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.

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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

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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.

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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.

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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.

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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.