Moduli of sheaves: a modern primer

We give a modern introduction to the moduli of sheaves. After reviewing the classical theory, we give a catalogue of results from the last decade. We then consider a more "symmetric" formulation of the theory by working with gerbes from the start.Comment: 26 pages, contribution to proceedings of 2015 AMS Summer Institute in Algebraic Geometr

Fast MLE Computation for the Dirichlet Multinomial

Given a collection of categorical data, we want to find the parameters of a Dirichlet distribution which maximizes the likelihood of that data. Newton's method is typically used for this purpose but current implementations require reading through the entire dataset on each iteration. In this paper, we propose a modification which requires only a single pass through the dataset and substantially decreases running time. Furthermore we analyze both theoretically and empirically the performance of the proposed algorithm, and provide an open source implementation

Specialized turbomolecular pumping stage for RF ion thrusters

This paper proposes the application of a highly specialized Turbomolecular Vacuum Pump (TMP) device as a subsystem for electrostatic RF ion thrusters, using D. Fearn’s Dual-Stage 4-Grid design as a cutting-edge example. The TMP turbine’s rotor impulse is transmitted via collisions to neutral gas atoms en route to their ionization, with the goal of producing an anisotropic ion flux that is directed at the extracting screen grid. Operating regimes of such thruster design are hypothesized, and electromagnetic complexities of realization of this concept are identified