Conferences

ISMB 2010
July 11-14, 2010
Poster: Incorporating developmental information in functional networks for Arabidopsis thaliana

RiboWest Conference
July 23-25, 2006
Poster: Hierarchical Model for Pseudoknotted RNA Secondary Structure Prediction

BC.NET/ Netera Advanced Networks Conference
April 25-26, 2006
Presentation: Security Analysis of an RF Biometric Fingerprint Scanner

UBC Multidisciplinary Undergraduate Research Conference
March 4, 2006
Poster: Security Analysis of a Biometric Fingerprint Scanner

Undergraduate Thesis
My final undergraduate project in the UBC Electrical and Computer Engineering Department was with Dr. Rafeef Abugharbieh. My topic was micro-array image processing in Matlab. The program was capable of taking as input a high-resolution image of a micro-array and performing operations on it to remove unimportant shapes and to ultimately recognize the spots. The final report is available below.

Report: Computational Analysis of Micro-Array Data

Undergraduate Research
I was awarded an Undergraduate Student Research Award (USRA) from the National Science and Engineering Research Council (NSERC) for three summers from 2004-2006.

Summer 2006
I worked with the UBC Computer Science Department under the supervision of Dr. Anne Condon. I was working in the Beta Lab. This project contributes to a problem with applications in the microbiology field: RNA secondary structure prediction. We implemented an algorithm that was theoretically devised by another grad student. Her algorithm includes RNA secondary structure prediction with pseudoknots. A paper on this work is available in the Conference Proceedings: Lectures in Computer Science of the 2007 Workshop on Algorithms in Bioinformatics (WABI).

Summer 2005
I worked with the UBC Computer Science Department under the supervision of Dr. Joel Friedman. This project was meant to be an extension on the Summer 2004 project. Because d-regular graphs have already been analyzed and researchers have already found most of their properties, I focused on graphs that are not d-regular. Specifically, I looked at a certain type of graph (one with connections between successive vertices and self loops at random vertices) and plotted the eigenvalues of its non-backtracking walk matrix. The eigenvalues for a specific shape that is similar to all such graphs and is determined by the number of total self-loops. The final report is available below.

Abstract:
A non-backtracking matrix is a matrix whose entry (i, j) is the number of irreducible walks from i to j. That is, a step in a walk from i to j is not allowed to return along the edge that it just came on. Tests were done on the eigenvalues of this non-backtracking matrix for graphs with n entries such that:

• There exists an edge e between vertices (i, i + 1) for all i where 1 ≤i ≤n − 1 and between (n, 1)
• Self-loops exist at some vertices

The tests revealed that graphs with self loops at equally spaced vertices yield different clusters of eigenvalues for the non-backtracking matrix than those graphs with self-loops arranged at random vertices. Among the graphs with equally spaced self-loops, plots of the non-backtracking matrix for graphs with very sparse self-loops approaches the unit circle while graphs with self-loops at denser intervals approaches a circle with radius √(d − 1) where d is the degree of a vertex. Graphs with randomly spaced self-loops yield plots with more disorderly points arranged in a similar shape to that given by graphs with equally spaced self-loops.

Report: Eigenvalues of Non-Backtracking Walks in a Graph

Summer 2004
I worked with the UBC Mathematics Department under the supervision of Dr. Joel Friedman. The final report is available below.

Abstract:
In this paper, a graph is discussed as being Ramanujan if its second largest eigenvalue, calculated from its adjacency matrix, follows the relation λ₂ ≤ 2√(d – 1). Several tests were performed regarding the percentage of Ramanujan graphs and covers, but the main focus was on the relationship between the signed cover and the base eigenvalues. Numerical tests done on d-regular Ramanujan graphs show that there is a threshold base eigenvalue where a good base expander has a greater chance of doing worse as a cover (i.e. the signed cover highest eigenvalue is greater than the base graph λ₂) then turns to a decent base expander that has a greater chance of doing no worse as a cover (i.e. the signed cover highest eigenvalue is smaller than the base graph λ₂). This threshold depends on both the degree of the vertices and the number of vertices, in that the threshold increases as these two quantities do.

Report: Ramanujan Graphs and their 2-Fold Covers