A Simple Geometric Representative for μ\mu of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.Comment: Updated 2018 to published version. 8 pages, AmS-TeX, no figure

The causes and consequences of seasonal variation in COPD exacerbations

Gavin C Donaldson, Jadwiga A Wedzicha Airways Disease Section, National Heart and Lung Institute, Imperial College London, London, UK Abstract: The time of year when patients experience exacerbations of chronic obstructive pulmonary disease is a much-overlooked feature of the disease. The higher incidence of exacerbations in winter has important consequences for patients in terms of increased morbidity and mortality. The seasonality also imposes a considerable burden on already-overloaded health care services, with both primary care consultations and hospital admissions increasing in number. The seasonality of exacerbations varies with latitude, and is greater in more temperate climates, where there may be less protection from outdoor and indoor cold exposure. The precise causes of the seasonality are unknown, but thought to be partly due to the increased prevalence of respiratory viral infections circulating in cold, damp conditions. Increased susceptibility to viral infection may also be a mechanism mediated through increased airway inflammation or possibly reduced vitamin D levels. The seasonality of exacerbations informs us about the triggers of exacerbations and suggests possible strategies to reduce their number. Keywords: exacerbations of COPD, seasonality, winter mortality, winter morbidit

Wages, Rents and Heterogeneous Moving Costs (second version)

The model of compensating differentials in regional labor and land markets was formalized by Roback (1982). The model interprets regional differences in constant quality wages and rents as compensating firms and residents for inter-regional differences in amenities. While the model assumes that the costs of relocating to a new city are zero, the results hold in the presence of moving costs for the marginal migrant. This paper extends the Roback model to allow for moving costs which vary among a city's residents and businesses. This modification of the model generates new interpretations of regional differences in rents and wages. The theoretical results suggests that the interpretation of inter-city rent and wage differentials as compensating is misguided, that such differentials are inappropriate as weights in QOL comparisons and stresses the importance of local housing and labor market parameters in the determination of these differentials. The importance of amenities is retained, but housing supply becomes the main other determinant of regional rents. Housing supply was ignored in the literature following on Roback's initial insight. The new perspective also provides a bridge between the neoclassical perspective implicit in Roback's approach and the newer literature on agglomeration economies. Working Paper 08-0

Synthesis of cyclopropanes via organoiron methodology: stereoselective preparation of cis-2-(2’-carboxycyclopropyl)glycine

A stereoselective route to cis-2-(2′-carboxycyclopropyl)glycine has been developed. exo-Nucleophilic addition to the (bicyclo[5.1.0]octadienyl)iron(1+) cation establishes the relative stereochemistry at the cyclopropane ring and the α-stereocenter. Subsequent removal of the metal and cleavage of the cyclic diene gave the protected target 10, which upon hydrolysis gave 1. A stereoselective route to cis-2-(2′-carboxycyclopropyl)glycine has been developed. exo-Nucleophilic addition to the (bicyclo[5.1.0]octadienyl)iron(1+) cation establishes the relative stereochemistry at the cyclopropane ring and the α-stereocenter

The effects of running, cycling, and duathlon exercise performance on cardiac function, haemodynamics and regulation

This thesis examined the effects of prolonged exercise, specifically Olympic Distance (OD)duathlon upon ultrasound derived indices of cardiac function, cardiac autonomic regulation measured via heart rate variability (HRV), and high-sensitivity cardiac troponin T (hs-cTnT)release. The primary aims were to (1) ascertain the influence of Olympic distance (OD) duathlon performance on cardiac function; (2) to investigate potential relationships between autonomic regulation, hs-cTnT release, and cardiac function, and (3) to investigate the effect of the individual legs of an OD duathlon on post-exercise cardiac function and to quantify the potential performance reserve of highly-trained endurance athletes when completing standalone legs of the duathlon. Findings from a systematic review and meta-analysis(Chapter 1) on research that performed serial echocardiographic and troponin measurements before and after exercise, intensity predicted changes in post-exercise cardiac troponin release and diastolic function. The findings agreed with previous meta-analyses using a more recent sample of studies; however, the recommendation for future studies to implement advanced cardiac imaging techniques, such as myocardial speckle tracking into their data collection would provide a more sensitive measure of post-exercise cardiac function. Whilst a large degree of heterogeneity in the results exists, this was in part explained by study exercise heart rate, participant age, and the prevalence of cardiac troponin release above the clinical detection threshold. The study performed in Chapter 3 was the first to investigate the effects of OD duathlon exercise on immediate and 24 hours post-exercise cardiac function. Additionally, a second OD duathlon was performed by participants with intra-leg measurements of cardiac function. In a highly trained cohort, there was evidence of transient post-exercise reductions in cardiac function and elevated serum high-sensitivity cardiac troponin T (hs-cTnT) above the clinical reference value, which was largely resolved within 24h of recovery. This study also demonstrated the reliability of lab-based duathlon exercise in a highly trained cohort and identified the pacing features of experienced multi-sport athletes that partially explained the different findings between the running and cycling legs of the duathlon. By investigating each leg of the duathlon individually (10k run, 5k run, 40k cycle), both at duathlon race-pace (DM) and maximal (Max) intensity on separate occasions, the performance reserve of the highly-trained cohort was quantified and further explored. The studies presented in Chapters 4 and 5 revealed that experienced duathletes were able to improve their speed across each leg by between 5-15% in a laboratory setting, compared to the duathlon effort. Additionally, the maximal effort 10k run leg provoked the most persistent changes to cardiac function that were present at 6h of recovery. Changes in cardiac function post DM 10k confirmed the findings of Chapter 3 that the greatest magnitude of cardiac perturbations occur following the initial 10k run leg. Aside from the Max 10k run and 40k cycle trials, all perturbations had resolved within 6h of recovery after each bout of exercise, highlighting the importance of recovery following maximal intensity efforts. The lack of 6h and 24h recovery data in Chapter 4, and Chapters 5 and 6, respectively is a shortcoming of these findings and therefore limits interpretation in the context of providing athletic guidance. Future research in this area should endeavour to include 6h and 24h recovery measures as standard, as multi-sport athletes typically perform multiple daily training sessions. The implications of substantial cardiac fatigue accumulation over many years of endurance training history are still unclear, and athletes may benefit from preventingits occurrence

Reactivity of (Bicyclo[5.1.0]octadienyl)iron(1+) Cations: Application to the Synthesis of cis-2-(2’-carboxycyclopropyl)glycines

The addition of carbon and heteroatom nucleophiles to (bicyclo[5.1.0]octadienyl)Fe(CO)2L+ cations 5 or 8 (L = CO, PPh3) generally proceeds via attack at the dienyl terminus on the face of the ligand opposite to iron to generate 6-substituted (bicyclo[5.1.0]octa-2,4-diene)iron complexes (11 or 13). In certain cases, these products are unstable with respect to elimination of a proton and the nucleophilic substituent to afford (cyclooctatetraene)Fe(CO)2L (4 or 7). Decomplexation of 13f, arising from addition of phthalimide to 8, gave N-(bicyclo[5.1.0]octa-3,5-dien-2-yl)phthalimide (19). Oxidative cleavage of 19 (RuCl3/NaIO4) followed by esterification gave the cyclopropane diester 22, which upon hydrolysis gave cis-2-(2‘-carboxycyclopropyl)glycine (CCG-III, 18) (eight steps from 4, 43% overall yield). This methodology was also utilized for preparation of stereospecifically deuterated CCG-III (d-18) and optically enriched (−)-18. Deprotonation of 22 resulted in cyclopropane ring opening to afford the benzoindolizidine (23)