Academic year 2006  2007
A Note on Stephan's Conjecture 77 by Chris Burns ('05) and Ben Purcell ('07)  This paper proves a conjecture made by Ralf Stephan based on an exhaustive analysis of the OnLine Encyclopedia of Integer Sequences. The conjecture concerns the reduction of binary strings in a one dimensional version of the Same Game. 
P.B. Kruskal ('05), J.J. Stanis, B.L. McNaughton, and P.J. Thomas 
A binless correlation measure reduces the variability of memory reactivation estimates. 
Academic year 2007  2008

Symplectic integrators have proven far superior to RungeKutta type methods in approximating the longterm, qualitative behavior of solutions to Hamiltonian systems of ODEs. In this paper we discuss what a symplectic map is and why these maps serve as the basis for a very effective numerical integration scheme for Hamiltonian systems. In particular, we use a fourthorder symplectic integration algorithm to unearth fractal structure in phase space for the trilinear 3body problem. We also provide a comparison with a fourthorder RungeKutta scheme. The surprisingly simple code for the symplectic integrator was written and executed in Matlab by the first author. 
Updated: November 29, 2007