment of quadratic Dirichlet $L$--functions over function fields at the central point $s=\tfrac{1}{2}$. Specifically, we compute the expected value of $L(\tfrac{1}{2},\chi)$ for an ensemble of hyperelliptic curves of genus $g$ over a fixed finite field as $g\rightarrow\infty$. Our approach relies on the use of the analogue of the approximate functional equation for such $L$--functions. The results presented here are the function field analogues of those obtained previously by Jutila in the number-field setting and are consistent with recent general conjectures for the moments of $L$--functions motivated by Random Matrix Theory.Comment: 22 pages, To appear in Journal of Number Theory Volume 132, Issue 12, December 2012, Pages 2793-281

Derivative moments for characteristic polynomials from the CUE

We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried out for finite matrix size and in the limit as the size of the matrices goes to infinity. The latter asymptotic calculation allows us to prove a long-standing conjecture from random matrix theory.Comment: 31 pages, 3 figure

Long COVID and cardiovascular disease: a prospective cohort study

Background Pre-existing cardiovascular disease (CVD) or cardiovascular risk factors have been associated with an increased risk of complications following hospitalisation with COVID-19, but their impact on the rate of recovery following discharge is not known. Objectives To determine whether the rate of patient-perceived recovery following hospitalisation with COVID-19 was affected by the presence of CVD or cardiovascular risk factors. Methods In a multicentre prospective cohort study, patients were recruited following discharge from the hospital with COVID-19 undertaking two comprehensive assessments at 5 months and 12 months. Patients were stratified by the presence of either CVD or cardiovascular risk factors prior to hospitalisation with COVID-19 and compared with controls with neither. Full recovery was determined by the response to a patient-perceived evaluation of full recovery from COVID-19 in the context of physical, physiological and cognitive determinants of health. Results From a total population of 2545 patients (38.8% women), 472 (18.5%) and 1355 (53.2%) had CVD or cardiovascular risk factors, respectively. Compared with controls (n=718), patients with CVD and cardiovascular risk factors were older and more likely to have had severe COVID-19. Full recovery was significantly lower at 12 months in patients with CVD (adjusted OR (aOR) 0.62, 95% CI 0.43 to 0.89) and cardiovascular risk factors (aOR 0.66, 95% CI 0.50 to 0.86). Conclusion Patients with CVD or cardiovascular risk factors had a delayed recovery at 12 months following hospitalisation with COVID-19. Targeted interventions to reduce the impact of COVID-19 in patients with cardiovascular disease remain an unmet need

Cognitive and psychiatric symptom trajectories 2–3 years after hospital admission for COVID-19: a longitudinal, prospective cohort study in the UK

Background COVID-19 is known to be associated with increased risks of cognitive and psychiatric outcomes after the acute phase of disease. We aimed to assess whether these symptoms can emerge or persist more than 1 year after hospitalisation for COVID-19, to identify which early aspects of COVID-19 illness predict longer-term symptoms, and to establish how these symptoms relate to occupational functioning. Methods The Post-hospitalisation COVID-19 study (PHOSP-COVID) is a prospective, longitudinal cohort study of adults (aged ≥18 years) who were hospitalised with a clinical diagnosis of COVID-19 at participating National Health Service hospitals across the UK. In the C-Fog study, a subset of PHOSP-COVID participants who consented to be recontacted for other research were invited to complete a computerised cognitive assessment and clinical scales between 2 years and 3 years after hospital admission. Participants completed eight cognitive tasks, covering eight cognitive domains, from the Cognitron battery, in addition to the 9-item Patient Health Questionnaire for depression, the Generalised Anxiety Disorder 7-item scale, the Functional Assessment of Chronic Illness Therapy Fatigue Scale, and the 20-item Cognitive Change Index (CCI-20) questionnaire to assess subjective cognitive decline. We evaluated how the absolute risks of symptoms evolved between follow-ups at 6 months, 12 months, and 2–3 years, and whether symptoms at 2–3 years were predicted by earlier aspects of COVID-19 illness. Participants completed an occupation change questionnaire to establish whether their occupation or working status had changed and, if so, why. We assessed which symptoms at 2–3 years were associated with occupation change. People with lived experience were involved in the study. Findings 2469 PHOSP-COVID participants were invited to participate in the C-Fog study, and 475 participants (191 [40·2%] females and 284 [59·8%] males; mean age 58·26 [SD 11·13] years) who were discharged from one of 83 hospitals provided data at the 2–3-year follow-up. Participants had worse cognitive scores than would be expected on the basis of their sociodemographic characteristics across all cognitive domains tested (average score 0·71 SD below the mean [IQR 0·16–1·04]; p<0·0001). Most participants reported at least mild depression (263 [74·5%] of 353), anxiety (189 [53·5%] of 353), fatigue (220 [62·3%] of 353), or subjective cognitive decline (184 [52·1%] of 353), and more than a fifth reported severe depression (79 [22·4%] of 353), fatigue (87 [24·6%] of 353), or subjective cognitive decline (88 [24·9%] of 353). Depression, anxiety, and fatigue were worse at 2–3 years than at 6 months or 12 months, with evidence of both worsening of existing symptoms and emergence of new symptoms. Symptoms at 2–3 years were not predicted by the severity of acute COVID-19 illness, but were strongly predicted by the degree of recovery at 6 months (explaining 35·0–48·8% of the variance in anxiety, depression, fatigue, and subjective cognitive decline); by a biocognitive profile linking acutely raised D-dimer relative to C-reactive protein with subjective cognitive deficits at 6 months (explaining 7·0–17·2% of the variance in anxiety, depression, fatigue, and subjective cognitive decline); and by anxiety, depression, fatigue, and subjective cognitive deficit at 6 months. Objective cognitive deficits at 2–3 years were not predicted by any of the factors tested, except for cognitive deficits at 6 months, explaining 10·6% of their variance. 95 of 353 participants (26·9% [95% CI 22·6–31·8]) reported occupational change, with poor health being the most common reason for this change. Occupation change was strongly and specifically associated with objective cognitive deficits (odds ratio [OR] 1·51 [95% CI 1·04–2·22] for every SD decrease in overall cognitive score) and subjective cognitive decline (OR 1·54 [1·21–1·98] for every point increase in CCI-20). Interpretation Psychiatric and cognitive symptoms appear to increase over the first 2–3 years post-hospitalisation due to both worsening of symptoms already present at 6 months and emergence of new symptoms. New symptoms occur mostly in people with other symptoms already present at 6 months. Early identification and management of symptoms might therefore be an effective strategy to prevent later onset of a complex syndrome. Occupation change is common and associated mainly with objective and subjective cognitive deficits. Interventions to promote cognitive recovery or to prevent cognitive decline are therefore needed to limit the functional and economic impacts of COVID-19. Funding National Institute for Health and Care Research Oxford Health Biomedical Research Centre, Wolfson Foundation, MQ Mental Health Research, MRC-UK Research and Innovation, and National Institute for Health and Care Research

Multiorgan MRI findings after hospitalisation with COVID-19 in the UK (C-MORE): a prospective, multicentre, observational cohort study

Introduction: The multiorgan impact of moderate to severe coronavirus infections in the post-acute phase is still poorly understood. We aimed to evaluate the excess burden of multiorgan abnormalities after hospitalisation with COVID-19, evaluate their determinants, and explore associations with patient-related outcome measures. Methods: In a prospective, UK-wide, multicentre MRI follow-up study (C-MORE), adults (aged ≥18 years) discharged from hospital following COVID-19 who were included in Tier 2 of the Post-hospitalisation COVID-19 study (PHOSP-COVID) and contemporary controls with no evidence of previous COVID-19 (SARS-CoV-2 nucleocapsid antibody negative) underwent multiorgan MRI (lungs, heart, brain, liver, and kidneys) with quantitative and qualitative assessment of images and clinical adjudication when relevant. Individuals with end-stage renal failure or contraindications to MRI were excluded. Participants also underwent detailed recording of symptoms, and physiological and biochemical tests. The primary outcome was the excess burden of multiorgan abnormalities (two or more organs) relative to controls, with further adjustments for potential confounders. The C-MORE study is ongoing and is registered with ClinicalTrials.gov, NCT04510025. Findings: Of 2710 participants in Tier 2 of PHOSP-COVID, 531 were recruited across 13 UK-wide C-MORE sites. After exclusions, 259 C-MORE patients (mean age 57 years [SD 12]; 158 [61%] male and 101 [39%] female) who were discharged from hospital with PCR-confirmed or clinically diagnosed COVID-19 between March 1, 2020, and Nov 1, 2021, and 52 non-COVID-19 controls from the community (mean age 49 years [SD 14]; 30 [58%] male and 22 [42%] female) were included in the analysis. Patients were assessed at a median of 5·0 months (IQR 4·2–6·3) after hospital discharge. Compared with non-COVID-19 controls, patients were older, living with more obesity, and had more comorbidities. Multiorgan abnormalities on MRI were more frequent in patients than in controls (157 [61%] of 259 vs 14 [27%] of 52; p5mg/L, OR 3·55 [1·23–11·88]; padjusted=0·025) than those without multiorgan abnormalities. Presence of lung MRI abnormalities was associated with a two-fold higher risk of chest tightness, and multiorgan MRI abnormalities were associated with severe and very severe persistent physical and mental health impairment (PHOSP-COVID symptom clusters) after hospitalisation. Interpretation: After hospitalisation for COVID-19, people are at risk of multiorgan abnormalities in the medium term. Our findings emphasise the need for proactive multidisciplinary care pathways, with the potential for imaging to guide surveillance frequency and therapeutic stratification. Funding: UK Research and Innovation and National Institute for Health Research

Post-acute COVID-19 neuropsychiatric symptoms are not associated with ongoing nervous system injury

A proportion of patients infected with severe acute respiratory syndrome coronavirus 2 experience a range of neuropsychiatric symptoms months after infection, including cognitive deficits, depression and anxiety. The mechanisms underpinning such symptoms remain elusive. Recent research has demonstrated that nervous system injury can occur during COVID-19. Whether ongoing neural injury in the months after COVID-19 accounts for the ongoing or emergent neuropsychiatric symptoms is unclear. Within a large prospective cohort study of adult survivors who were hospitalized for severe acute respiratory syndrome coronavirus 2 infection, we analysed plasma markers of nervous system injury and astrocytic activation, measured 6 months post-infection: neurofilament light, glial fibrillary acidic protein and total tau protein. We assessed whether these markers were associated with the severity of the acute COVID-19 illness and with post-acute neuropsychiatric symptoms (as measured by the Patient Health Questionnaire for depression, the General Anxiety Disorder assessment for anxiety, the Montreal Cognitive Assessment for objective cognitive deficit and the cognitive items of the Patient Symptom Questionnaire for subjective cognitive deficit) at 6 months and 1 year post-hospital discharge from COVID-19. No robust associations were found between markers of nervous system injury and severity of acute COVID-19 (except for an association of small effect size between duration of admission and neurofilament light) nor with post-acute neuropsychiatric symptoms. These results suggest that ongoing neuropsychiatric symptoms are not due to ongoing neural injury

Large-scale phenotyping of patients with long COVID post-hospitalization reveals mechanistic subtypes of disease

One in ten severe acute respiratory syndrome coronavirus 2 infections result in prolonged symptoms termed long coronavirus disease (COVID), yet disease phenotypes and mechanisms are poorly understood1. Here we profiled 368 plasma proteins in 657 participants ≥3 months following hospitalization. Of these, 426 had at least one long COVID symptom and 233 had fully recovered. Elevated markers of myeloid inflammation and complement activation were associated with long COVID. IL-1R2, MATN2 and COLEC12 were associated with cardiorespiratory symptoms, fatigue and anxiety/depression; MATN2, CSF3 and C1QA were elevated in gastrointestinal symptoms and C1QA was elevated in cognitive impairment. Additional markers of alterations in nerve tissue repair (SPON-1 and NFASC) were elevated in those with cognitive impairment and SCG3, suggestive of brain–gut axis disturbance, was elevated in gastrointestinal symptoms. Severe acute respiratory syndrome coronavirus 2-specific immunoglobulin G (IgG) was persistently elevated in some individuals with long COVID, but virus was not detected in sputum. Analysis of inflammatory markers in nasal fluids showed no association with symptoms. Our study aimed to understand inflammatory processes that underlie long COVID and was not designed for biomarker discovery. Our findings suggest that specific inflammatory pathways related to tissue damage are implicated in subtypes of long COVID, which might be targeted in future therapeutic trials