A configuration $(p_q, n_k)$ is a collection of $p$ points and $n$ straight lines in the Euclidean plane so that every point has $q$ straight lines passing through it and every line has $k$ points lying on it. A configuration is astral if it has precisely $\lfloor {q+1\over2} \rfloor$ symmetry classes (transitivity classes) of lines and $\lfloor{k+1\over2} \rfloor$ symmetry classes of points. An even astral configuration is an astral configuration configuration where $q$ and $k$ are both even. This paper completes the classification of all even astral configurations.

A conjecture of Branko Grünbaum concerning what astral (n 4 ) configurations exist is shown to be true.

We describe the design, fabrication, and validation of a cryogenically-compatible quasioptical thermal source designed to be used for characterization of detector arrays. The source is constructed using a graphite-loaded epoxy mixture that is molded into a tiled pyramidal structure. The mold is fabricated using a hardened steel template produced via a wire EDM process. The absorptive mixture is bonded to a copper backplate enabling thermalization of the entire structure. The source reflectance is measured from 30-300 GHz and compared to models.

A simplicial arrangement of pseudolines is a collection of topological lines in the projective plane where each region that is formed is triangular. This paper refines and develops David Eppstein's notion of a kaleidoscope construction for symmetric pseudoline arrangements to construct and analyze several infinite families of simplicial pseudoline arrangements with high degrees of geometric symmetry. In particular, all simplicial pseudoline arrangements with the symmetries of a regular $k$-gon and three symmetry classes of pseudolines, consisting of the mirrors of the $k$-gon and two other symmetry classes, plus sometimes the line at infinity, are classified, and other interesting families (with more symmetry classes of pseudolines) are discussed.

A geometric k-configuration is a collection of points and straight lines in the plane so that k points lie on each line and k lines pass through this point. We introduce a new construction method for constructing k-configurations with non-trivial dihedral or chiral (i.e., purely rotational) symmetry, for any k ≥ 3; the configurations produced have 2 k−2 symmetry classes of points and lines. The construction method produces the only known infinite class of symmetric geometric 7-configurations, the second known infinite class of symmetric geometric 6-configurations, and the only known 6-configurations with chiral symmetry.

An obstacle representation of a graph G is a straight-line drawing of G in the plane together with a collection of connected subsets of the plane, called obstacles, that block all non-edges of G while not blocking any of the edges of G. The obstacle number obs(G) is the minimum number of obstacles required to represent G.We study the structure of graphs with obstacle number greater than one. We show that the icosahedron has obstacle number 2, thus answering a question of Alpert, Koch, & Laison asking whether all planar graphs have obstacle number at most 1. We also show that the 1-skeleton of a related polyhedron, the gyroelongated 4-bipyramid, has obstacle number 2. The order of this graph is 10, which is also the order of the smallest known graph with obstacle number 2.Some of our methods involve instances of the Satisfiability problem; we make use of various "SAT solvers" in order to produce computer-assisted proofs.

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BackgroundFull disclosure of patient safety events (PSE) is desired by patients and their families, is required by the Joint Commission and many state laws, and is vital to improving patient outcomes. A key barrier to consistent disclosure of patient safety events is a self-reported lack of proper training. Physicians must be trained to recognize when a PSE has occurred and effectively carry out disclosure, all while caring for a patient who is actively experiencing the consequences of an unintended outcome. Immersive simulation provides the opportunity to practice this complex skill.ObjectiveTo develop and evaluate a simulation-based workshop for pediatric residents on the disclosure of patient safety events.MethodsA workshop in PSE disclosure was developed according to literature review, expert consultation, and feedback from hospital administration. The three-hour workshop included a simulated PSE with a subsequent standardized debriefing, interactive didactic session, and additional simulation-based hands-on practice in disclosure. Participants completed an anonymous survey at one-week and three-months post workshop, assessing workshop satisfaction, subsequent clinical experience, and perceived change to their practice.ResultsDuring the one-year study period, 27/31 (87.0%) second year residents completed the workshop. At the one-week follow-up, all study participants reported increased confidence and preparedness in their ability to lead the initial disclosure conversation. All study participants felt that the simulated scenarios were realistic and relevant to their current clinical duties and 33.3% (n=9) stated that they would like to repeat this workshop prior to completion of their training. At the three-month follow-up, 29.6% (N=8) of study participants reported involvement in the disclosure of a patient safety event since the workshop with all eight reporting feeling adequately prepared by the workshop for this experience. Study participants indicated that post training they were more likely to engage the attending physician, risk management and patient relations in the disclosure conversation (p <=0.05). The estimated cost of this simulation training for 27 residents was $6,993, not accounting for the 39 hours per clinician facilitator.ConclusionsImmersive simulation is uniquely suited for teaching difficult conversation skills that are encountered during acute care, including the disclosure of patient safety events. While hands-on practice is critical, faculty and simulation resources required for continued implementation may not be sustainable long-term. Future training curricula should leverage creative and innovative adult-learning techniques to reach a wide range of members of the care team with less resource utilization.