Universal Taylor series, conformal mappings and boundary behaviour

A holomorphic function f on a simply connected domain {\Omega} is said to possess a universal Taylor series about a point in {\Omega} if the partial sums of that series approximate arbitrary polynomials on arbitrary compacta K outside {\Omega} (provided only that K has connected complement). This paper shows that this property is not conformally invariant, and, in the case where {\Omega} is the unit disc, that such functions have extreme angular boundary behaviour.Comment: 12 pages. To appear in Annales de l'Institut Fourier (Grenoble

Examining consent for interventional research in potential deceased organ donors: a narrative review

In the last decade, research in transplant medicine has focused on developing interventions in the management of the deceased organ donor to improve the quality and quantity of transplantable organs. Despite the promise of interventional donor research, there remain debates about the ethics of this research, specifically regarding gaining research consent. Here, we examine the concerns and ambiguities around consent for interventional donor research, which incorporate questions about who should consent for interventional donor research and what people are being asked to consent for. We highlight the US and UK policy responses to these concerns and argue that, whereas guidance in this area has done much to clarify these ambiguities, there is little consideration of the nature, practicalities and context around consent in this area, particularly regarding organ donors and their families. We review wider studies of consent in critical care research and social science studies of consent in medical research, to gain a broader view of consent in this area as a relational and contextual process. We contend a lack of consideration has been given to: what it might mean to consent to interventional donor research; how families, patients and health professionals might experience providing and seeking this consent; who is best placed to have these discussions; and the socio‐institutional contexts affecting these processes. Further, empirical research is required to establish an ethical and sensitive model for consent in interventional donor research, ensuring the principles enshrined in research ethics are met and public trust in organ donation is maintained

Quantum kinetic theory VII: The influence of vapor dynamics on condensate growth

We extend earlier models of the growth of a Bose-Einstein condensate to include the full dynamical effects of the thermal cloud by numerically solving a modified quantum Boltzmann equation. We determine the regime in which the assumptions of the simple model are a reasonable approximation, and compare our new results with those that were earlier compared with experimental data. We find good agreement with our earlier modelling, except at higher condensate fractions, for which a significant speedup is found. We also investigate the effect of temperature on condensate growth, and find that this has a surprisingly small effect. The discrepancy between theory and experiment remains, since the speedup found in these computations does not occur in the parameter regime specified in the the experiment.Comment: Fourteen pages, TeX source with 11 figures. Changes : Extended section on formalism to include a derivation of the ergodic Boltzmann equation that we use, and a fuller explanation of the numerical methods. Explained more fully the possible errors with the experimental data. Added section detailing the source of possible errors in this formulation. Added comparison of our work with the manuscript cond-mat/0001323, and some analysis of the fits to the MIT growth curve

Number-Phase Wigner Representation for Efficient Stochastic Simulations

Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many problems using these techniques remain intractable over long integrations times. We present a number-phase Wigner representation that can be unraveled into SDEs. We demonstrate convergence to the correct solution for an anharmonic oscillator with small dampening for significantly longer than other phase space representations. This process requires an effective sampling of a non-classical probability distribution. We describe and demonstrate a method of achieving this sampling using stochastic weights.Comment: 7 pages, 1 figur

All-optical versus electro-optical quantum-limited feedback

All-optical feedback can be effected by putting the output of a source cavity through a Faraday isolator and into a second cavity which is coupled to the source cavity by a nonlinear crystal. If the driven cavity is heavily damped, then it can be adiabatically eliminated and a master equation or quantum Langevin equation derived for the first cavity alone. This is done for an input bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the intercavity coupling involves only the intensity (or one quadrature) of the driven cavity, then the effect on the source cavity is identical to that which can be obtained from electro-optical feedback using direct (or homodyne) detection. If the coupling involves both quadratures, this equivalence no longer holds, and a coupling linear in the source amplitude can produce a nonclassical state in the source cavity. The analogous electro-optic scheme using heterodyne detection introduces extra noise which prevents the production of nonclassical light. Unlike the electro-optic case, the all-optical feedback loop has an output beam (reflected from the second cavity). We show that this may be squeezed, even if the source cavity remains in a classical state.Comment: 21 pages. This is an old (1994) paper, but one which I thought was worth posting because in addition to what is described in abstract it has: (1) the first formulation (to my knowledge) of quantum trajectories for an arbitrary (i.e. squeezed, thermal etc.) broadband bath; (2) the prediction of a periodic modification to the detuning and damping of an oscillator for the simplest sort of all-optical feedback (i.e. a mirror) as seen in the recent experiment "Forces between a Single Atom and Its Distant Mirror Image", P. Bushev et al, Phys. Rev. Lett. 92, 223602 (2004

Diagnosis of antiphospholipid syndrome in routine clinical practice.

The updated international consensus criteria for definite antiphospholipid syndrome (APS) are useful for scientific clinical studies. However, there remains a need for diagnostic criteria for routine clinical use. We audited the results of routine antiphospholipid antibodies (aPLs) in a cohort of 193 consecutive patients with aPL positivity-based testing for lupus anticoagulant (LA), IgG and IgM anticardiolipin (aCL) and anti-ß(2)glycoprotein-1 antibodies (aß(2)GPI). Medium/high-titre aCL/aβ(2)GPI was defined as >99th percentile. Low-titre aCL/aβ(2)GPI positivity (>95(th )< 99(th) percentile) was considered positive for obstetric but not for thrombotic APS. One hundred of the 145 patients fulfilled both clinical and laboratory criteria for definite APS. Twenty-six women with purely obstetric APS had persistent low-titre aCL and/or aβ(2)GPI. With the inclusion of these patients, 126 of the 145 patients were considered to have APS. Sixty-seven out of 126 patients were LA-negative, of whom 12 had aCL only, 37 had aβ(2)GPI only and 18 positive were for both. The omission of aCL or aβ(2)GPI testing from investigation of APS would have led to a failure to diagnose APS in 9.5% and 29.4% of patients, respectively. Our data suggest that LA, aCL and aβ(2)GPI testing are all required for the accurate diagnosis of APS and that low-titre antibodies should be included in the diagnosis of obstetric APS

Quantum turbulence in condensate collisions: an application of the classical field method

We apply the classical field method to simulate the production of correlated atoms during the collision of two Bose-Einstein condensates. Our non-perturbative method includes the effect of quantum noise, and provides for the first time a theoretical description of collisions of high density condensates with very large out-scattered fractions. Quantum correlation functions for the scattered atoms are calculated from a single simulation, and show that the correlation between pairs of atoms of opposite momentum is rather small. We also predict the existence of quantum turbulence in the field of the scattered atoms--a property which should be straightforwardly measurable.Comment: 5 pages, 3 figures: Rewritten text, replaced figure

Disruption of reflecting Bose-Einstein condensates due to inter-atomic interactions and quantum noise

We perform fully three-dimensional simulations, using the truncated Wigner method, to investigate the reflection of Bose-Einstein condensates from abrupt potential barriers. We show that the inter-atomic interactions can disrupt the internal structure of a cigar-shaped cloud with a high atom density at low approach velocities, damping the center-of-mass motion and generating vortices. Furthermore, by incorporating quantum noise we show that scattering halos form at high approach velocities, causing an associated condensate depletion. We compare our results to recent experimental observations.Comment: 5 figure