For Amenda Chow, graduate studies is all about finding answers and multidisciplinary research.
“Control theory is based on the idea of purposely introducing an input into a dynamical system to steer the system to a desired objective. Questions such as the choice, implementation, and robustness of the control arise. My research focuses on infinite-dimensional systems, especially that of nonlinear partial differential equations (PDEs) and their stability,” said Chow. “Many unanswered questions remain in the control of infinite-dimensional systems such as, for a given nonlinear infinite-dimensional system, can the stability of the corresponding linear system be applied to the original nonlinear system? The answer is only partial known.”
After completing a degree in Applied Mathematics with a minor in Statistics at the University of Alberta, Chow decided to come to Waterloo for graduate studies based on reputation and relationships.
“The University of Waterloo has a strong reputation for mathematics. I was especially attracted to the fact that this university has an entire faculty devoted to the study of mathematics. This enables a broad scope of course offerings, diverse research opportunities and a variety of unique program specializations. There is also a strong relationship between faculties, which allows for greater interdisciplinary research and collaboration,” said Chow.
During her time in Waterloo, Chow has found a home both inside and outside of the lab through various activities and by embracing campus life.
“The Graduate House is my favourite spot on campus. It is the campus restaurant and pub, exclusively for graduate students. A visit to the Grad House is similar to a trip to the home of a family member or a friend. The atmosphere is always vibrant, cozy and fun. It is often the place to hear live music, participate in trivia and eat healthy fare on a graduate student budget. The Grad House hosts countless thesis defense celebrations and is a symbol of the University of Waterloo's graduate student community.”
After finishing an undergraduate degree at l'institut national des sciences appliquées de Lyon in France, Andrew Giuliani knew Waterloo would allow him to partake in world-class research while advancing his career.
"I chose scientific computing in Applied Math because during my undergrad, I was always interested in the mathematical models and tools engineers employed to complete simulations. I also liked programming; so scientific computing was a natural choice," said Giuliani.
Scientific computing is a broad subject but Giuliani is focusing on the implementation of the discontinuous Galerkin method for solving hyperbolic conservation laws on graphics processing units.
Knowing that he wanted to continue his education, Giuliani started looking at institutions that had a reputation he could be proud of.
“I chose Waterloo because it's a world renowned university, and the research I’m able to complete here interests me quite a bit. Mathematics at Waterloo is well known in Canada, and abroad.”
It’s not all work for our graduate students though – each has time for fun.
“In my free time, I like going for runs and seeing my friends,” said Giuliani. “My favourite spot on campus is the Graduate House. It's a good place to relax and chat with friends after work.”
Robert Harry Jonsson
Thesis projects and long hours in the lab aren’t foreign for Robert Jonsson. He completed a Bachelor of Science in Physics and a Pre-Diploma in Mathematics at the Universities ofRegensburg and Erlangen-Nurembergin Germany before heading to Cambridge, UK, for a Master of Advanced Study in Mathematics, all before coming to Waterloo in 2011. With that for a background, enrolling in a PhD program in Quantum Information isn’t much of a surprise.
“This field looks at what happens to quantum phenomena like entanglement in scenarios where relativistic effects become important as for strong accelerations or on curved spacetimes. The goal is both to deepen our understanding of the interplay between Quantum Theory and Relativity as well as to look for novel ways to process Quantum Information using relativistic effects,” said Jonsson.
The opportunity to meet his potential supervisor and gain a deeper understanding of the research happening here at Waterloo sealed the deal when it was time to choose a school for completing his PhD.
“For foundational theoretical physics Waterloo is just the place to be! In particular for my field of research, which combines quantum information with gravity, it is ideal to have the Institute for Quantum Computing and the Perimeter Institute here in town. Obviously Physics is the single most exciting subject there is to study and to pursue research in. Within Theoretical Physics, I found Relativistic Quantum Information very interesting, because I think it approaches deep and foundational questions in a fresh and appealing way,” said Jonsson.
Campus life aside, Jonsson enjoys the diversity found in both Waterloo and it’s neighbouring city, Kitchener.
“I am passionate about music and play the violin myself. So I was very happy to find that Kitchener-Waterloo has to offer a rich variety of classical symphonic and chamber concerts as well as opportunities to make music both on and off campus. I enjoy a lot to be playing with different orchestras and chamber ensembles here at the university and in town.”
Due to rapid advances of medical digital imaging technologies such as Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) scanners, the amount of image data being acquired each day has been increasing exponentially. Consequently, efficient storage, transmission, retrieval and display of medical image information in large-scale databases have become a major challenge that urgently requires solutions. Therefore, the use of image compression techniques is inevitable. Ilona Kowalik-Urbaniak’s research seeks to prove to skeptics that image quality and file size don’t necessarily have to be tradeoffs.
Ilona, a Waterloo PhD student, is under the supervision of Prof. Edward Vrscay from the Department of Applied Mathematics and Prof. Zhou Wang from the Department of Electrical Engineering. “My scholarship is the NSERC/MITACS Industrial Scholarship, in collaboration with AGFA Healthcare Inc. Also, we are collaborating with Dr. David Koff, who is the Chair of the Department of Radiology at McMaster University,” she says. Together, they are examining diagnostically lossy medical image compression; methods that decrease file size while preserving diagnostically relevant information.
The major lossy compression techniques on the market today are JPEG and JPEG2000. Increasing the compression of an image reduces the size of computer memory required to store it. This, however, is accompanied by greater elimination of image features, resulting in loss of quality. This is fine for family photographs, but medical images require special attention. Ilona’s challenge is to improve upon the existing methods and develop specialized compression methods for medical images.
The issue gets even more complicated, for the requirements vary depending on the condition and body part being dealt with. Ilona therefore also focuses her studies on quality assessment measures, which determine whether physicians would be able to draw valid conclusions from the generated image. Inaccurate readings could potentially lead to overlooking tumours or partially obstructed arteries. As of now, these measures are either subjective, or primitively drawn from Mean Squared Error calculations. “We need new methods to be able to measure the quality of compressed images, and the distortions as the compression ratio increases,” says Ilona.
Holding a Bachelor degree in Computer Science and a master’s degree in Mathematics, Ilona found the transition into applied mathematics to be particularly smooth, especially since her field is medical image processing. “My computer science background is helping me with designing algorithms. We do our simulations in Matlab, so definitely that is a big plus, because I don’t have to spend hours and hours figuring out how to program something,” she remarks.
Ilona entered her specialized studies in image processing knowing that it is an area with lots of opportunities. Industry, government, as well as post-secondary institutions have a demand for people with specialized skills in this field; these potentially include mathematicians, engineers, computer scientists, biologists, and physicists.
Ilona certainly welcomes any career paths that open up for her. If the industry needs her, then that’s where she’ll be, but she would love to continue in academia. She says, “I always use this very famous quote from Socrates, ‘"The only real wisdom is knowing how little we know". Demotivation probably comes from the fact that when we learn more, we realize how much more there is to learn. But if you look at it from a different perspective, it’s a beautiful thing!”
Waterloo’s Faculty of Mathematics ended up on Jared Penney’s radar after he spent time participating in the Centre for Education in Mathematics and Computing’s annual math competitions. While he chose to complete an undergraduate degree in Applied Mathematics and Chemistry at Memorial University, it was Waterloo at the top of his list for graduate studies.
“Waterloo has an excellent reputation and the Applied Math program is very strong,” said Penney.
Currently, Penny is doing research in the field of fluid dynamics and computational modeling.
“At the moment I'm particularly interested in porous media flow and double-diffusive instabilities,” said Penney. “Fluid dynamics offers a diverse range of problems to study, from laboratory scale microfluidics to atmospheric turbulence. I am curious to learn how fluid motion both affects and is affected by chemical reactions, and how this can be applied to large scale environmental flows.”
When he isn’t in the lab, you can find him biking around the city or in his favourite spot on campus.
“My favourite spot on campus is the Graduate House. They have a good selection of beers on tap.”