Subdiagrams of Bratteli diagrams supporting finite invariant measures

We study finite measures on Bratteli diagrams invariant with respect to the tail equivalence relation. Amongst the proved results on finiteness of measure extension, we characterize the vertices of a Bratteli diagram that support an ergodic finite invariant measure.Comment: 9 page

Invariant Measures on Stationary Bratteli Diagrams

We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the Vershik map). These measures are completely described by the incidence matrix of the diagram. Since such diagrams correspond to substitution dynamical systems, this description gives an algorithm for finding invariant probability measures for aperiodic non-minimal substitution systems. Several corollaries of these results are obtained. In particular, we show that the invariant measures are not mixing and give a criterion for a complex number to be an eigenvalue for the Vershik map.Comment: 40 pages. Exposition is reworke

Gas gun shock experiments with single-pulse x-ray phase contrast imaging and diffraction at the Advanced Photon Source

The highly transient nature of shock loading and pronounced microstructure effects on dynamic materials response call for {\it in situ}, temporally and spatially resolved, x-ray-based diagnostics. Third-generation synchrotron x-ray sources are advantageous for x-ray phase contrast imaging (PCI) and diffraction under dynamic loading, due to their high photon energy, high photon fluxes, high coherency, and high pulse repetition rates. The feasibility of bulk-scale gas gun shock experiments with dynamic x-ray PCI and diffraction measurements was investigated at the beamline 32ID-B of the Advanced Photon Source. The x-ray beam characteristics, experimental setup, x-ray diagnostics, and static and dynamic test results are described. We demonstrate ultrafast, multiframe, single-pulse PCI measurements with unprecedented temporal ($<$100 ps) and spatial ($\sim$2 $\mu$m) resolutions for bulk-scale shock experiments, as well as single-pulse dynamic Laue diffraction. The results not only substantiate the potential of synchrotron-based experiments for addressing a variety of shock physics problems, but also allow us to identify the technical challenges related to image detection, x-ray source, and dynamic loading

Perfect orderings on finite rank Bratteli diagrams

Given a Bratteli diagram B, we study the set OB of all possible orderings on B and its subset PB consisting of perfect orderings that produce Bratteli–Vershik topological dynamical systems (Vershik maps). We give necessary and sufficient conditions for the ordering ω to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths constrains significantly the values of the entries of the incidence matrices and the structure of the diagram B. Our proofs are based on the new notions of skeletons and associated graphs, defined and studied in the paper. For a Bratteli diagram B of rank k, we endow the set OB with product measure µ and prove that there is some 1 ≤ j ≤ k such that µalmost all orderings on B have j maximal and j minimal paths. If j is strictly greater than the number of minimal components that B has, then µ-almost all orderings are imperfect

Contextualizing the relevance of basic sciences: small-group simulation with debrief for first- and second-year medical students in an integrated curriculum.

There has been a call for increased integration of basic and clinical sciences during preclinical years of undergraduate medical education. Despite the recognition that clinical simulation is an effective pedagogical tool, little has been reported on its use to demonstrate the relevance of basic science principles to the practice of clinical medicine. We hypothesized that simulation with an integrated science and clinical debrief used with early learners would illustrate the importance of basic science principles in clinical diagnosis and management of patients.Small groups of first- and second-year medical students were engaged in a high-fidelity simulation followed by a comprehensive debrief facilitated by a basic scientist and clinician. Surveys including anchored and open-ended questions were distributed at the conclusion of each experience.The majority of the students agreed that simulation followed by an integrated debrief illustrated the clinical relevance of basic sciences (mean ± standard deviation: 93.8% ± 2.9% of first-year medical students; 96.7% ± 3.5% of second-year medical students) and its importance in patient care (92.8% of first-year medical students; 90.4% of second-year medical students). In a thematic analysis of open-ended responses, students felt that these experiences provided opportunities for direct application of scientific knowledge to diagnosis and treatment, improving student knowledge, simulating real-world experience, and developing clinical reasoning, all of which specifically helped them understand the clinical relevance of basic sciences.Small-group simulation followed by a debrief that integrates basic and clinical sciences is an effective means of demonstrating the relationship between scientific fundamentals and patient care for early learners. As more medical schools embrace integrated curricula and seek opportunities for integration, our model is a novel approach that can be utilized