Localization over complex-analytic groupoids and conformal renormalization

We present a higher index theorem for a certain class of etale one-dimensional complex-analytic groupoids. The novelty is the use of the local anomaly formula established in a previous paper, which represents the bivariant Chern character of a quasihomomorphism as the chiral anomaly associated to a renormalized non-commutative chiral field theory. In the present situation the geometry is non-metric and the corresponding field theory can be renormalized in a purely conformal way, by exploiting the complex-analytic structure of the groupoid only. The index formula is automatically localized at the automorphism subset of the groupoid and involves a cap-product with the sum of two different cyclic cocycles over the groupoid algebra. The first cocycle is a trace involving a generalization of the Lefschetz numbers to higher-order fixed points. The second cocycle is a non-commutative Todd class, constructed from the modular automorphism group of the algebra.Comment: 38 pages. v2: some inconsistencies with the use of pseudogroups have been fixe

Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings

We construct two quantum spin chains Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the periodic chain. The two Hamiltonians, respectively built using the distinguished and the fermionic bases of U_q(sl(2|1)) differ only in the boundary terms. They are actually equivalent, but the equivalence is non local. Reflection equations are solved to get exact solvability on open chains with non trivial boundary conditions. Two families of diagonal solutions are found. The centre and the Scasimirs of the quantum enveloping algebra of sl(2|1) appear as tools for the construction of exactly solvable Hamiltonians.Comment: 22 pages, LaTeX2e, uses amsfonts; some references added and typos correcte

The Multivariate Resultant is NP-hard in any Characteristic

The multivariate resultant is a fundamental tool of computational algebraic geometry. It can in particular be used to decide whether a system of n homogeneous equations in n variables is satisfiable (the resultant is a polynomial in the system's coefficients which vanishes if and only if the system is satisfiable). In this paper we present several NP-hardness results for testing whether a multivariate resultant vanishes, or equivalently for deciding whether a square system of homogeneous equations is satisfiable. Our main result is that testing the resultant for zero is NP-hard under deterministic reductions in any characteristic, for systems of low-degree polynomials with coefficients in the ground field (rather than in an extension). We also observe that in characteristic zero, this problem is in the Arthur-Merlin class AM if the generalized Riemann hypothesis holds true. In positive characteristic, the best upper bound remains PSPACE.Comment: 13 page

How useful are the estimates of the economic consequences of Brexit?

In this blog, Josh De Lyon (LSE's Centre for Economic Performance) discusses some of the concerns with the economic forecasts of the effects of Brexit and suggests that the available reports are informative of the likely consequences of Brexit. He also provides an insight into how such research should be interpreted, beyond the headline-grabbing figures reported in the news

Emergency medical dispatch recognition, clinical intervention and outcome of patients in traumatic cardiac arrest from major trauma : an observational study

© Author(s) (or their employer(s)) 2018. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.OBJECTIVES: The aim of this study is to describe the demographics of reported traumatic cardiac arrest (TCA) victims, prehospital resuscitation and survival to hospital rate. SETTING: Helicopter Emergency Medical Service (HEMS) in south-east England, covering a resident population of 4.5 million and a transient population of up to 8 million people. PARTICIPANTS: Patients reported on the initial 999 call to be in suspected traumatic cardiac arrest between 1 July 2016 and 31 December 2016 within the trust's geographical region were identified. The inclusion criteria were all cases of reported TCA on receipt of the initial emergency call. Patients were subsequently excluded if a medical cause of cardiac arrest was suspected. OUTCOME MEASURES: Patient records were analysed for actual presence of cardiac arrest, prehospital resuscitation procedures undertaken and for survival to hospital rates. RESULTS: 112 patients were reported to be in TCA on receipt of the 999/112 call. 51 (46%) were found not to be in TCA on arrival of emergency medical services. Of the 'not in TCA cohort', 34 (67%) received at least one advanced prehospital medical intervention (defined as emergency anaesthesia, thoracostomy, blood product transfusion or resuscitative thoracotomy). Of the 61 patients in actual TCA, 10 (16%) achieved return-of-spontaneous circulation. In 45 (88%) patients, the HEMS team escorted the patient to hospital. CONCLUSION: A significant proportion of patients reported to be in TCA on receipt of the emergency call are not in actual cardiac arrest but are critically unwell requiring advanced prehospital medical intervention. Early activation of an enhanced care team to a reported TCA call allows appropriate advanced resuscitation. Further research is warranted to determine which interventions contribute to improved TCA survival.Peer reviewedFinal Published versio

A novel method of non-clinical dispatch is associated with a higher rate of critical Helicopter Emergency Medical Service intervention

Background - Helicopter Emergency Medical Services (HEMS) are a scarce resource that can provide advanced emergency medical care to unwell or injured patients. Accurate tasking of HEMS is required to incidents where advanced pre-hospital clinical care is needed. We sought to evaluate any association between non-clinically trained dispatchers, following a bespoke algorithm, compared with HEMS paramedic dispatchers with respect to incidents requiring a critical HEMS intervention. Methods - Retrospective analysis of prospectively collected data from two 12-month periods was performed (Period one: 1st April 2014 – 1st April 2015; Period two: 1st April 2016 – 1st April 2017). Period 1 was a Paramedic-led dispatch process. Period 2 was a non-clinical HEMS dispatcher assisted by a bespoke algorithm. Kent, Surrey & Sussex HEMS (KSS HEMS) is tasked to approximately 2500 cases annually and operates 24/7 across south-east England. The primary outcome measure was incidence of a HEMS intervention.Results - A total of 4703 incidents were included; 2510 in period one and 2184 in period two. Variation in tasking was reduced by introducing non-clinical dispatchers. There was no difference in median time from 999 call to HEMS activation between period one and two (period one; median 7 min (IQR 4–17) vs period two; median 7 min (IQR 4–18). Non-clinical dispatch improved accuracy of HEMS tasking to a mission where a critical care intervention was required (OR 1.25, 95% CI 1.04–1.51, p = 0.02).Conclusion - The introduction of non-clinical, HEMS-specific dispatch, aided by a bespoke algorithm improved accuracy of HEMS tasking. Further research is warranted to explore where this model could be effective in other HEMS services.Peer reviewedFinal Published versio