Error Estimates for Approximate Solutions of the Riccati Equation with Real or Complex Potentials

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati equation. We explain the general strategy for applying these estimates and illustrate the method in typical examples, where the approximate solutions are obtained by glueing together WKB and Airy solutions of corresponding one-dimensional Schrodinger equations. Our method is motivated by and has applications to the analysis of linear wave equations in the geometry of a rotating black hole.Comment: 23 pages, LaTeX, 13 figures, minor improvements (published version

An Assessment of Dialysis Provider's Attitudes towards Timing of Dialysis Initiation in Canada

Background: Physicians' perceptions and opinions may influence when to initiate dialysis. Objective: To examine providers' perspectives and opinions regarding the timing of dialysis initiation. Design: Online survey. Setting: Community and academic dialysis practices in Canada. Participants: A nationally-representative sample of dialysis providers. Measurements and Methods: Dialysis providers opinions assessing reasons to initiate dialysis at low or high eGFR. Responses were obtained using a 9-point Likert scale. Early dialysis was defined as initiation of dialysis in an individual with an eGFR greater than or equal to 10.5 ml/min/m 2 . A detailed survey was emailed to all members of the Canadian Society of Nephrology (CSN) in February 2013. The survey was designed and pre-tested to evaluate duration and ease of administration. Results: One hundred and forty one (25% response rate) physicians participated in the survey. The majority were from urban, academic centres and practiced in regionally administered renal programs. Very few respondents had a formal policy regarding the timing of dialysis initiation or formally reviewed new dialysis starts (N = 4, 3.1%). The majority of respondents were either neutral or disagreed that late compared to early dialysis initiation improved outcomes (85–88%), had a negative impact on quality of life (89%), worsened AVF or PD use (84–90%), led to sicker patients (83%) or was cost effective (61%). Fifty-seven percent of respondents felt uremic symptoms occurred earlier in patients with advancing age or co-morbid illness. Half (51.8%) of the respondents felt there was an absolute eGFR at which they would initiate dialysis in an asymptomatic patient. The majority of respondents would initiate dialysis for classic indications for dialysis, such as volume overload (90.1%) and cachexia (83.7%) however a significant number chose other factors that may lead them to early dialysis initiation including avoiding an emergency (28.4%), patient preference (21.3%) and non-compliance (8.5%). Limitations: 25% response rate. Conclusions: Although the majority of nephrologists in Canada who responded followed evidence-based practice regarding the timing of dialysis initiation, knowledge gaps and areas of clinical uncertainty exist. The implementation and evaluation of formal policies and knowledge translation activities may limit potentially unnecessary early dialysis initiation

Quantum Tunneling in the Wigner Representation

Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.Comment: 18 pages, LATEX, no figure

Imagining transitions in old age through the visual matrix method: thinking about what is hard to bear

Dominant discourses of ageing are often confined to what is less painful to think about and therefore idealise or denigrate ageing and later life. We present findings from an exploratory psychosocial study, in a Nordic context into three later-life transitions: from working life to retirement, from mental health to dementia, and from life to death. Because, for some, these topics are hard to bear, and therefore defended against and routinely excluded from everyday awareness, we used a method led by imagery and affect - the Visual Matrix - to elicit participants’ free associative personal and collective imagination. Through analysis of data extracts, on the three transitions, we illustrate oscillations between defending against the challenges of ageing and realism in facing the anxieties it can provoke. A recurring theme includes the finality of individual life and the inter-generational continuity, which together link life and death, hope and despair, separation and connectedness

Psychosocial factors and health as determinants of quality of life in community-dwelling older adults.

PURPOSE: It is important to understand the determinants of differences in quality of life in old age and to include a wide range of possible predictors. The present study investigated the determinants of quality of life in two groups of older adults for whom there was an unusually informative set of possible predictor variables. METHOD: Participants were members of the Lothian Birth Cohorts of 1921 (n = 550) or 1936 (n = 1,091). Four facets of quality of life (QoL) and general QoL were measured using the WHOQOL-BREF. Possible determinants included personality traits, measured with the International Personality Item Pool (IPIP) scales; childhood and old age general cognitive ability, measured with the Moray House Test; minor psychological symptoms, measured with the Hospital Anxiety and Depression Scale (HADS); physical health, assessed by grip strength and cardiovascular disease history; and sociodemographic factors, assessed by interview. RESULTS: Linear regression analyses revealed that HADS depression had the greatest influence on quality of life. Personality traits, most notably Emotional Stability, also predicted quality of life to varying degrees, along with factors reflecting current life circumstances. There were differences between the two cohorts in the variables which predicted quality of life. There were different, conceptually relevant, contributions to the different QoL facets. CONCLUSIONS: Personality traits and minor depressive symptoms have an important influence on self-reported quality of life in old age. Quality of life may be influenced more by current than past circumstances, and this relationship may change with age

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject