Dynamical versus diffraction spectrum for structures with finite local complexity

It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.Comment: 27 pages; some minor revisions and improvement

Truncated long-range percolation on oriented graphs

We consider different problems within the general theme of long-range percolation on oriented graphs. Our aim is to settle the so-called truncation question, described as follows. We are given probabilities that certain long-range oriented bonds are open; assuming that the sum of these probabilities is infinite, we ask if the probability of percolation is positive when we truncate the graph, disallowing bonds of range above a possibly large but finite threshold. We give some conditions in which the answer is affirmative. We also translate some of our results on oriented percolation to the context of a long-range contact process.Comment: 9 pages, 1 figur

Training less-experienced faculty improves reliability of skills assessment in cardiac surgery

OBJECTIVE: Previous work has demonstrated high inter-rater reliability in the objective assessment of simulated anastomoses among experienced educators. We evaluated the inter-rater reliability of less-experienced educators and the impact of focused training with a video-embedded coronary anastomosis assessment tool. METHODS: Nine less-experienced cardiothoracic surgery faculty members from different institutions evaluated 2 videos of simulated coronary anastomoses (1 by a medical student and 1 by a resident) at the Thoracic Surgery Directors Association Boot Camp. They then underwent a 30-minute training session using an assessment tool with embedded videos to anchor rating scores for 10 components of coronary artery anastomosis. Afterward, they evaluated 2 videos of a different student and resident performing the task. Components were scored on a 1 to 5 Likert scale, yielding an average composite score. Inter-rater reliabilities of component and composite scores were assessed using intraclass correlation coefficients (ICCs) and overall pass/fail ratings with kappa. RESULTS: All components of the assessment tool exhibited improvement in reliability, with 4 (bite, needle holder use, needle angles, and hand mechanics) improving the most from poor (ICC range, 0.09-0.48) to strong (ICC range, 0.80-0.90) agreement. After training, inter-rater reliabilities for composite scores improved from moderate (ICC, 0.76) to strong (ICC, 0.90) agreement, and for overall pass/fail ratings, from poor (kappa = 0.20) to moderate (kappa = 0.78) agreement. CONCLUSIONS: Focused, video-based anchor training facilitates greater inter-rater reliability in the objective assessment of simulated coronary anastomoses. Among raters with less teaching experience, such training may be needed before objective evaluation of technical skills

Cooperative Behavior of Kinetically Constrained Lattice Gas Models of Glassy Dynamics

Kinetically constrained lattice models of glasses introduced by Kob and Andersen (KA) are analyzed. It is proved that only two behaviors are possible on hypercubic lattices: either ergodicity at all densities or trivial non-ergodicity, depending on the constraint parameter and the dimensionality. But in the ergodic cases, the dynamics is shown to be intrinsically cooperative at high densities giving rise to glassy dynamics as observed in simulations. The cooperativity is characterized by two length scales whose behavior controls finite-size effects: these are essential for interpreting simulations. In contrast to hypercubic lattices, on Bethe lattices KA models undergo a dynamical (jamming) phase transition at a critical density: this is characterized by diverging time and length scales and a discontinuous jump in the long-time limit of the density autocorrelation function. By analyzing generalized Bethe lattices (with loops) that interpolate between hypercubic lattices and standard Bethe lattices, the crossover between the dynamical transition that exists on these lattices and its absence in the hypercubic lattice limit is explored. Contact with earlier results are made via analysis of the related Fredrickson-Andersen models, followed by brief discussions of universality, of other approaches to glass transitions, and of some issues relevant for experiments.Comment: 59 page

Dynamical versus diffraction spectrum for structures with finite local complexity

It is well known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as ergodic Delone dynamical systems, both via suitable embeddings. The connection is rather well understood when the spectrum is pure point, where the two spectral notions are essentially equivalent. In general, however, the dynamical spectrum is richer. Here, we consider (uniquely) ergodic systems of finite local complexity and establish the equivalence of the dynamical spectrum with a collection of diffraction spectra of the system and certain factors. This equivalence gives access to the dynamical spectrum via these diffraction spectra. It is particularly useful as the diffraction spectra are often simpler to determine and, in many cases, only very few of them need to be calculated.</p

Statistical Mechanics of Classical and Disordered Systems

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