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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).

Visit SFU GPS - Choose a USRA for the value and duration of Full-Time USRAs.

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.*

*We encourage applications from women and men, including visible minorities, aboriginal people and persons with disabilities.*

**Here is a graphic that summarizes the application process for both NSERC USRAs and VPR USRAs.**

**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. Additionally, we cannot guarantee that every applicant will be matched with a project/supervisor or receive a USRA.

### NSERC Application - Step One

**Due by: February 01, 2024 @ Noon**

- 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 27, 2024 @ Noon**

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

- Email your applicant’s reference number to your selected supervisor and have them complete Form 202: Part II.
- Your supervisor should send a PDF of the form for you to review and confirm that the information is correct.
- Once you have confirmed the information is correct, your supervisor should send a PDF of the form to the Math Chair's Assistant (mcs@sfu.ca).
- Lastly, your supervisor should “submit” the form online via the NSERC site and notify the Math Chair's Assistant afterwards.
**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 01, 2024 @ Noon**

- Interested and eligible students should contact the supervisor with regards to the project they would like to work on.
**If you are an international student**: Prior to applying, please consult with International Student Services (intl_advising@sfu.ca) to ensure you do not violate the terms of your work/study permit (i.e. please make sure you are eligible to apply for and hold a USRA).

- Complete the student portion of 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 27, 2024 @ Noon**

**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

## Summer 2024 USRA Competition

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 (adcockb@sfu.ca)**

**Project: Active learning for scientific machine learning**

We are seeking an undergraduate to join an exciting project on the development of novel active learning techniques for scientific machine learning.

Scientific machine learning is new field of research that fuses machine learning and scientific computing techniques to tackle challenging problems in computational science and engineering. This could, for example, involve using a deep neural network to solve a PDE or training a generative model to compute fast and accurate solutions to an inverse problem. Active learning is an important subfield of machine learning in which the learning algorithm can choose where to query the underlying ground truth to improve the accuracy of the learned model. As machine learning techniques come to be more commonly used in computational science and engineering, where data is often expensive to obtain, there is a pressing need to develop novel active learning algorithms to further advance the field.

This project will involve the development and implementation of novel active learning algorithms for scientific machine learning. Several possible avenues of investigation are random feature models for learning high-dimensional functions or generative models for inverse problems in imaging. The precise research direction will be determined based on the student’s background and interests. Ideally, the research conducted will include both computational and theoretical components.

Up to 2 students are invited to work on this project.

**Requirements:** Linear algebra (MATH 240 or equivalent, preferred), basic analysis (MATH 242 or equivalent), numerical analysis (MACM 316 or equivalent) and proficiency with MATLAB or Python are essential. Experience with machine learning is useful but not required.

**Dr. Ben Ashby (****bashby@sfu.ca****)**

**Project: Modelling the eco-evolutionary dynamics of microbes**

Microbes are found throughout the natural world. They can be both helpful and harmful to other organisms, from aiding in digestion to causing infectious diseases. Much of what we know about microbial evolution stems from not only experiments in the laboratory, but also mathematical modelling to understand and predict how genetic and environmental factors drive selection for key traits. In this project, you will use mathematical models to understand the ecological and evolutionary dynamics of microbes. You will be expected to adapt and analyse systems of ODEs to answer key questions about how various microbial traits evolve. This work forms part of a longstanding research program about microbial evolution along the parasitism-mutualism continuum.

Up to 2 students are invited to work on this project.

**Requirements**: Previous experience with dynamical systems (ODEs) and coding in MATLAB or Python.

#### Dr. Cedric Chauve (cchauve@sfu.ca) and Dr. Mahsa Faizrahnemoon (mfaizrah@sfu.ca)

**Project: optimization-based method to modify detected plasmids**

Plasmids are small circular pieces of DNA found in bacterial cells that are important due to their role in the spread of antimicrobial resistance (AMR), a major public health concern. Therefore, the problem of discovering plasmids in sequencing data from bacterial pathogens is a very active research area in bioinformatics which is a research field aimed at designing computational methods for the analysis of biological data.

In order to detect plasmids from sequencing data we have recently developed a Mixed Integer-Linear Program (MILP) approach that analyzes a graph known as the assembly graph, generated when sequencing data is assembled. Our method is designed based on an iterative optimization framework and outperforms existing methods. However, its iterative nature leads to well characterized errors such as splitting or mixing in the plasmids.

The project we propose is to develop a post-processing method, based on local search in this graph in order to refine and improve the solution obtained by the iterative MILP. The post-processing algorithm will focus on detecting and improving the error of mixing plasmids and will be evaluated on a large-scale real data set for which the ground truth (actual plasmids) is known.

**Requirements**: The student should have a keen interest in the application of mathematical and computational methods in biology as well as working with large data. Strong programming skills (in python) and a good background in graph theory and optimization is required. No specific biology background is required although it is expected the student will develop some knowledge about genomics and plasmids during the course of the project. This project offers the opportunity to discover the application of mathematical methods in the context of data science.

**Dr. Nadish de Silva (nadish_de_silva@sfu.ca) **

**Project: Simulating and correcting quantum computers via the stabiliser formalism**

Small quantum computers are currently under construction. How will we verify that they are working correctly? We might try to simulate their operation on an existing conventional supercomputer. This would be slow and difficult, however, as quantum computers, by design, perform tasks beyond the abilities of conventional computers. Thus, clever schemes have been devised to classically simulate quantum computers as efficiently as possible within limited regimes. Studying this question also gives us insight into the poorly understood mechanisms that drive quantum computational power.

In the longer term, how will we protect highly sensitive quantum data from errors while operating on them? As quantum data cannot be copied or directly observed, more clever schemes have been devised to enable quantum computation in the face of environmental noise.

This project will centre on the mathematics used to answer both these questions: the stabiliser formalism. The goal will be to better understand the stabiliser formalism and to utilise it towards facilitating quantum error correction and verifying near-term quantum computers.

The precise question tackled in the project, and the balance between theory and numerical computations, will depend on the interests and skills of the student.

**Requirements:** Strong background in mathematics and computer science. Coding skills in Python could be an asset but are not strictly necessary.

#### Dr. Razvan Fetecau (van@sfu.ca)

**Project: Emergent collective behaviours on nonlinear spaces**

This project concerns mathematical models of swarming and self-collective behaviour. The topic has received a great amount of interest in recent years due to applications of such models in a variety of areas, including population biology (chemotaxis of cells, swarming or flocking of animals), physics and chemistry (self-assembly of nano-particles), robotics and space missions, and opinion formation. The models have demonstrated emergence of very complex behaviours as a consequence of individuals following simple interaction rules, without any leader or external coordination.

More specifically, the project will consider applications to swarming on nonlinear spaces, such as surfaces in 3 dimensions. The student will implement numerical methods to simulate the models on various surfaces (eg., sphere, hyperboloid). The major interest is to investigate numerically (and possibly analytically) the emergent behaviours, in particular the qualitative properties of the swarm equilibria.

**Requirements**: Strong background in differential equations (MATH 260/310, MATH 314), and numerical methods for differential equations (MACM 316). MACM 416 and/or MATH 418 are not required, but they would be great assets. Some experience with Matlab would be very helpful.

**Dr. Alexander Rutherford (arruther@sfu.ca)**

**Project: Simulation Modelling for Inventory Management of Red Blood Cells**

Blood is a crucial life-saving product that is needed for both routine surgeries and life-threatening emergencies. Maintaining sufficient stocks of red blood cells is important for emergencies, especially at remote hospitals. However, red blood cells are perishable and managing these stocks in British Columbia is challenging without wastage of this precious resource. In this project, you will work with a research team that is developing a stochastic simulation model to optimize best practices for red blood cell distribution and inventory management in BC. This research project is a collaboration with the BC Provincial Blood Coordinating Office and Canadian Blood Services.

**Requirements: **This project is well-suited to a student interested in applications of mathematical modelling to healthcare and social services. Good communication and writing skills are an asset. A course in probability models, simulation modelling, or operations research would be beneficial (MATH 208W, MATH 348, or Math 402W). Programming experience in at least one of R, Python, or Java is required.

**Dr. Steve Ruuth (sruuth@sfu.ca) and Dr. Razvan Fetecau (van@sfu.ca)**

**Project: Numerical Methods for Partial Differential Equations on Surfaces**

We are seeking an undergraduate student to join a research project focused on the numerical and analytical exploration of specific partial differential equations (PDEs) formulated on surfaces. This research opportunity considers eigenvalues/eigenfunctions associated with the *p*-Laplacian operator, with a special emphasis on the infinity Laplacian as *p* approaches infinity. These operators and PDEs find applications in diverse fields, including image processing and game theory.

The student will:

- Conduct a thorough review of relevant existing literature to build a comprehensive understanding of the topic.
- Implement numerical methods for simulating the identified PDEs. The focus will be on simulation over simple surfaces, such as a sphere or a cylinder.
- Explore and analyze the implemented numerical methods, with the possibility of extending the investigation to include analytical approaches.

This research assistant position offers a unique opportunity for hands-on engagement with cutting-edge mathematical concepts and their practical applications. If you are a motivated and skilled undergraduate student with a keen interest in numerical methods and partial differential equations, we encourage you to apply.

Up to 2 students are invited to work on this project.

**Requirements**: Prospective candidates should meet the following criteria:

- Successful completion (with grades in the A range) of MACM 316 and MATH 314.
- Proficiency and experience in programming.

**Dr. Jessica Stockdale (jessica_stockdale@sfu.ca) and Dr. Caroline Colijn (ccolijn@sfu.ca)**

**Project: Genomic Clustering Unveiled: TB Transmission in Malawi**

In the management of infectious disease outbreaks, grouping cases into clusters and understanding their underlying epidemiology are fundamental tasks. One way to create clusters is using the genome sequences of pathogens collected from infected hosts. By exploring the patterns of genetic similarity, we can identify which cases are more likely to be clustered together. However, it may not be feasible to culture and sequence all pathogen isolates in an outbreak, so this sequence data may not be available for all cases.

We have an exciting set of data from Blantyre, Malawi, with 800 whole-genome sequences from tuberculosis infections over the period from 2015 to 2019. We have additional data for many individuals who had TB, but whose sample was not successfully sequenced. Yet these individuals are part of the TB transmission dynamics in this setting, and it’s important to understand as much as we can about transmission clusters: who infects whom, cluster growth and transmission dynamics.

In this project, we will use innovative mathematical and statistical models to bring information about unsequenced cases into the genomic epidemiology of TB in Malawi. We will start with a recently-developed method that creates pairwise relatedness data for individuals. We will define transmission graphs and clusters using the genomic data, and explore the performance of clustering as a tool to represent them. We will then use statistical modelling to assign unsequenced cases to clusters, and characterise how the clusters grew over time and what kinds of transmission dynamics would best explain them. We will then explore other applications of our statistical model e.g. determining whether a pair of unsequenced cases are likely to cluster together, identifying clusters that are of particular interest for predicting future TB transmissions, and identifying which individuals are most likely to be members of these worrisome clusters.

Recommended reading:

- Statistical model for clustering and whole-genome sequence data
- A background paper about TB in Malawi

**Requirements**: Some experience in statistics (regression) and/or computing would be beneficial. An ideal student would have an interest in disease and/or genomics, but no experience is required.

**Dr. Jessica Stockdale (****jessica_stockdale@sfu.ca****) and Dr. Alexander Rutherford (****arruther@sfu.ca****)**

**Project: Mathematical Modelling for Improving Community Care and Pandemic Preparedness**

The COVID-19 Pandemic highlighted gaps in community and primary healthcare in British Columbia, especially for people who are vulnerable and marginalised from the healthcare system. Community Health Centres in Vancouver provide outreach services to people with mental health, addiction, and chronic health issues to connect them with the healthcare system and social services. In this project, we will use mathematical modelling to understand and quantify gaps in delivery of healthcare and social services by analysing data and building simulated representations of the healthcare system. This simulation modelling will also allow us to explore alternative strategies for healthcare delivery.

This project will provide the student with experience in using data analytics and simulation modelling to inform healthcare policy and improve service delivery. It will provide a unique opportunity to work with healthcare providers to strengthen the healthcare system. The work will be done in collaboration with Vancouver Coastal Health, and there may be opportunities for work on-site at VCH.

**Requirements**: Students should have an interest and some experience in mathematical modelling, operations research and/or statistical/data analysis. Good communication skills and an interest in working with external partners would be an asset. Project will involve some programming e.g. in R, Python.

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

**Project: Recent Developments in Analysis of Nonlinear Kinetic Equations**

This project aims at understanding and applying the De Giorgi-Nash-Moser-type tools developed recently to treat nonlinear kinetic equations with singular kernels. The plan is to first review several important references in this direction and then to study the blow-up rate near t = 0 for solutions in L^p spaces.

**Requirements**: Students are required to have taken Math 425 and Math 418.

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

**Project: Diversities and l1 embeddings of hyper graphs**

There is an interesting collection of results and conjectures about the relation between the topology of a graph and the distortion necessary to embed it in l1 space. For example, a graph can be embedded in l1 without distortion if it does not contain the complete bipartite graph K(2,3) as a minor. A still open conjecture is that planar graphs can be embedded in l1 with constant distortion. In both cases, embedding a graph in l1 means embedding the shortest path metric of the graph into l1 space of some dimension.

We have developed a parallel theory to that of graphs and metric spaces with hypergraphs and diversities. A hypergraph is like a graph, but edges are allowed to have arbitrarily many points. A diversity is like a metric space, but instead of a number being assigned to every pair of points, there is a number for all finite sets of points. Just as there is a natural l1 metric space in arbitrary dimensions, there is also a natural l1 diversity.

Every weighted hypergraph induces a diversity on the set of vertices. This project will begin the investigation of the relation between the structure of hypergraphs and the embedding of their corresponding diversities into l1.

**Requirements: **Familiarity with basic graph theory.

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

**Project: The Motion of Solids Immersed In Gas **

This project aims to study the motion of solids immersed in rarefied gas. Instead of viewing the gas as a fluid, we will take a more microscopic view and use kinetic equations as models. Motion of the solid will be governed by Newton’s Second Law. Mathematically, the solid will provide a moving boundary for the kinetic equation and the collision of gas particles with the surface of the solid generates a drag force. Altogether, the coupled system will be nonlinear and nonlocal. We are interested in investigating the well-posedness of such systems, especially when the kinetic equation goes beyond the free transport.

**Requirements**: Students participating in this project are required to have taken Math 425 and Math 418/PHYS 384.

**Dr. Bojan Mohar (mohar@sfu.ca) and Dr. Maxwell Levit (maxwell_levit@sfu.ca)**

**Project: The algebraic theory of directed graphs**

The adjacency matrix A(G) of a simple undirected graph G relates the graph theoretic structure of G to the spectrum (multiset of eigenvalues) of A(G). This relationship has diverse applications, from bounding measures of complexity of boolean functions, to building algorithms for data visualization, to the characterization of extremal networks.

The matrix A(G) above gives us a good handle on the spectral theory of undirected graphs, but it is limited to graphs whose edges are unordered pairs {u,v} of vertices. Far less is known about the spectral theory of directed graphs, whose edges (now called arcs) are ordered pairs (u,v).

In this project we will start with a recently proposed definition of an adjacency matrix M(D) for the directed graph D which counts arcs using sixth roots of unity. One compelling reason for this definition is that the matrix M(D) is Hermitian, so its eigenvalues are real numbers. Another reason is that if (u,v) and (v,u) are both arcs of D, then M(D)_{u,v}=1, recovering the convention that an undirected edge is the same as a pair of arcs in opposite directions.

So far, we have these promising facts and a handful of theoretical results that mirror the undirected setting, but there is still a great deal to do in order to ``test'' this definition. In order for M(D) to be useful, we need to understand the relationship between its spectrum and the graph theoretic properties of D.

Here are some examples of the kinds of questions we'd like answer in this project: Which digraphs have few distinct M(D)-eigenvalues? How does the connectivity of D relate to the spectrum of M(D)? How many non-isomorphic digraphs D and D' can we find in which M(D) and M(D') have the same spectrum?

**Requirements**: Linear algebra. Some experience with graph theory. Some experience coding in Python or equivalent is a plus.

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

**Project: Mathematics of the Weather**

Students are invited to join a research effort 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 undergraduates in the third or fourth year of their degree. Some background in a differential equations is essential, as is proficiency in a computational environment such as Matlab. Participants should have a natural curiosity for the workings of the Earth's atmosphere.