A New Accelerated Method for Molecular Dynamics Simulations of Nanocrystalline Materials

Alexander Bondarenko

I will present a novel approach for accelerating conventional integration algorithms for Molecular Dynamics (MD) simulations of nanocrystalline materials.  Our method is based on Multiple Time-Step (MTS) idea, which recognizes several time scales present for the atomic forces and evaluates secondary slow-varying forces inexpensively.  The novel idea in our approach is the approximation of the slow-varying forces by Taylor expansion in displacement.  I will present numerical experiments showing that for ennard-Jones systems in solid state this method give a speed-up of at least 2 times over the conventional 5th order Gear redictor-corrector method, while maintaining reasonable (comparable) energy conservation and internal stress levels.  I will also comment on applicability of this method to systems governed by more realistic potentials, such as EAM and Glue, and gained speed-ups.


Extending Ruppert's Algorithm

Steven E. Pav

Ruppert's algorithm is a method of constructing conforming (2-d) Delaunay Triangulations with (shape) quality guarantees for oderately restricted input. Recent work with Noel Walkington, Guy Blelloch, and Gary Miller has focused on the following extensions:
 * Eliminating input restrictions in two dimensions.
 * Extending the algorithm to create 3-d triangulations for (less moderately) restricted input.
 * Seeing (then proving) that the 3-d case is actually sufficient for arbitrary dimensions. (this result still tenuous)
This talk will feature an introduction to Delaunay triangulations, triangle geometry, local feature size, Ruppert's proof methodology, and the aforementioned extensions.  As a grand finale, portraits of Lake Superior meshed by Ruppert's method will astound, amaze, and dispel all doubts


Combinatorial and computational problems arising in the design of hybridization based chips.

Bjarni Halldorsson

Recent advances in biotechnology allow for building chips to recognize DNA and proteins.  We start with giving the motivation for building these chips. We then give a description of the computational problems that arise and our implementation. Lastly, we point to some combinatorial problems that arise and our solution to some of them.


Black and Scholes Model with Proportional Transaction Costs

Juan Carlos Rivera

In the Black-Scholes financial model most of the natural questions, from a financial point of view, have been resolved: pricing, edging, utility maximization. One of its main characteristics is the assumption of a frictionless market. In the extended BS model with pressence of proportional transaction costs, we compare both questions and answers to those problems, trying to arrive to the dual theory behind the problem.


The Stable Circuit Problem

Rachel Rue

A min/max/average circuit is a circuit each of whose gates outputs  the minimum, the maximum, or the average of its inputs.   An
input to a gate may be the output of any gate in the circuit, or it may be 0 or 1.   Feedback is allowed. A stable assignment of values to the outputs is one for which every gate outputs the correct value, given its inputs.  The problem is to find an algorithm which produces a stable assignment for an n-gate  max/min/average circuit in time polynomial in n.   It can be shown that there always exists some stable assignment. It can also be shown that simply starting the circuit in some assignment and letting it run can take nfinite time to converge to a solution: consider the circuit with a single average gate G, where G outputs the average of G and 1.  If the output of G is initially set to 0, it will be reset to 1/2 ,  3/4, 7/8, 15/16, and so on.  The talk will present a variety of partial results, and show how the stable circuit problem encodes several other widely studied problems.


Set Variables in Higher Order Theorem Proving

Chad E. Brown

Often the key step in a proof is the construction of an appropriate set or relation. Accordingly, one of the difficult problems when proving theorems in higher order logic is instantiating set or relation variables.  In my talk, I will indicate some approaches I am using to attack this problem.