Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

Characterization of the stretched exponential trap-time distributions in one-dimensional coupled map lattices

Stretched exponential distributions and relaxation responses are encountered in a wide range of physical systems such as glasses, polymers and spin glasses. As found recently, this type of behavior occurs also for the distribution function of certain trap time in a number of coupled dynamical systems. We analyze a one-dimensional mathematical model of coupled chaotic oscillators which reproduces an experimental set-up of coupled diode-resonators and identify the necessary ingredients for stretched exponential distributions.Comment: 8 pages, 8 figure

Relationship between dynamical heterogeneities and stretched exponential relaxation

We identify the dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for particles in atomic or molecular systems, or spin states in magnetic materials. At the onset of the dynamical heterogeneity, the distribution of time intervals spent in such domains or traps becomes stretched exponential at long time. We rigorously show that once this is the case, the autocorrelation function of the renewal process formed by these time intervals is also stretched exponential at long time.Comment: 8 pages, 4 figures, submitted to PR

The phase transition of the quantum Ising model is sharp

An analysis is presented of the phase transition of the quantum Ising model with transverse field on the d-dimensional hypercubic lattice. It is shown that there is a unique sharp transition. The value of the critical point is calculated rigorously in one dimension. The first step is to express the quantum Ising model in terms of a (continuous) classical Ising model in d+1 dimensions. A so-called `random-parity' representation is developed for the latter model, similar to the random-current representation for the classical Ising model on a discrete lattice. Certain differential inequalities are proved. Integration of these inequalities yields the sharpness of the phase transition, and also a number of other facts concerning the critical and near-critical behaviour of the model under study.Comment: Small changes. To appear in the Journal of Statistical Physic

An automated workflow based on hip shape improves personalized risk prediction for hip osteoarthritis in the CHECK study

Objective: To design an automated workflow for hip radiographs focused on joint shape and tests its prognostic value for future hip osteoarthritis. Design: We used baseline and 8-year follow-up data from 1,002 participants of the CHECK-study. The primary outcome was definite radiographic hip osteoarthritis (rHOA) (Kellgren–Lawrence grade ≥2 or joint replacement) at 8-year follow-up. We designed a method to automatically segment the hip joint from radiographs. Subsequently, we applied machine learning algorithms (elastic net with automated parameter optimization) to provide the Shape-Score, a single value describing the risk for future rHOA based solely on joint shape. We built and internally validated prediction models using baseline demographics, physical examination, and radiologists scores and tested the added prognostic value of the Shape-Score using Area-Under-the-Curve (AUC). Missing data was imputed by multiple imputation by chained equations. Only hips with pain in the corresponding leg were included. Results: 84% were female, mean age was 56 (±5.1) years, mean BMI 26.3 (±4.2). Of 1,044 hips with pain at baseline and complete follow-up, 143 showed radiographic osteoarthritis and 42 were replaced. 91.5% of the hips had follow-up data available. The Shape-Score was a significant predictor of rHOA (odds ratio per decimal increase 5.21, 95%-CI (3.74–7.24)). The prediction model using demographics, physical examination, and radiologists scores demonstrated an AUC of 0.795, 95%-CI (0.757–0.834). After addition of the Shape-Score the AUC rose to 0.864, 95%-CI (0.833–0.895). Conclusions: Our Shape-Score, automatically derived from radiographs using a novel machine learning workflow, may strongly improve risk prediction in hip osteoarthritis

Surgical Task Shifting in Sub-Saharan Africa

Kathryn Chu and colleagues discuss some of the experiences of surgical task shifting to date, and outline lessons from task shifting in the delivery of HIV/AIDS care