Schubert calculus of Richardson varieties stable under spherical Levi subgroups

We observe that the expansion in the basis of Schubert cycles for $H^*(G/B)$ of the class of a Richardson variety stable under a spherical Levi subgroup is described by a theorem of Brion. Using this observation, along with a combinatorial model of the poset of certain symmetric subgroup orbit closures, we give positive combinatorial descriptions of certain Schubert structure constants on the full flag variety in type $A$. Namely, we describe $c_{u,v}^w$ when $u$ and $v$ are inverse to Grassmannian permutations with unique descents at $p$ and $q$, respectively. We offer some conjectures for similar rules in types $B$ and $D$, associated to Richardson varieties stable under spherical Levi subgroups of SO(2n+1,\C) and SO(2n,\C), respectively.Comment: Section 4 significantly shortened, and other minor changes made as suggested by referees. Final version, to appear in Journal of Algebraic Combinatoric

Computation of protein geometry and its applications: Packing and function prediction

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The algorithms of Delaunay triangulation, computation of voids and pockets, as well volume/area computation are also described. In addition, applications in packing analysis of protein structures and protein function prediction are also discussed.Comment: 32 pages, 9 figure

Magnetic Coordinate Systems

Geospace phenomena such as the aurora, plasma motion, ionospheric currents and associated magnetic field disturbances are highly organized by Earth's main magnetic field. This is due to the fact that the charged particles that comprise space plasma can move almost freely along magnetic field lines, but not across them. For this reason it is sensible to present such phenomena relative to Earth's magnetic field. A large variety of magnetic coordinate systems exist, designed for different purposes and regions, ranging from the magnetopause to the ionosphere. In this paper we review the most common magnetic coordinate systems and describe how they are defined, where they are used, and how to convert between them. The definitions are presented based on the spherical harmonic expansion coefficients of the International Geomagnetic Reference Field (IGRF) and, in some of the coordinate systems, the position of the Sun which we show how to calculate from the time and date. The most detailed coordinate systems take the full IGRF into account and define magnetic latitude and longitude such that they are constant along field lines. These coordinate systems, which are useful at ionospheric altitudes, are non-orthogonal. We show how to handle vectors and vector calculus in such coordinates, and discuss how systematic errors may appear if this is not done correctly

Using role-play to improve students’ confidence and perceptions of communication in a simulated volcanic crisis

Traditional teaching of volcanic science typically emphasises scientific principles and tends to omit the key roles, responsibilities, protocols, and communication needs that accompany volcanic crises. This chapter provides a foundation in instructional communication, education, and risk and crisis communication research that identifies the need for authentic challenges in higher education to challenge learners and provide opportunities to practice crisis communication in real-time. We present an authentic, immersive role-play called the Volcanic Hazards Simulation that is an example of a teaching resource designed to match professional competencies. The role-play engages students in volcanic crisis concepts while simultaneously improving their confidence and perceptions of communicating science. During the role-play, students assume authentic roles and responsibilities of professionals and communicate through interdisciplinary team discussions, media releases, and press conferences. We characterised and measured the students’ confidence and perceptions of volcanic crisis communication using a mixed methods research design to determine if the role-play was effective at improving these qualities. Results showed that there was a statistically significant improvement in both communication confidence and perceptions of science communication. The exercise was most effective in transforming low-confidence and low-perception students, with some negative changes measured for our higher-learners. Additionally, students reported a comprehensive and diverse set of best practices but focussed primarily on the mechanics of science communication delivery. This curriculum is a successful example of how to improve students’ communication confidence and perceptions