This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse ...

A novel tracking paradigm for flying geometric trajectories using tethered kites is presented. It is shown how the differential-geometric notion of turning angle can be used as a one-dimensional representation of the kite trajectory, and how this leads to a single-input single-output (SISO) tracking problem. Based on this principle a Lyapunov-based nonlinear adaptive controller is developed tha...

This letter demonstrates the potential for using diffuse ultrasound measurements to detect damage in concrete. Two different solutions to the diffusion equation, an infinite three-dimensional (3D) volume model that neglects geometric boundaries and a finite 3D cuboid model, are used for the required curve fitting procedure to determine the influence of geometric boundaries on the solution. The ...

We analyze two models of random geometries : planar hyper-cubic random surfaces and four dimensional simplicial quantum gravity. We show for the hyper-cubic random surface model that a geometrical constraint does not change the critical properties of the model compared to the model without this constraint. We analyze the phase diagram for the model with extrinsic curvature. For four dimensional...

Under certain mild condition, the Pareto-optimal set (PS) of a continuous multiobjective optimization problem, with m objectives, is a piece-wise continuous (m 1)-dimensional manifold. This regularity property is important, yet has been unfortunately ignored in many evolutionary multiobjective optimization (EMO) studies. The first work that explicitly takes advantages of this regularity propert...