Phil Gaudreau

● Attended the Pacific Institute for the Mathematical Sciences Math Modelling in Industry Workshop, University of British-Colombia, Canada
● Investigated the modeling and optimization of traffic light systems.
● Modeled car queue lengths at different types of traffic light intersections using a stochastic system of differential equations.
● Used under 1GB of Vancouver traffic data to estimate parameters in our model.
● Using Python, we optimized the duration of green lights in… Show more

● Attended the Pacific Institute for the Mathematical Sciences Math Modelling in Industry Workshop, University of British-Colombia, Canada
● Investigated the modeling and optimization of traffic light systems.
● Modeled car queue lengths at different types of traffic light intersections using a stochastic system of differential equations.
● Used under 1GB of Vancouver traffic data to estimate parameters in our model.
● Using Python, we optimized the duration of green lights in order to minimize the average waiting time. Show less

● Attended the 2016 Industrial Problem Solving Workshop at the Fields Institute in Toronto, Canada.
● With the contribution of the premier photography community and licensing marketplace that is 500px Inc., I worked in a team to predict the licensability of photos on their website.
● Gained some experience in computer vision and image processing algorithms such as adaptive Gaussian filters, principal component analysis, and convolutional neural networks.
● Using Python and Julia, we… Show more

● Attended the 2016 Industrial Problem Solving Workshop at the Fields Institute in Toronto, Canada.
● With the contribution of the premier photography community and licensing marketplace that is 500px Inc., I worked in a team to predict the licensability of photos on their website.
● Gained some experience in computer vision and image processing algorithms such as adaptive Gaussian filters, principal component analysis, and convolutional neural networks.
● Using Python and Julia, we trained a logistic regression classifier as well as a random forest classifier using over 1.5GB of images.

● http://www.fields.utoronto.ca/sites/default/files/IPSW%20500px%20Report.pdf Show less

● Spent some time at the Bamfield Marine Sciences Center as a visiting researcher.
● Validated an ecological phenomenon known as optimal foraging theory by examining if west coast Canadian bears actively chose which streams to catch salmon based on the complexity of the stream (bank depth, number of tree logs, current speed, etc..)
● Using the programming language R and under 1GB of field data, we trained a mixed-effect generalized linear model to test our hypothesis.
● Worked closely… Show more

● Spent some time at the Bamfield Marine Sciences Center as a visiting researcher.
● Validated an ecological phenomenon known as optimal foraging theory by examining if west coast Canadian bears actively chose which streams to catch salmon based on the complexity of the stream (bank depth, number of tree logs, current speed, etc..)
● Using the programming language R and under 1GB of field data, we trained a mixed-effect generalized linear model to test our hypothesis.
● Worked closely with ecologists applying mathematical and statistical methods to ecological problems. Show less

In quantum mechanics, the Schrödinger equation is the staple for investigating and understanding quantum phenomena. Adjunct with the Schrödinger equation, the mathematical and physical laboratory that are anharmonic oscillator potentials provide a powerful tool for modeling complex quantum systems. In my thesis work, we successfully apply the the double exponential Sinc-collocation method (DESCM) to the classical anharmonic potential for the numerical evaluation of energy eigenvalues. The DESCM… Show more

In quantum mechanics, the Schrödinger equation is the staple for investigating and understanding quantum phenomena. Adjunct with the Schrödinger equation, the mathematical and physical laboratory that are anharmonic oscillator potentials provide a powerful tool for modeling complex quantum systems. In my thesis work, we successfully apply the the double exponential Sinc-collocation method (DESCM) to the classical anharmonic potential for the numerical evaluation of energy eigenvalues. The DESCM was able to achieve unprecedented accuracy even in the case of multiple wells. This great success has lead us to our current research endeavors. In our current work, we wish to adapt the DESCM to the rational-anharmonic potential as well as the Coulombic-anharmonic potential. The rational-anharmonic potential has several complex singularities which impede the convergence of the DESCM. As a result, we investigate conformal mappings in order to relocate these complex singularities accelerating the convergence of the DESCM. The Coulombic-anharmonic potential has singularities at the end points of its domain which can affect the numerical stability of the DESCM. Subsequently, we investigate methods to remedy these numerical problems. Additionally, we wish to exploit the added symmetrical properties of the matrices generated by the DESCM in the presence of even potentials. We have been able to show that this added symmetry results in centrosymmetry. This added symmetry can be exploited to reduce the complexity of the DESCM by half.

The Julia code from my PhD thesis work on the DESCM is available on Github at https://github.com/pjgaudre/DESincEig.jl Show less

"Doctor, how long do I have left?" This is a question that is not only hard to ask, but is also hard to answer. In this project, we succeeded to shed light on the problems (and possible solutions) to obtaining a meaningful answer to this question via survival analysis.

Survival analysis is a far reaching and highly lucrative subject of study. Although we only explored the application to prediction of survival time for cancer patients, these tools and methods can be applied to a broad… Show more

"Doctor, how long do I have left?" This is a question that is not only hard to ask, but is also hard to answer. In this project, we succeeded to shed light on the problems (and possible solutions) to obtaining a meaningful answer to this question via survival analysis.

Survival analysis is a far reaching and highly lucrative subject of study. Although we only explored the application to prediction of survival time for cancer patients, these tools and methods can be applied to a broad class of problems. Those problems have the form "What are the chances that an event will occur after a certain time?". This event could be a nuclear war, a machine failing, an accident occurring or (some more cheerful examples) a lottery win, a birth, or even something as mundane as a day with nice weather.

Developing a variant of the Patient Specific Survival Prediction via Multitask logistic regression (PSSP via MTLR) algorithm, we trained a model using 1GB of data from Edmonton Cross Cancer Institute. We changed the original objective function for parameter learning to include a regularizing term minimizing the absolute loss between the predicted mean death and actual death time. For censored patients, we did not have their death-time and hence use a Kaplan-Meier estimate of the death time given the censored time. Show less

The monitoring of bird migrations in Alberta poses many difficulties due to Alberta's large land mass, its variety in landscapes and expert knowledge needed for classification of bird calls. This problem is also motivated by the constant monitoring of biodiversity near the Alberta oilsands. Through the use of ARUs (Automated Recording Units), millions of minutes of raw audio data has been recorded in the hopes of monitoring Alberta's precious ornithological communities. In this research work… Show more

The monitoring of bird migrations in Alberta poses many difficulties due to Alberta's large land mass, its variety in landscapes and expert knowledge needed for classification of bird calls. This problem is also motivated by the constant monitoring of biodiversity near the Alberta oilsands. Through the use of ARUs (Automated Recording Units), millions of minutes of raw audio data has been recorded in the hopes of monitoring Alberta's precious ornithological communities. In this research work, we investigate the classification of 14 Albertan birds species based on their respective bird calls. Using various machine learning algorithms such as random forests, neural networks, support vector machines and k-nearest neighbors, we were able to successfully classify fourteen species of Albertan birds based solely on their bird calls.

The 2GB of raw birds calls was graciously provided by the bird specialist Dr. Erin Bayne. By training a support vector machine, I was able to obtain over 95% accuracy.
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Every year, Maclean’s publishes a ranking of all Canadian universities from data they collect from all Canadian universities. Using this data, they publish a yearly ranking. How do they rank the universities based on this data? Dr. Mizera, from the university of Alberta graciously accepted to lend me his Maclean’s 2004 dataset to investigate their methodology.

Using the programing language R, I implemented an algorithm using principal component analysis, cluster analysis and a ridge… Show more

Every year, Maclean’s publishes a ranking of all Canadian universities from data they collect from all Canadian universities. Using this data, they publish a yearly ranking. How do they rank the universities based on this data? Dr. Mizera, from the university of Alberta graciously accepted to lend me his Maclean’s 2004 dataset to investigate their methodology.

Using the programing language R, I implemented an algorithm using principal component analysis, cluster analysis and a ridge regression to obtain a solution to their ranking algorithm. Show less