Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Fetal Movement Counting Improved Identification of Fetal Growth Restriction and Perinatal Outcomes – a Multi-Centre, Randomized, Controlled Trial

Background Fetal movement counting is a method used by the mother to quantify her baby's movements, and may prevent adverse pregnancy outcome by a timely evaluation of fetal health when the woman reports decreased fetal movements. We aimed to assess effects of fetal movement counting on identification of fetal pathology and pregnancy outcome. Methodology In a multicentre, randomized, controlled trial, 1076 pregnant women with singleton pregnancies from an unselected population were assigned to either perform fetal movement counting from gestational week 28, or to receive standard antenatal care not including fetal movement counting (controls). Women were recruited from nine Norwegian hospitals during September 2007 through November 2009. Main outcome was a compound measure of fetal pathology and adverse pregnancy outcomes. Analysis was performed by intention-to-treat. Principal Findings The frequency of the main outcome was equal in the groups; 63 of 433 (11.6%) in the intervention group, versus 53 of 532 (10.7%) in the control group [RR: 1.1 95% CI 0.7–1.5)]. The growth-restricted fetuses were more often identified prior to birth in the intervention group than in the control group; 20 of 23 fetuses (87.0%) versus 12 of 20 fetuses (60.0%), respectively, [RR: 1.5 (95% CI 1.0–2.1)]. In the intervention group two babies (0.4%) had Apgar scores <4 at 1 minute, versus 12 (2.3%) in the control group [RR: 0.2 (95% CI 0.04–0.7)]. The frequency of consultations for decreased fetal movement was 71 (13.1%) and 57 (10.7%) in the intervention and control groups, respectively [RR: 1.2 (95% CI 0.9–1.7)]. The frequency of interventions was similar in the groups. Conclusions Maternal ability to detect clinically important changes in fetal activity seemed to be improved by fetal movement counting; there was an increased identification of fetal growth restriction and improved perinatal outcome, without inducing more consultations or obstetric intervention

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Integrating Positive and Clinical Psychology: Viewing Human Functioning as Continua from Positive to Negative Can Benefit Clinical Assessment, Interventions and Understandings of Resilience

In this review we argue in favour of further integration between the disciplines of positive and clinical psychology. We argue that most of the constructs studied by both positive and clinical psychology exist on continua ranging from positive to negative (e.g., gratitude to ingratitude, anxiety to calmness) and so it is meaningless to speak of one or other field studying the “positive” or the “negative”. However, we highlight historical and cultural factors which have led positive and clinical psychologies to focus on different constructs; thus the difference between the fields is more due to the constructs of study rather than their being inherently “positive” or “negative”. We argue that there is much benefit to clinical psychology of considering positive psychology constructs because; (a) constructs studied by positive psychology researchers can independently predict wellbeing when accounting for traditional clinical factors, both cross-sectionally and prospectively, (2) the constructs studied by positive psychologists can interact with risk factors to predict outcomes, thereby conferring resilience, (3) interventions that aim to increase movement towards the positive pole of well-being can be used encourage movement away from the negative pole, either in isolation or alongside traditional clinical interventions, and (4) research from positive psychology can support clinical psychology as it seeks to adapt therapies developed in Western nations to other cultures

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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