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## NSERC | VPR

The Undergraduate Student Research Awards (USRA) give students hands-on research experience while working on actual projects. These awards prepare students to pursue graduate studies and encourage interest in research careers.

The awards are supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and SFU's Vice-President, Research (VPR).

Full-Time USRA awards are valued at $6,000 for a minimum of 16 weeks, 35 hours per week. The faculty will supplement this amount with an aditional minimum $2,512 + 9.8% (for statutory benefits). These awards are provided to encourage undergraduate student interest in research and graduate studies.

Working on a USRA project can potentially be counted towards a co-op work term. Please contact the Science Co-op Office to learn more.

## Eligibility for USRA's

**SFU Graduate and Postdoctoral Studies USRA guidelines can be found here:**

**NSERC USRA guidelines can be found here:**

## Procedures for applying for Math USRA's...

*Please be sure to review full eligibility criteria, guidelines, and application forms on the NSERC USRA and Graduate and Postdoctoral Studies: USRA websites listed above, BEFORE beginning the application process.*

***Please Note**: While we do our best to match students up with their preferred projects/supervisors, we cannot guarantee a preferred match due to the competitive nature of the awards.

### NSERC Application - Step One

**Due by: February 10, 2021**

- Interested and eligible students should contact the supervisor with regards to the project they would like to work on.
- Students must create an NSERC Online Account, complete the application for an Undergraduate Student Research Award Form 202: Part I, and upload scanned copies of their official or unofficial transcripts. Advising transcripts are not acceptable.
- Students must email the following documents to the Math Chair's Assistant (mcs@sfu.ca):
- Cover letter with a ranked list of at least three choices of projects

- A curriculum vitae (CV)
- A PDF of Form 202: Part I
- Copies of transcripts
- Their NSERC Online Reference number
- Two reference letters
**NOTE:**Your references should directly email their reference letters to the Math Chair's Assistant (mcs@sfu.ca) by the deadline above. We do not accept reference letters submitted by applicants.

- Cover letter with a ranked list of at least three choices of projects

### NSERC Application - Step Two

**Due by: February 24, 2021**

**If you are nominated for an NSERC USRA:**

- Email your selected supervisor and have them complete Form 202: Part II; your supervisor will need to know your applicant’s reference number to do so.
- Your proposed supervisor must complete Form 202: Part II online, email it as a PDF to the Math Chair's Assistant (mcs@sfu.ca), and confirm with you.
- You must verify your application online and advise your supervisor.
**Do not submit yet.** - Your supervisor will submit the application online. This completes the NSERC administration process.
**NOTE:**The SFU Graduate & Postdoctoral Studies (GPS) Office makes the final decision for awarding all USRAs. An award is not guaranteed until GPS sends out an award letter.

### VPR Application - Step One

**Due by: February 10, 2021**

Note: If students do not meet the eligibility criteria for an NSERC USRA, they may be eligible for a VPR USRA. For example, international students, or students wishing to work with a faculty member whose research support is not from NSERC are eligible for a VPR.

- Interested and eligible students should contact the supervisor with regards to the project they would like to work on.
- Fill out the VPR USRA Application Form (located on SFU GPS: Deadlines + Application Procedures website).
- Email the following documents to the Math Chair's Assistant (mcs@sfu.ca):
- A cover letter indicating a ranked list of at least three choices of projects

- A curriculum vitae (CV)
- A PDF of your VPR USRA Application Form
- A copy of your unofficial transcript
- Two letters of reference
**NOTE:**Your references should directly email their reference letters to the Math Chair's Assistant (mcs@sfu.ca) by the deadline above. We do not accept reference letters submitted by applicants.

- A cover letter indicating a ranked list of at least three choices of projects

### VPR Application - Step Two

**Due by: February 24, 2021**

**If you are nominated for a VPR USRA:**

- Email your selected supervisor and ask them to complete Page 2 of your VPR USRA Application Form.
- Your supervisor must email the completed form as a PDF to the Math Chair’s Assistant (mcs@sfu.ca)
**NOTE**: The SFU Graduate & Postdoctoral Studies (GPS) Office makes the final decision for awarding all USRAs. An award isn’t guaranteed until GPS sends out an award letter.

## Current Research Projects

Below are the available research projects in mathematics from faculty members who are taking on qualified undergraduate students. Unless otherwise specified, each project is available to one student only.

**Dr. Ben Adcock (ben_adcock@sfu.ca)**

**Project: Machine learning-based image reconstruction**

Fast, accurate and robust image reconstruction is a key task in modern society, with a myriad of uses in science and industry. Machine learning has been heralded as a “new frontier” for image reconstruction, promising to bring significant advances in terms of computational speed and accuracy. Yet, substantial open questions remain about how to best do this, and whether this leads to robust and reliable algorithms. In this project, we will explore and develop machine learning algorithms for image reconstruction based on neural networks and deep learning. The focus will be on understanding examining these methods from the perspectives of speed, accuracy and robustness.

**Requirements:** *Candidates should have a strong mathematical background. Analysis, linear algebra, numerical analysis and Matlab experience are essential. Previous knowledge of optimization and image processing are beneficial, but not strictly necessary.*

**Dr. Nils Bruin (nbruin@sfu.ca)**

**Project: Computational arithmetic geometry**

Arithmetic geometry studies the interplay between number theory and algebraic geometry: the properties of integer and rational solutions to polynomial equations. It is an area that is particularly suited for computational exploration and many of the deep conjectures and theorems were found using computationally gathered evidence.

**Requirements:*** Good algebraic foundations are a must. Coding experience or at least a willingness to learn coding is big bonus.*

**Dr. Imin Chen (ichen@sfu.ca)**

**Project: Generalized Fermat Equations**

This project will investigate the generalized Fermat equation A x^r + B y^q = C z^p over number fields from the modern point of view of Galois representations and modular forms, building on the methods used to prove Fermat's Last Theorem which have been successively refined in the last 20 years. In particular, we will study the current state of the art methods to tackle specific cases over totally real fields using Frey elliptic curves.

**Requirements:** *MATH 342, MATH 440, and programming experience.*

**Dr. Jake Levinson (jake_levinson@sfu.ca)**

**Project: Combinatorial algebraic geometry of curves**

Algebraic geometry is the study of polynomial equations and the spaces they describe (called algebraic varieties). We often understand these spaces using tools from combinatorics. This project will involve curves, particularly rational (parametrized) curves; possible specific topics could include enumerative calculations or topology related to real rational curves.

**Requirements:** *Linear algebra (Math 240) and abstract algebra of rings and ideals (Math 340), especially if you enjoyed polynomial rings and quotient rings. Additional algebra is a plus (Math 341 -- Groups; Math 440 -- Galois Theory; Math 441 -- Commutative Algebra and Algebraic Geometry).*

**Dr. Bojan Mohar (mohar@sfu.ca)**

**Project: Random embeddings of graphs on surfaces**

2-cell embeddings of graphs in surfaces admit a simple combinatorial description. In several applications within mathematics, theoretical physics and theoretical computer science, the notion of a random 2-cell embedding plasys a prominent role. The student working on this project will be asked to provide computational support offering random simulations that will enable us to test different hypotheses and open problems in this area.

**Requirements**: *A course in Graph Theory, e.g. MATH 345 or MACM 201 completed with grade A or A+. Basic programming skills with a software that can be used for extensive computation (e.g. Maple or SAGE or Python, etc.).*

**Dr. David Muraki (muraki@sfu.ca)**

**Project: Computation of Fluid Models for Atmospheric Science **

Students are invited to join a research group that uses computational models to understand the fluid mechanics of the weather. There are active projects that investigate a variety of atmospheric phenomena.

One current area of interest involves projects connected with the question, "What is the shape of a cloud"? We have developed a new mathematical model for the motion of cloud edges --- one that has already confirmed the behaviour of "lenticular" clouds caused by airflow over mountains, and somewhat rare phenomenon known as a "holepunch" cloud (search for images!).

**Requirements:** *Students should be independently motivated and in the third or fourth year of their degree. Some background in partial differential equations is essential, as is proficiency in a computational environment such as Matlab. Students should have a broad curiosity of things both mathematical and scientific. *

**Dr. Alexander Rutherford (arruther@sfu.ca) and Dr. Caroline Colijn (ccolijn@sfu.ca)**

**Project: Flattening the Curve – Modelling the Public Health Response to the COVID-19 Pandemic**

Public health interventions, such as social distancing and mask wearing, have played an important role in preventing the BC healthcare system from becoming overwhelmed during the COVID-19 pandemic. Our research group is currently working with the BC Ministry of Health to model hospital capacity during the pandemic. This project will involve developing an epidemic model for COVID-19 that is able to capture transmission reduction measures. If time permits, vaccination strategies will also be incorporated into the model. The results of the modelling will inform work that we are doing with the Ministry of Health to forecast critical care requirements under different epidemic control scenarios.

**Requirements: ***This project is well-suited to a student interested in epidemic modelling, data science, and operations research. A course in probability models or operations research would be beneficial (Math 348, Math 208W, or Math 402W). Programming experience in R, MATLAB, or python is required.*

**Dr. Weiran Sun (weiran_sun@sfu.ca)**

**Project: Hypocoercivity of A Non-classical Kinetic Equation**

In this project we are interested in exploring possible hypocoercivity of a non-classical kinetic equation used to model bacteria motion. Although a rather general framework has established by Dolbeault-Mouhot-Schmeiser to show hypocoercivity for transport equations without smoothing effect, such framework does not apply to the equation that we are studying. The aim of this project to identify hidden structures of the equation which can lead to hypocoercivity.

**Requirements**: *Math 320 and Math 418.*

**Dr. Paul Tupper (pft3@sfu.ca)**

**Project: Mathematical Models of Drug Tolerance and Optimal Treatment Plans**

Drug tolerance is the phenomenon where the effect of a drug diminishes with repeated use, and is important both in understanding addiction and in therapeutic drug use. As an example, caffeine is an effective stimulant, but the effect of one cup of coffee in a heavy caffeine-consumer is much less than in someone who hasn't had caffeine for days. What is the optimal consumption of caffeine for someone who wants the occasional benefits of increased alertness? Similar questions can be asked about any medication, from antidepressants to analgesics. In this project we will review the literature on mathematical models of drug tolerance, simulate the models, compare with experimental results, and develop optimal treatment regimes.

**Requirements:** *Candidates should have a strong mathematical background and knowledge of Matlab or another high-level programming language.*

### Dr. Nilima Nigam (nigam@sfu.ca) and Dr. James Wakeling (wakeling@sfu.ca)

**Project: Mathematical modeling and simulation for muscle biomechanics**

The use of mathematical models and computational strategies allows us to explore details of the biomechanics of muscles which may not be amenable to experimental observation in vivo or in situ. A highly interdisciplinary collaboration involving research groups from BPK and Math uses mathematical and computational tools, coupled with experimental data, to gain insight into the 3-D impacts of mass, architecture, and regionalized activation on the dynamics of muscle. We invite __up to 2 USRA scholars__ to join this endeavour. The overarching goals of these projects will be to mathematically model physiological questions of particular interest, integrate these models into our existing computational platform, and conduct carefully-designed numerical experiments. The specific physiological questions of interest will be developed in concert with the student; past projects have included the impact of transverse compression on muscle-force output, the impact of isotropic material stiffness on a fibre-reinforced composite such as muscle, and the impact of curved geometries.

**Requirements:** *Candidates should have a strong mathematical background including coursework on partial differential equations, with some experience in numerical analysis/scientific computing. Familiarity with physics or physiology is an asset, though not required. Successful candidates will be willing to read research papers, document their work to the standards expected in the experimental sciences, and work in a collegial team environment.*

### Dr. Cedric Chauve (cchauve@sfu.ca)

**Project: Zero-shot learning for gating single-cell flow cytometry data**

The project will be officially supervised by Dr. Cedric Chauve with collaboration from Alice Yue, a PhD student in the School of Computing Sciences at SFU.

Flow cytometry (FCM) is a pervasive technique used to diagnose and research diseases in the immune system. Despite availability of computational techniques, FCM analysis is still predominantly done manually. This project aims to develop a FCM analysis tool that incorporates expert knowledge to produce easily interpretable results circumventing issues associated with existing FCM analysis tools.

The successful applicant will develop a zero-shot learning algorithm that recommends high quality classification schemes to help identify cell populations in FCM data.

Identification of cell populations in FCM is a pervasive problem in FCM analysis. While many computational tools applying traditional machine learning and clustering algorithms have met some success in solving the problem, none of them were able to completely replace manual analysis. This is because while computational tools are more efficient, they lack one or more of the following: incorporation of expert and user knowledge, interpretable results reminiscent of a manual gating strategy, and the ability to generalize its results across variable FCM samples.

We propose a two-step process for cell population identification in FCM. First, we recommend to users, one or more possible classification schemes. The user can choose one of the classification schemes and optionally refine them for his or her needs. Second, we take the finalized classification scheme and project it onto the rest of the FCM samples.

For the summer project, we will focus on the first step and frame it as a zero-shot learning problem. We define each classification scheme as a unique image segmentation of a 2D FCM scatterplot where instead of colours, the values in this scatterplot image reflect a 2D kernel density distribution. Given a training sample set, we will train a machine learning model. This trained model should be able to output one or more classification schemes given a query sample. Out of the top few classification schemes the model outputs, there should be at least one classification scheme that matches with our ground truth segmentation yielding a high F1 score during evaluation.

We expect the student to implement the model and turn it into an open-source package with well documented scripts such that the work would be reproducible in the future.

**Requirements:** *Applicants should be close to finishing an undergraduate degree in computing science, computational biology, statistics, or a related field. Experience in implementing and validating machine learning models using programming languages Python, R, Julia, or C++ are desired.*

### Dr. Ladislav Stacho (lstacho@sfu.ca)

**Project: Inverse Protein Folding Problem for Some Simple Structures in HP-model**

The inverse protein folding problem is that of designing an amino acid sequence which has a particular native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein–protein interactions. To simply the problem, the protein is laid out on a 2D spatial lattice with each monomer occupying exactly one square and neighbouring monomers occupy neighbouring squares. The free energy is minimized when the maximum number of non-neighbour hydrophobic monomers are adjacent in the lattice.

The student working on this project will investigate well known HP-model of this problem, and will search for minimum energy designs for some simple target structures.

**Requirements:** *A Graph Theory course such as MATH 345 or MACM 201 completed with grade A or A+. Basic programming skills with a software that can be used for extensive computation (e.g. Maple or SAGE or Python, etc.). *