Digital Commons Network^™

On Agent Communication In Large Groups, Gary R. Greenfield

Department of Math & Statistics Technical Report Series

The problem is fundamental and natural, yet deep - to simulate the simplest possible form of communication that can occur within a large multi-agent system. It would be prohibitive to try and survey all of the research on "communication" in general so we must restrict our focus. We will devote our efforts to synthetic communication occurring within large groups. In particular, we would like to discover a model for communication that will serve as an abstract model, a prototype, for simulating communication within large groups of biological organisms.

Octary Codewords With Power Envelopes Of 3∗2M, Katherine M. Nieswand, Kara N. Wagner

Department of Math & Statistics Technical Report Series

This paper examines codewords of length 2^m in Z₈ with envelope power maxima of 3 ∗ 2^m. Using the general form for Golay pairs as a base, a general form is derived for the set of coset leaders that generate these codewords. From this general form it will be proven that there exists at least one element in the coset that achieves a power of 3 ∗ 2^m for each m-even and m-odd case.

The Set Of Hemispheres Containing A Closed Curve On The Sphere, Mary Kate Boggiano, Mark Desantis

Department of Math & Statistics Technical Report Series

Suppose you get in your car and take a drive on the sphere of radius R, so that when you return to your starting point the odometer indicates you've traveled less than 2πR. Does your path, γ, have to lie in some hemisphere?

This question was presented to us by Dr. Robert Foote of Wabash College. Previous authors chose two points, A and B, on γ such that these points divided γ into two arcs of equal length. Then they took the midpoint of the great circle arc joining A and B to be the North Pole and showed that …