Exponential asymptotics and special theory for optical tunnelling

Mathematically this thesis involves an investigation of the non-self-adjomt Sturm- Liouville problem comprising the differential equation, y"(x) + (A + ex2)y(x) = 0 with a linear homogeneous boundary condition at x = 0 and an “outgoing wave ” condition as x —»• oo, in a number of different settings. The purpose of such an investigation is to obtain an accurate estimate for the imaginary part of the eigenvalue A. Physically, this singular eigenproblem arises m the mathematical modelling of radiation losses m bent fibre-optic waveguides, with the imaginary part of the desired eigenvalue providing a measure of the magnitude of loss due to bending. The imaginary part of the desired eigenvalue turns out to be of much smaller order [0(e _ i —► 0+] than the perturbation of the real part [0 (e),£ —»• 0+]. To overcome the resulting computational difficulties we appeal to the area of exponential asymptotics and become involved m the smoothing of Stokes discontmumties. A number of exponentially improved approximations are required for proper estimation of Im \ and these are obtained either directly from the literature or by application of recent results. The non-self-adjomt nature of the above tunnelling problem results from the unusual condition at infinity. While we investigate this problem directly, using special functions and variational techniques, and obtain an accurate estimate for imaginary part of the desired eigenvalue, an alternative setting is also found. This more abstract approach involves the theory of “resonance poles” in quantum mechanics. We show that under certain conditions, satisfied by the tunnelling problem being considered, the “eigenvalue” of a non-self-adjomt problem corresponds to a pole in the Titchmarsh-Weyl function m(A) for a related but formally self-adjomt problem

Effect of Hydrocortisone on Mortality and Organ Support in Patients With Severe COVID-19: The REMAP-CAP COVID-19 Corticosteroid Domain Randomized Clinical Trial.

Importance: Evidence regarding corticosteroid use for severe coronavirus disease 2019 (COVID-19) is limited. Objective: To determine whether hydrocortisone improves outcome for patients with severe COVID-19. Design, Setting, and Participants: An ongoing adaptive platform trial testing multiple interventions within multiple therapeutic domains, for example, antiviral agents, corticosteroids, or immunoglobulin. Between March 9 and June 17, 2020, 614 adult patients with suspected or confirmed COVID-19 were enrolled and randomized within at least 1 domain following admission to an intensive care unit (ICU) for respiratory or cardiovascular organ support at 121 sites in 8 countries. Of these, 403 were randomized to open-label interventions within the corticosteroid domain. The domain was halted after results from another trial were released. Follow-up ended August 12, 2020. Interventions: The corticosteroid domain randomized participants to a fixed 7-day course of intravenous hydrocortisone (50 mg or 100 mg every 6 hours) (n = 143), a shock-dependent course (50 mg every 6 hours when shock was clinically evident) (n = 152), or no hydrocortisone (n = 108). Main Outcomes and Measures: The primary end point was organ support-free days (days alive and free of ICU-based respiratory or cardiovascular support) within 21 days, where patients who died were assigned -1 day. The primary analysis was a bayesian cumulative logistic model that included all patients enrolled with severe COVID-19, adjusting for age, sex, site, region, time, assignment to interventions within other domains, and domain and intervention eligibility. Superiority was defined as the posterior probability of an odds ratio greater than 1 (threshold for trial conclusion of superiority >99%). Results: After excluding 19 participants who withdrew consent, there were 384 patients (mean age, 60 years; 29% female) randomized to the fixed-dose (n = 137), shock-dependent (n = 146), and no (n = 101) hydrocortisone groups; 379 (99%) completed the study and were included in the analysis. The mean age for the 3 groups ranged between 59.5 and 60.4 years; most patients were male (range, 70.6%-71.5%); mean body mass index ranged between 29.7 and 30.9; and patients receiving mechanical ventilation ranged between 50.0% and 63.5%. For the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively, the median organ support-free days were 0 (IQR, -1 to 15), 0 (IQR, -1 to 13), and 0 (-1 to 11) days (composed of 30%, 26%, and 33% mortality rates and 11.5, 9.5, and 6 median organ support-free days among survivors). The median adjusted odds ratio and bayesian probability of superiority were 1.43 (95% credible interval, 0.91-2.27) and 93% for fixed-dose hydrocortisone, respectively, and were 1.22 (95% credible interval, 0.76-1.94) and 80% for shock-dependent hydrocortisone compared with no hydrocortisone. Serious adverse events were reported in 4 (3%), 5 (3%), and 1 (1%) patients in the fixed-dose, shock-dependent, and no hydrocortisone groups, respectively. Conclusions and Relevance: Among patients with severe COVID-19, treatment with a 7-day fixed-dose course of hydrocortisone or shock-dependent dosing of hydrocortisone, compared with no hydrocortisone, resulted in 93% and 80% probabilities of superiority with regard to the odds of improvement in organ support-free days within 21 days. However, the trial was stopped early and no treatment strategy met prespecified criteria for statistical superiority, precluding definitive conclusions. Trial Registration: ClinicalTrials.gov Identifier: NCT02735707

Exponential asymptotics and special theory for optical tunnelling

Mathematically this thesis involves an investigation of the non-self-adjomt Sturm- Liouville problem comprising the differential equation, y"(x) + (A + ex2)y(x) = 0 with a linear homogeneous boundary condition at x = 0 and an “outgoing wave ” condition as x —»• oo, in a number of different settings. The purpose of such an investigation is to obtain an accurate estimate for the imaginary part of the eigenvalue A. Physically, this singular eigenproblem arises m the mathematical modelling of radiation losses m bent fibre-optic waveguides, with the imaginary part of the desired eigenvalue providing a measure of the magnitude of loss due to bending. The imaginary part of the desired eigenvalue turns out to be of much smaller order [0(e _ i —► 0+] than the perturbation of the real part [0 (e),£ —»• 0+]. To overcome the resulting computational difficulties we appeal to the area of exponential asymptotics and become involved m the smoothing of Stokes discontmumties. A number of exponentially improved approximations are required for proper estimation of Im and these are obtained either directly from the literature or by application of recent results. The non-self-adjomt nature of the above tunnelling problem results from the unusual condition at infinity. While we investigate this problem directly, using special functions and variational techniques, and obtain an accurate estimate for imaginary part of the desired eigenvalue, an alternative setting is also found. This more abstract approach involves the theory of “resonance poles” in quantum mechanics. We show that under certain conditions, satisfied by the tunnelling problem being considered, the “eigenvalue” of a non-self-adjomt problem corresponds to a pole in the Titchmarsh-Weyl function m(A) for a related but formally self-adjomt problem

The impact of Equity Focused Health Impact Assessments on local planning for after hours care to better meet the needs of vulnerable populations: An exploratory study.

This research project looked at the suitability and feasibility of conducting Equity Focused Health Impact Assessments (EFHIAs) on the After Hours Care Plans (AHCPs) of three Medicare Locals in three different states. Given the potential benefits of adopting EFHIA in primary health care planningthis project sought to answer two exploratory research questions regarding the use of EFHIA in the development of Medicare Local AHCPs: 1. Is it effective and feasible to adopt EFHIA in local health planning in order to improve vulnerable group's access to high quality after hours care and to improve equity in services? 2. Is EFHIA an effective mechanism for engaging health consumers and other members of vulnerable groups in local health planning?The research reported in this paper is a project of the Australian Primary Health Care Research Institute which is supported by a grant from the Australian Government Department of Health and Ageing under the Primary Health Care Research Evaluation and Development Strategy