Steady and Stable: Numerical Investigations of Nonlinear Partial Differential Equations

Excerpt: Mathematics is a language which can describe patterns in everyday life as well as abstract concepts existing only in our minds. Patterns exist in data, functions, and sets constructed around a common theme, but the most tangible patterns are visual. Visual demonstrations can help undergraduate students connect to abstract concepts in advanced mathematical courses. The study of partial differential equations, in particular, benefits from numerical analysis and simulation

Closed Strings with Low Harmonics and Kinks

Low-harmonic formulas for closed relativistic strings are given. General parametrizations are presented for the addition of second- and third-harmonic waves to the fundamental wave. The method of determination of the parametrizations is based upon a product representation found for the finite Fourier series of string motion in which the constraints are automatically satisfied. The construction of strings with kinks is discussed, including examples. A procedure is laid out for the representation of kinks that arise from self-intersection, and subsequent intercommutation, for harmonically parametrized cosmic strings.Comment: 39, CWRUTH-93-

Self-consistent solution of the Schwinger-Dyson equations for the nucleon and meson propagators

The Schwinger-Dyson equations for the nucleon and meson propagators are solved self-consistently in an approximation that goes beyond the Hartree-Fock approximation. The traditional approach consists in solving the nucleon Schwinger-Dyson equation with bare meson propagators and bare meson-nucleon vertices; the corrections to the meson propagators are calculated using the bare nucleon propagator and bare nucleon-meson vertices. It is known that such an approximation scheme produces the appearance of ghost poles in the propagators. In this paper the coupled system of Schwinger-Dyson equations for the nucleon and the meson propagators are solved self-consistently including vertex corrections. The interplay of self-consistency and vertex corrections on the ghosts problem is investigated. It is found that the self-consistency does not affect significantly the spectral properties of the propagators. In particular, it does not affect the appearance of the ghost poles in the propagators.Comment: REVTEX, 7 figures (available upon request), IFT-P.037/93, DOE/ER/40427-12-N9

Masses of ground and excited-state hadrons

We present the first Dyson-Schwinger equation calculation of the light hadron spectrum that simultaneously correlates the masses of meson and baryon ground- and excited-states within a single framework. At the core of our analysis is a symmetry-preserving treatment of a vector-vector contact interaction. In comparison with relevant quantities the root-mean-square-relative-error/degree-of freedom is 13%. Notable amongst our results is agreement between the computed baryon masses and the bare masses employed in modern dynamical coupled-channels models of pion-nucleon reactions. Our analysis provides insight into numerous aspects of baryon structure; e.g., relationships between the nucleon and Delta masses and those of the dressed-quark and diquark correlations they contain.Comment: 25 pages, 7 figures, 4 table

Guidelines for Modeling and Reporting Health Effects of Climate Change Mitigation Actions

Background: Modeling suggests that climate change mitigation actions can have substantial human health benefits that accrue quickly and locally. Documenting the benefits can help drive more ambitious and health-protective climate change mitigation actions; however, documenting the adverse health effects can help to avoid them. Estimating the health effects of mitigation (HEM) actions can help policy makers prioritize investments based not only on mitigation potential but also on expected health benefits. To date, however, the wide range of incompatible approaches taken to developing and reporting HEM estimates has limited their comparability and usefulness to policymakers. Objective: The objective of this effort was to generate guidance for modeling studies on scoping, estimating, and reporting population health effects from climate change mitigation actions. Methods: An expert panel of HEM researchers was recruited to participate in developing guidance for conducting HEM studies. The primary literature and a synthesis of HEM studies were provided to the panel. Panel members then participated in a modified Delphi exercise to identify areas of consensus regarding HEM estimation. Finally, the panel met to review and discuss consensus findings, resolve remaining differences, and generate guidance regarding conducting HEM studies. Results: The panel generated a checklist of recommendations regarding stakeholder engagement: HEM modeling, including model structure, scope and scale, demographics, time horizons, counterfactuals, health response functions, and metrics; parameterization and reporting; approaches to uncertainty and sensitivity analysis; accounting for policy uptake; and discounting. Discussion: This checklist provides guidance for conducting and reporting HEM estimates to make them more comparable and useful for policymakers. Harmonization of HEM estimates has the potential to lead to advances in and improved synthesis of policy-relevant research that can inform evidence-based decision making and practice

Global, regional, and national cancer incidence, mortality, years of life lost, years lived with disability, and disability-adjusted life-years for 32 cancer groups, 1990 to 2015: A Systematic Analysis for the Global Burden of Disease Study Global Burden of Disease Cancer Collaboration

IMPORTANCE: Cancer is the second leading cause of death worldwide. Current estimates on the burden of cancer are needed for cancer control planning. OBJECTIVE: To estimate mortality, incidence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs) for 32 cancers in 195 countries and territories from 1990 to 2015. EVIDENCE REVIEW: Cancer mortality was estimated using vital registration system data, cancer registry incidence data (transformed to mortality estimates using separately estimated mortality to incidence [MI] ratios), and verbal autopsy data. Cancer incidence was calculated by dividing mortality estimates through the modeled MI ratios. To calculate cancer prevalence, MI ratios were used to model survival. To calculate YLDs, prevalence estimates were multiplied by disability weights. The YLLs were estimated by multiplying age-specific cancer deaths by the reference life expectancy. DALYs were estimated as the sum of YLDs and YLLs. A sociodemographic index (SDI) was created for each location based on income per capita, educational attainment, and fertility. Countries were categorized by SDI quintiles to summarize results. FINDINGS: In 2015, there were 17.5 million cancer cases worldwide and 8.7 million deaths. Between 2005 and 2015, cancer cases increased by 33%, with population aging contributing 16%, population growth 13%, and changes in age-specific rates contributing 4%. For men, the most common cancer globally was prostate cancer (1.6 million cases). Tracheal, bronchus, and lung cancer was the leading cause of cancer deaths and DALYs in men (1.2 million deaths and 25.9 million DALYs). For women, the most common cancer was breast cancer (2.4 million cases). Breast cancer was also the leading cause of cancer deaths and DALYs for women (523 000 deaths and 15.1 million DALYs). Overall, cancer caused 208.3 million DALYs worldwide in 2015 for both sexes combined. Between 2005 and 2015, age-standardized incidence rates for all cancers combined increased in 174 of 195 countries or territories. Age-standardized death rates (ASDRs) for all cancers combined decreased within that timeframe in 140 of 195 countries or territories. Countries with an increase in the ASDR due to all cancers were largely located on the African continent. Of all cancers, deaths between 2005 and 2015 decreased significantly for Hodgkin lymphoma (-6.1% [95% uncertainty interval (UI), -10.6% to -1.3%]). The number of deaths also decreased for esophageal cancer, stomach cancer, and chronic myeloid leukemia, although these results were not statistically significant. CONCLUSION AND RELEVANCE: As part of the epidemiological transition, cancer incidence is expected to increase in the future, further straining limited health care resources. Appropriate allocation of resources for cancer prevention, early diagnosis, and curative and palliative care requires detailed knowledge of the local burden of cancer. The GBD 2015 study results demonstrate that progress is possible in the war against cancer. However, the major findings also highlight an unmet need for cancer prevention efforts, including tobacco control, vaccination, and the promotion of physical activity and a healthy diet

SARS-CoV-2-specific nasal IgA wanes 9 months after hospitalisation with COVID-19 and is not induced by subsequent vaccination

BACKGROUND: Most studies of immunity to SARS-CoV-2 focus on circulating antibody, giving limited insights into mucosal defences that prevent viral replication and onward transmission. We studied nasal and plasma antibody responses one year after hospitalisation for COVID-19, including a period when SARS-CoV-2 vaccination was introduced. METHODS: In this follow up study, plasma and nasosorption samples were prospectively collected from 446 adults hospitalised for COVID-19 between February 2020 and March 2021 via the ISARIC4C and PHOSP-COVID consortia. IgA and IgG responses to NP and S of ancestral SARS-CoV-2, Delta and Omicron (BA.1) variants were measured by electrochemiluminescence and compared with plasma neutralisation data. FINDINGS: Strong and consistent nasal anti-NP and anti-S IgA responses were demonstrated, which remained elevated for nine months (p < 0.0001). Nasal and plasma anti-S IgG remained elevated for at least 12 months (p < 0.0001) with plasma neutralising titres that were raised against all variants compared to controls (p < 0.0001). Of 323 with complete data, 307 were vaccinated between 6 and 12 months; coinciding with rises in nasal and plasma IgA and IgG anti-S titres for all SARS-CoV-2 variants, although the change in nasal IgA was minimal (1.46-fold change after 10 months, p = 0.011) and the median remained below the positive threshold determined by pre-pandemic controls. Samples 12 months after admission showed no association between nasal IgA and plasma IgG anti-S responses (R = 0.05, p = 0.18), indicating that nasal IgA responses are distinct from those in plasma and minimally boosted by vaccination. INTERPRETATION: The decline in nasal IgA responses 9 months after infection and minimal impact of subsequent vaccination may explain the lack of long-lasting nasal defence against reinfection and the limited effects of vaccination on transmission. These findings highlight the need to develop vaccines that enhance nasal immunity. FUNDING: This study has been supported by ISARIC4C and PHOSP-COVID consortia. ISARIC4C is supported by grants from the National Institute for Health and Care Research and the Medical Research Council. Liverpool Experimental Cancer Medicine Centre provided infrastructure support for this research. The PHOSP-COVD study is jointly funded by UK Research and Innovation and National Institute of Health and Care Research. The funders were not involved in the study design, interpretation of data or the writing of this manuscript

Accelarated immune ageing is associated with COVID-19 disease severity

Background The striking increase in COVID-19 severity in older adults provides a clear example of immunesenescence, the age-related remodelling of the immune system. To better characterise the association between convalescent immunesenescence and acute disease severity, we determined the immune phenotype of COVID-19 survivors and non-infected controls. Results We performed detailed immune phenotyping of peripheral blood mononuclear cells isolated from 103 COVID-19 survivors 3–5 months post recovery who were classified as having had severe (n = 56; age 53.12 ± 11.30 years), moderate (n = 32; age 52.28 ± 11.43 years) or mild (n = 15; age 49.67 ± 7.30 years) disease and compared with age and sex-matched healthy adults (n = 59; age 50.49 ± 10.68 years). We assessed a broad range of immune cell phenotypes to generate a composite score, IMM-AGE, to determine the degree of immune senescence. We found increased immunesenescence features in severe COVID-19 survivors compared to controls including: a reduced frequency and number of naïve CD4 and CD8 T cells (p < 0.0001); increased frequency of EMRA CD4 (p < 0.003) and CD8 T cells (p < 0.001); a higher frequency (p < 0.0001) and absolute numbers (p < 0.001) of CD28−ve CD57+ve senescent CD4 and CD8 T cells; higher frequency (p < 0.003) and absolute numbers (p < 0.02) of PD-1 expressing exhausted CD8 T cells; a two-fold increase in Th17 polarisation (p < 0.0001); higher frequency of memory B cells (p < 0.001) and increased frequency (p < 0.0001) and numbers (p < 0.001) of CD57+ve senescent NK cells. As a result, the IMM-AGE score was significantly higher in severe COVID-19 survivors than in controls (p < 0.001). Few differences were seen for those with moderate disease and none for mild disease. Regression analysis revealed the only pre-existing variable influencing the IMM-AGE score was South Asian ethnicity ( = 0.174, p = 0.043), with a major influence being disease severity ( = 0.188, p = 0.01). Conclusions Our analyses reveal a state of enhanced immune ageing in survivors of severe COVID-19 and suggest this could be related to SARS-Cov-2 infection. Our data support the rationale for trials of anti-immune ageing interventions for improving clinical outcomes in these patients with severe disease

Effects of sleep disturbance on dyspnoea and impaired lung function following hospital admission due to COVID-19 in the UK: a prospective multicentre cohort study

Background: Sleep disturbance is common following hospital admission both for COVID-19 and other causes. The clinical associations of this for recovery after hospital admission are poorly understood despite sleep disturbance contributing to morbidity in other scenarios. We aimed to investigate the prevalence and nature of sleep disturbance after discharge following hospital admission for COVID-19 and to assess whether this was associated with dyspnoea. Methods: CircCOVID was a prospective multicentre cohort substudy designed to investigate the effects of circadian disruption and sleep disturbance on recovery after COVID-19 in a cohort of participants aged 18 years or older, admitted to hospital for COVID-19 in the UK, and discharged between March, 2020, and October, 2021. Participants were recruited from the Post-hospitalisation COVID-19 study (PHOSP-COVID). Follow-up data were collected at two timepoints: an early time point 2–7 months after hospital discharge and a later time point 10–14 months after hospital discharge. Sleep quality was assessed subjectively using the Pittsburgh Sleep Quality Index questionnaire and a numerical rating scale. Sleep quality was also assessed with an accelerometer worn on the wrist (actigraphy) for 14 days. Participants were also clinically phenotyped, including assessment of symptoms (ie, anxiety [Generalised Anxiety Disorder 7-item scale questionnaire], muscle function [SARC-F questionnaire], dyspnoea [Dyspnoea-12 questionnaire] and measurement of lung function), at the early timepoint after discharge. Actigraphy results were also compared to a matched UK Biobank cohort (non-hospitalised individuals and recently hospitalised individuals). Multivariable linear regression was used to define associations of sleep disturbance with the primary outcome of breathlessness and the other clinical symptoms. PHOSP-COVID is registered on the ISRCTN Registry (ISRCTN10980107). Findings: 2320 of 2468 participants in the PHOSP-COVID study attended an early timepoint research visit a median of 5 months (IQR 4–6) following discharge from 83 hospitals in the UK. Data for sleep quality were assessed by subjective measures (the Pittsburgh Sleep Quality Index questionnaire and the numerical rating scale) for 638 participants at the early time point. Sleep quality was also assessed using device-based measures (actigraphy) a median of 7 months (IQR 5–8 months) after discharge from hospital for 729 participants. After discharge from hospital, the majority (396 [62%] of 638) of participants who had been admitted to hospital for COVID-19 reported poor sleep quality in response to the Pittsburgh Sleep Quality Index questionnaire. A comparable proportion (338 [53%] of 638) of participants felt their sleep quality had deteriorated following discharge after COVID-19 admission, as assessed by the numerical rating scale. Device-based measurements were compared to an age-matched, sex-matched, BMI-matched, and time from discharge-matched UK Biobank cohort who had recently been admitted to hospital. Compared to the recently hospitalised matched UK Biobank cohort, participants in our study slept on average 65 min (95% CI 59 to 71) longer, had a lower sleep regularity index (–19%; 95% CI –20 to –16), and a lower sleep efficiency (3·83 percentage points; 95% CI 3·40 to 4·26). Similar results were obtained when comparisons were made with the non-hospitalised UK Biobank cohort. Overall sleep quality (unadjusted effect estimate 3·94; 95% CI 2·78 to 5·10), deterioration in sleep quality following hospital admission (3·00; 1·82 to 4·28), and sleep regularity (4·38; 2·10 to 6·65) were associated with higher dyspnoea scores. Poor sleep quality, deterioration in sleep quality, and sleep regularity were also associated with impaired lung function, as assessed by forced vital capacity. Depending on the sleep metric, anxiety mediated 18–39% of the effect of sleep disturbance on dyspnoea, while muscle weakness mediated 27–41% of this effect. Interpretation: Sleep disturbance following hospital admission for COVID-19 is associated with dyspnoea, anxiety, and muscle weakness. Due to the association with multiple symptoms, targeting sleep disturbance might be beneficial in treating the post-COVID-19 condition. Funding: UK Research and Innovation, National Institute for Health Research, and Engineering and Physical Sciences Research Council

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