Band Distributions for Quantum Chaos on the Torus

Band distributions (BDs) are introduced describing quantization in a toral phase space. A BD is the uniform average of an eigenstate phase-space probability distribution over a band of toral boundary conditions. A general explicit expression for the Wigner BD is obtained. It is shown that the Wigner functions for {\em all} of the band eigenstates can be reproduced from the Wigner BD. Also, BDs are shown to be closer to classical distributions than eigenstate distributions. Generalized BDs, associated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum correspondence on the torus to arbitrary rational values of the scaled Planck constant.Comment: 12 REVTEX page

Renormalization of Quantum Anosov Maps: Reduction to Fixed Boundary Conditions

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number ($k$) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for {\em all} $k$ BCs is exactly equivalent to that of the renormalized QAM (with Planck's constant $\hbar ^{\prime}=\hbar /k$) at some {\em fixed} BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of ``crystalline'' eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.Comment: REVTEX, 12 pages, 1 table. To appear in Physical Review Letter

Longmeyer Exposes or Creates Uncertainty about the Duty to Inform Remainder Beneficiaries of a Revocable Trust

This article discusses the surprising Longmeyer decision, handed down by the Supreme Court of Kentucky earlier this year in which a predecessor trustee was held to have a duty to give certain notifications to former remainder beneficiaries of a revocable trust. The authors then examine how Longmeyer might have been decided in other states and under other statutory schemes. The article concludes with observations concerning when certain notices to trust beneficiaries may be conducive to effective trust administration and suggestions to those who administer trusts on how best to comply with beneficiary notice requirements

Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated using the following PO formulas: (a) The curvature expansion of the Ruelle zeta function. (b) The average of the PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b) agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (c) gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to {\em uniformity sum rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum rules follow from general arguments and are supported by much numerical evidence.Comment: 6 Tables, 2 Figures (postscript); To appear in Physical Review

Antiresonance and Localization in Quantum Dynamics

The phenomenon of quantum antiresonance (QAR), i.e., exactly periodic recurrences in quantum dynamics, is studied in a large class of nonintegrable systems, the modulated kicked rotors (MKRs). It is shown that asymptotic exponential localization generally occurs for $\eta$ (a scaled $\hbar$) in the infinitesimal vicinity of QAR points $\eta_0$. The localization length $\xi_0$ is determined from the analytical properties of the kicking potential. This ``QAR-localization" is associated in some cases with an integrable limit of the corresponding classical systems. The MKR dynamical problem is mapped into pseudorandom tight-binding models, exhibiting dynamical localization (DL). By considering exactly-solvable cases, numerical evidence is given that QAR-localization is an excellent approximation to DL sufficiently close to QAR. The transition from QAR-localization to DL in a semiclassical regime, as $\eta$ is varied, is studied. It is shown that this transition takes place via a gradual reduction of the influence of the analyticity of the potential on the analyticity of the eigenstates, as the level of chaos is increased.Comment: To appear in Physical Review E. 51 pre-print pages + 9 postscript figure

VBP15, a glucocorticoid analogue, is effective at reducing allergic lung inflammation in mice

Asthma is a chronic inflammatory condition of the lower respiratory tract associated with airway hyperreactivity and mucus obstruction in which a majority of cases are due to an allergic response to environmental allergens. Glucocorticoids such as prednisone have been standard treatment for many inflammatory diseases for the past 60 years. However, despite their effectiveness, long-term treatment is often limited by adverse side effects believed to be caused by glucocorticoid receptor-mediated gene transcription. This has led to the pursuit of compounds that retain the anti-inflammatory properties yet lack the adverse side effects associated with traditional glucocorticoids. We have developed a novel series of steroidal analogues (VBP compounds) that have been previously shown to maintain anti-inflammatory properties such as NFκB-inhibition without inducing glucocorticoid receptor-mediated gene transcription. This study was undertaken to determine the effectiveness of the lead compound, VBP15, in a mouse model of allergic lung inflammation. We show that VBP15 is as effective as the traditional glucocorticoid, prednisolone, at reducing three major hallmarks of lung inflammation--NFκB activity, leukocyte degranulation, and pro-inflammatory cytokine release from human bronchial epithelial cells obtained from patients with asthma. Moreover, we found that VBP15 is capable of reducing inflammation of the lung in vivo to an extent similar to that of prednisone. We found that prednisolone--but not VBP15 shortens the tibia in mice upon a 5 week treatment regimen suggesting effective dissociation of side effects from efficacy. These findings suggest that VBP15 may represent a potent and safer alternative to traditional glucocorticoids in the treatment of asthma and other inflammatory diseases.Supported in part by grants from the NIH (1R41HL104939-01B; 1K26RR032082; 1P50AR060836-01; 1U54HD071601; 2R24HD050846-06, R01 HL033152- 25), DOD grants (W81XWH-11-1-0330; W81XWH-11-1-0782; W81XWH-10-1-0659; W81XWH-11-1-0809; W81XWH-09-1-0599) a translational research grant from MDA, pilot grant from Parent Project Muscular Dystrophy (PPMD), and a contribution from the Clark Family Foundation

Demographic, multi-morbidity and genetic impact on myocardial involvement and its recovery from COVID-19 : protocol design of COVID-HEART-a UK, multicentre, observational study

Acknowledgements CB acknowledges British Heart Foundation support (RE/18/6134217). GPM is funded by a NIHR Research Professorship (RP‐2017‐08‐ST2‐007). CM is funded by a NIHR Clinician Scientist Award (CS‐2015‐15‐003). VMF and SN acknowledge the NIHR Oxford BRC for support of this study. CBD is in part supported by the NIHR Biomedical Research Centre at University Hospitals Bristol NHS Foundation Trust and the University of Bristol. Additional support was provided by the NIHR Leicester Biomedical Research Centre and the NIHR Leeds Clinical Research Facility. The views expressed in this publication are those of the author(s) and not necessarily those of the NHS, the National Institute for Health Research or the Department of Health and Social Care. We thank the patients and staff who have supported this project. Dr. Warren J. Manning served as a Guest Editor for this manuscript. Study Management and Recruitment centres: Grant applicants: JP Greenwood (chief investiga‐ tor), GP McCann, C Berry, M Dweck, J Moon, CM Miller, A Chiribiri, S Prasad, VM Ferreira, C Bucciarelli‐Ducci, D Dawson. Data repository and statistical analysis: Glasgow Clinical Trials Unit. Senior study statistician: Prof A McConnachie, GCTU. Local Principle Investigators and Recruitment Centres: Prof John Green‐ wood, Leeds Teaching Hospitals NHS Trust, UK; Prof Gerry McCann, Glenfield Hospital, Leicester, UK; Prof Dana Dawson, Aberdeen Royal Infirmary, UK; Prof Marc Dweck, Royal Infirmary of Edinburgh, UK; Prof Vanessa Ferreira, JohnRadcliffe Hospital, Oxford, UK; Prof Colin Berry, Queen Elizabeth University Hospital, Glasgow, UK; Dr Peter Swoboda, Pinderfields Hospital, Wakefield, UK; Dr Richard Steeds, Queen Elizabeth Hospital, Birmingham, UK; Prof James Moon, UCL Hospital London, UK; Dr Christopher Miller, Wythenshawe Hospital, Manchester, UK; Dr Timothy Fairbairn, Liverpool Heart and Chest Hospital, UK; Dr Andrew Flett, Southampton General Hospital, UK; Prof Marianna Fontana, Royal Free Hospital, London, UK; Dr Thomas Green, Northumbria NHS Trust, UK; Prof Amedeo Chiribiri, St Thomas’ Hospital, London, UK; Dr Chiara Bucciarelli‐Ducci, University Hospitals Bristol and Weston NHS Trust, UK; Dr Graham Cole, Hammersmith Hospital, London, UK; Prof Sanjay Prasad, Royal Brompton Hospital, London, UK; Dr Adam McDiarmid, Freeman Hospital, New‐ castle Upon Tyne, UK; Dr Nicholas Bunce, St Georges Hospital, London, UK; Dr Prathap Kanagala, Aintree University Hospital, Liverpool, UK; Prof Nicholas Bellenger, The Royal Devon and Exeter Hospital, UK; Dr Tishi Ninan, Swansea Bay University Hospital, UK; Dr Khaled Alfakih, Lewisham University Hospital, London, UK; Prof James Moon, St Bartholomew’s Hospital, London, UK. Funding COVID‐HEART is funded by the National Institute for Health Research (NIHR) and UK Research and Innovation (UKRI) COVID‐19 Rapid Response Rolling Call (Grant Number COV0254), and sponsored by the University of Leeds, UK. The study has been endorsed by the British Society of Cardiovascular Magnetic Resonance (BSCMR) Research Group, and nationally prioritised, and received both BHF‐NIHR Cardiovascular Partnership Flagship Status, and the NIHR Urgent Public Health Group identified it as an Urgent Public Health (UPH) study. Funding for the translation of the patient information leaflets into non‐ English languages was provided by the West Yorkshire and Humber Clinical Research Network (CV070).Peer reviewedPublisher PD

Dominance, reproductive behaviours and female mate choice in sterilised versus non-sterilised invasive male crayfish

© 2020, The Author(s). Many methods of controlling invasive crayfishes have limited success because they fail to target all life stages of the population, notably by capturing only large adults that can result in increased juvenile recruitment by removing intraspecific predation. An alternative approach uses the sterile male release technique that involves the mass release of sterile males into the environment, which then mate with fertile females, resulting in unfertilised eggs and, ultimately, reduced juvenile recruitment. This does, however, rely on the sterilised males exhibiting behaviours similar to non-sterilised (entire) males and remaining attractive to females during mate choice. Post-copulatory male guarding behaviour and female promiscuity might also be affected by male sterilisation. To test for the presence of normal reproductive behaviours in sterilised male American signal crayfish Pacifastacus leniusculus, a two-stage experiment examined how sterilisation affects female mate choice and promiscuity, male hierarchical status (relative dominance) and post-copulation guarding. Sterilised males showed similar reproductive behaviours to entire males and remained as attractive to females, with no differences in relative dominance. Post-copulation, guarding behaviours were also unaffected. Females did not display promiscuous behaviour and this was unaffected by whether males were entire or sterilised. The results demonstrated that sterilised males were equally as capable as entire males of achieving dominance and winning mates. In combination, these findings suggest that male sterilisation could be an effective control technique to help reduce juvenile recruitment in wild P. leniusculus populations by reducing reproductive success

Aortic stiffness in aortic stenosis assessed by cardiovascular MRI: a comparison between bicuspid and tricuspid valves

Objectives To compare aortic size and stiffness parameters on MRI between bicuspid aortic valve (BAV) and tricuspid aortic valve (TAV) patients with aortic stenosis (AS). Methods MRI was performed in 174 patients with asymptomatic moderate-severe AS (mean AVAI 0.57 ± 0.14 cm2/m2) and 23 controls on 3T scanners. Valve morphology was available/analysable in 169 patients: 63 BAV (41 type-I, 22 type-II) and 106 TAV. Aortic cross-sectional areas were measured at the level of the pulmonary artery bifurcation. The ascending and descending aorta (AA, DA) distensibility, and pulse wave velocity (PWV) around the aortic arch were calculated. Results The AA and DA areas were lower in the controls, with no difference in DA distensibility or PWV, but slightly lower AA distensibility than in the patient group. With increasing age, there was a decrease in distensibility and an increase in PWV. After correcting for age, the AA maximum cross-sectional area was higher in bicuspid vs. tricuspid patients (12.97 [11.10, 15.59] vs. 10.06 [8.57, 12.04] cm2, p < 0.001), but there were no significant differences in AA distensibility (p = 0.099), DA distensibility (p = 0.498) or PWV (p = 0.235). Patients with BAV type-II valves demonstrated a significantly higher AA distensibility and lower PWV compared to type-I, despite a trend towards higher AA area. Conclusions In patients with significant AS, BAV patients do not have increased aortic stiffness compared to those with TAV despite increased ascending aortic dimensions. Those with type-II BAV have less aortic stiffness despite greater dimensions. These results demonstrate a dissociation between aortic dilatation and stiffness and suggest that altered flow patterns may play a role. Key Points • Both cellular abnormalities secondary to genetic differences and abnormal flow patterns have been implicated in the pathophysiology of aortic dilatation and increased vascular complications associated with bicuspid aortic valves (BAV). • We demonstrate an increased ascending aortic size in patients with BAV and moderate to severe AS compared to TAV and controls, but no difference in aortic stiffness parameters, therefore suggesting a dissociation between dilatation and stiffness. • Sub-group analysis showed greater aortic size but lower stiffness parameters in those with BAV type-II AS compared to BAV type-I