On the Morgan-Shalen compactification of the SL(2,C) character varieties of surface groups

http://arxiv.org/PS_cache/math/pdf/9810/9810034v1.pdfA gauge theoretic description of the Morgan-Shalen compactification of the SL(2, C) character variety of the fundamental group of a hyperbolic surface is given in terms of a natural compactification of the moduli space of Higgs bundles via the Hitchin map

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Formal matched asymptotics for degenerate Ricci flow neckpinches

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Stabilising Lyme Regis – a strategic approach

Coastal erosion and landslides have been a constant threat to Lyme Regis in West Dorset, UK for over 250 years. By the 1980s, the frequency and scale of coastal erosion and land instability had reached a point whereby the local council realised that a change from the previous ad hoc repair and protection approach was needed to secure the long-term future of the town. An environmental improvements initiative was developed from then onwards to provide a strategic and integrated programme of coast protection and cliff stabilisation measures designed to mitigate the increasing threat of climate change, coastal erosion and landslides, while respecting the site’s unique heritage and environmental interests. This paper outlines the background and principal phases of the project that have been successfully delivered over the period 1990–2015

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction

Social marketing and healthy eating : Findings from young people in Greece

This document is the Accepted Manuscript version. The final publication is available at Springer via http://dx.doi.org/10.1007/s12208-013-0112-xGreece has high rates of obesity and non-communicable diseases owing to poor dietary choices. This research provides lessons for social marketing to tackle the severe nutrition-related problems in this country by obtaining insight into the eating behaviour of young adults aged 18–23. Also, the main behavioural theories used to inform the research are critically discussed. The research was conducted in Athens. Nine focus groups with young adults from eight educational institutions were conducted and fifty-nine participants’ views towards eating habits, healthy eating and the factors that affect their food choices were explored. The study found that the participants adopted unhealthier nutritional habits after enrolment. Motivations for healthy eating were good health, appearance and psychological consequences, while barriers included lack of time, fast-food availability and taste, peer pressure, lack of knowledge and lack of family support. Participants reported lack of supportive environments when deciding on food choices. Based on the findings, recommendations about the development of the basic 4Ps of the marketing mix, as well as of a fifth P, for Policy are proposedPeer reviewe

The CloudUPDRS smartphone software in Parkinson’s study: cross-validation against blinded human raters

Digital assessments of motor severity could improve the sensitivity of clinical trials and personalise treatment in Parkinson’s disease (PD) but have yet to be widely adopted. Their ability to capture individual change across the heterogeneous motor presentations typical of PD remains inadequately tested against current clinical reference standards. We conducted a prospective, dual-site, crossover-randomised study to determine the ability of a 16-item smartphone-based assessment (the index test) to predict subitems from the Movement Disorder Society-Unified Parkinson’s Disease Rating Scale part III (MDS-UPDRS III) as assessed by three blinded clinical raters (the reference-standard). We analysed data from 60 subjects (990 smartphone tests, 2628 blinded video MDS-UPDRS III subitem ratings). Subject-level predictive performance was quantified as the leave-one-subject-out cross-validation (LOSO-CV) accuracy. A pre-specified analysis classified 70.3% (SEM 5.9%) of subjects into a similar category to any of three blinded clinical raters and was better than random (36.7%; SEM 4.3%) classification. Post hoc optimisation of classifier and feature selection improved performance further (78.7%, SEM 5.1%), although individual subtests were variable (range 53.2–97.0%). Smartphone-based measures of motor severity have predictive value at the subject level. Future studies should similarly mitigate against subjective and feature selection biases and assess performance across a range of motor features as part of a broader strategy to avoid overly optimistic performance estimates

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs

The changes in renal function after a single dose of intravenous furosemide in patients with compensated liver cirrhosis

BACKGROUND: Patients with compensated Child-A cirrhosis have sub clinical hypovolemia and diuretic treatment could result in renal impairment. AIM: To evaluate the changes in renal functional mass as reflected by DMSA uptake after single injection of intravenous furosemide in patients with compensated liver cirrhosis. METHODS: Eighteen cirrhotic patients were divided in two groups; eight patients (group 1, age 56 ± 9.6 yrs, Gender 5M/3F, 3 alcoholic and 5 non alcoholic) were given low intravenous 40 mg furosemide and ten other patients (group 2, age 54 ± 9.9, Gender 6M/4F, 4 alcoholic and 6 non alcoholic) were given high 120 mg furosemide respectively. Renoscintigraphy with 100MBq Of Tc 99 DMSA was given intravenously before and 90 minutes after furosemide administration and SPECT imaging was determined 3 hours later. All patients were kept under low sodium diet (80mEq/d) and all diuretics were withdrawn for 3 days. 8-hours UNa exertion, Calculated and measured Creatinine clearance (CCT) were performed for all patients. RESULTS: Intravenous furosemide increased the mean renal DMSA uptake in 55% of patients with compensated cirrhosis and these changes persist up to three hours after injection. This increase was at the same extent in either low or high doses of furosemide. (From 12.8% ± 3.8 to 15.2% ± 2.2, p < 0.001 in Gr I as compared to 10.6% ± 4.6 to 13.5% ± 3.6 in Gr 2, p < 0.001). In 8 patients (45%, 3 pts from Gr 1 and 5 pts from Gr 2) DMSA uptake remain unchanged. The mean 8 hrs UNa excretion after intravenous furosemide was above 80 meq/l and was higher in Gr 2 as compared to Gr 1 respectively (136 ± 37 meq/l) VS 100 ± 36.6 meq/l, P = 0.05). Finally, basal global renal DMSA uptake was decreased in 80% of patients; 22.5 ± 7.5% (NL > 40%), as compared to normal calculated creatinine clearance (CCT 101 ± 26), and measured CCT of 87 ± 30 cc/min (P < 0.001). CONCLUSION: A single furosemide injection increases renal functional mass as reflected by DMSA in 55% of patients with compensated cirrhosis and identify 45% of patients with reduced uptake and who could develop renal impairment under diuretics. Whether or not albumin infusion exerts beneficial effect in those patients with reduced DMSA uptake remains to be determined