Edgar N. Reyes

Optimization using simulated annealing

Presents the simulated annealing algorithm (a stochastic optimization technique used in solving combinatorial optimization problems) and discuss an application in solving problems pertaining to engineering. The application upon which we will concentrate is global wiring of integrated circuits.

Answering typical student questions in hyperbolic geometry: a transformation group approach

It is shown that the bisector of a segment of a geodesic and the bisector of an angle in hyperbolic geometry can be expressed in terms of points which are equidistant from the end points of the segment, and points that are equidistant from the rays of the angle, respectively. An important tool in the approach is that the shortest distance between a point and a geodesic is the perpendicular distance.

Homomorphisms of ergodic group actions and conjugacy of skew product actions

Let G be a locally compact group acting ergodically on X. We discuss relationships between homomorphisms on the measured groupoid X×G, conjugacy of skew product extensions, and similarity of measured groupoids. To do this, we describe the structure of homomorphisms on X×G whose restriction to an extension given by a skew product action is the trivial homomorphism.