Group

Topic

Abstract

Neil Johnson, Nasim Shomali

Polyominos in Sage

We created a polyomino library for sage. Poltominos of course being shapes created from adjacently tiled squares. We implemented lots of functionality to manipulate and keep track of sets of these pieces.

Matthew Zemek

Implementing Optional Line Numbering for Error Tracking

As Sage currently exists there is no option to add line numbers while programming and troubleshooting, making such an addition a clear and simple modification to the interface to increase accessibility. If time allows an option to pan between coding errors by line number will be added as well.

Quan Lam

Classifying Music By Genre using Linear Discriminant Analysis and Principal Component Analysis with Sage

The Linear Discriminant Analysis and Principal Component Analysis are popular techniques used in statistics, pattern recognition, machine learning, etc. These techniques can be useful in detecting a "pattern" of an audio file comparing to a certain training set and classify it into genres, except that a music file usually contains a large amount of information that would make the procedure take quite some time. With the computational power of the Sage system as well as all the well define libraries of functions, applying these techniques to music files would be practical.

Chris Johnson

A Poker Equity Calculator

An equity calculator is a useful tool in playing and understanding poker. These are the percentages next to hands in televised poker. For example, a pair of queens is a 54/46 favorite versus ace-king suited. This project will compute hand equities statistically by analyzing the results over a significant sample.

Andrew Piper, Charlie Sprague

Image Filtering in Sage

Using fourier analysis within Sage to decompose an image into its fourier modes and use a linear filter to remove as much 'noise' as possible while retaining an acceptable amount image quality. By using a 2 dimensional fourier transform the dominant modes of the image become apparent and a specific filter can be applied to reduce the amount of noise to near zero creating a somewhat cleaner looking image.

Kevin Wierman

A Monte Carlo Simulation of the Statistics of Social

I plan to create a model of the social norms of interpersonal interactions on the Seattle Metro busses. This will include deterministic algorithms to simulate seat choice and grouping of people based off of random variables assigned to an "event" (person entering the bus/exiting the bus). Sage will be used in order to provide an easy integration of graphics and statistical tools as well as access to precompiled code.

Andrea Frank, Spencer Hawes, Harmony Mak, Brian Manion, Eddie Tsay, Spencer Wood

Tools for the Quantitative Finance Library

Presenting various tools that will be of use to people interested in quantitative finance. Topics included (not a complete list): Value-at-Risk, univariate statistics, covariance matrices of several assets, and the Black-Scholes Option Pricing Model.

Michael Snider

Elliptic Curve Cryptography

Over the past 26 years, elliptic curves over finite fields have been used to perform public-key encryption. Sage does a really good job at creating and handling elliptic curves. Taking advantage of this I will demonstrate an implementation of this encryption method. Using Sage, I plan to demonstrate a few different examples of how this works over a few different elliptic curves including some special curves that are optimized for this sort of process.

Andrew Richman

Using Markov Chains to produce statistically similar sound

Markov Chains have been used to produce music before, but usually based on note values. With Sage's power to process large arrays of numbers quickly, I use Markov Chains to produce statistically similar sounds using the data from wave files instead of notation. I believe that this will produce more organic sounding music because it will preserve the imperfections that make us perceive music the way we do.

Sunnye Kim, Daniel Riness

Linear Optimization Checking

An introduction to Linear Programming and the methods used to solve standard LP's. For students initially going in to Linear Programming, a lot of matrix algebra is thrown at them with some new ways to pivot, augment matrices, etc..., we will give a brief overview of standard form LP's, how you pivot, how the pivoting process works (and how there are multiple ways to get to the same solution), as well as at least one (movement along the vertices of a convex polyhedron) graphical aspect of LP (and if time permits, the use of the gradient of the cost function) for 2 and 3 dimensions. The actual pivoting algorithm can be expanded way beyond that.

Alex Holland

Guessing closed form representations of a given sequence of

I plan on mimicking wolfram alpha's "possible closed form" function which, when given an input such as [14, 17, 20, 23, 26] will give an output like "a_n = 3n + 11" (where it assumes the input given is the first few terms of a sequence and it guesses what that sequence is)I hope to have this working for several types of datasets, not just integers, such as the input [.2, .4, .6, .8, 1] returning "a_n = n/5", etc...