Global Position Systems and other navigation systems that collect spatial data through an array of sensors carried on by people and distributed in space have changed the way we navigate complex environments, such as cities. However, indoor navigation without reliable GPS signals relies on wall-mounted antennas, WiFi, or quantum sensors. Despite the gains of such technologies, underlying these n...

Several optimal three-dimensional orbital transfer problems are solved for thrust-limited spacecrafts using collocation and nonlinear programming techniques. The solutions for full nonlinear equations of motion are obtained where the integrals of the free Keplerian motion in three dimensions are utilized for coasting arcs. In order to limit the solution space, interior-point constraints are use...

Fig. 1. Visualizations of the hemoglobin molecule undergoing dynamic deformation as oxygen binds to it. (a) A primal space visualization of the first time step with the heme group identified. (b) Visualization of the complementary space of the first time step shows the geometry of the interior. The surface has been made transparent, revealing a large tunnel through the surface (yellow) with man...

This is an expository article, explaining recent work by D. Groisser and myself [GS] on the extent to which the boundary region of moduli space contributes to the “simple type” condition of Donaldson theory. The presentation is intended to complement [GS], presenting the essential ideas rather than the analytical details. It is shown that the boundary region of moduli space contributes 6/64 of ...