Research

My research projects lie in the fields of mathematics, biology and data science. I am interested in introducing and developing new mathematical methods for biology and medicine. Specifically, my current projects include developing methods based on discrete mathematics, topology and geometry for phylogenetics, genomics and molecular biology, aiming to help solve problems in epidemiology, public health and medicine.
Infectious disease modelling
Throughout the COVID-19 pandemic, as stay-at-home orders have been implemented to limit community transmission, transmission within household units has posed a challenge. Using an epidemiological model, we compare two health regions, one with more larger, multi-generational households and the other with more single-person households. We determine that the differences in the size of households between the two regions can cause significant differences in COVID-19 incidence. Our results also suggest that offering individuals a place to isolate outside their households can reduce transmission effectively in regions with larger households. This study is based on data from British Columbia, Canada.
Publication
- Modelling the impact of household size distribution on the transmission dynamics of COVID-19
With Lisa McQuarrie, Yexuan Song and Caroline Colijn
To appear in Journal of the Royal Society Interface
Preprint, DOI: 10.1101/2021.01.12.21249707
Polynomial phylogenetic analysis
In this project, we introduce graph polynomials for phylogenetic analysis. We define a polynomial that uniquely represents trees and use the polynomial with statistical and machine learning tools to solve problems in phylogenetics and evolutionary biology, which shows that graph polynomials are promising methods for phylogenetic analysis and for other related tasks.
Publications
- A tree distinguishing polynomial
Discrete Applied Mathematics
DOI: 10.1016/j.dam.2020.08.019 - Polynomial phylogenetic analysis of tree shapes
With Priscila Biller, Matthew Gould and Caroline Colijn
Preprint, DOI: 10.1101/2020.02.10.942367
Invited Conference Talks
- A tree distinguishing polynomial - an introduction to polynomial tree metrics
SMB Annual Meeting, Université de Montréal, Montréal, QC.
July 2019 - A tree distinguishing polynomial - an introduction to polynomial tree metrics
CAIMS Annual Meeting, Whistler, BC.
June 2019 - A tree distinguishing polynomial - an introduction to polynomial tree metrics
CanaDAM 2019, Simon Fraser University, Vancouver, BC.
May 2019
Monte-Carlo kDNA Model
Kinetoplast DNA or kDNA is a network of circular DNA in a mitochondrion of the organisms kinetoplastids, which include parasites that cause serious diseases like African sleeping sickness and Chagas disease. We develop a Monte-Carlo based model for the kDNA network using tools based on topology and discrete mathematics, aiming to study the structures and the mechanisms of the mitochondrial DNA.
Publications
- Estimating properties of kinetoplast DNA by fragmentation reactions
With Lara Ibrahim, Yuanan Diao, Michele Klingbeil and Javier Arsuaga
Journal of Physics A: Mathematical and Theoretical
DOI: 10.1088/1751-8121/aaf15f - Characterizing the topology of kinetoplast DNA using random knotting
With Ryan Polischuk, Yuanan Diao and Javier Arsuaga
Topology and Geometry of Biopolymers, Contemporary Mathematics
DOI: 10.1090/conm/746
Invited Conference Talks
- Estimating properties of kinetoplast DNA by fragmentation reactions
Workshop on Knotted Fields, Beijing University of Technology, Beijing, China.
September 2019
Braid indices of alternating links
In this project, we solved a long-standing problem in knot theory. We fully characterized the alternating links whose braid indices equal the number of Seifert circles in their reduced diagrams. We also conjectured that for any alternating link, its braid index equals the difference of the number of Seifert circles in its reduced diagram and its reduction number. We proved the conjecture is true for a large class of alternating links including Montesinos links.
Publications
- The braid index of reduced alternating links
With Yuanan Diao and Gábor Hetyei
Mathematical Proceedings of the Cambridge Philosophical Society
DOI: 10.1017/S0305004118000907 - The HOMFLY polynomial of links in closed braid form
With Yuanan Diao and Gábor Hetyei
Discrete Mathematics
DOI: 10.1016/j.disc.2018.09.027 - A diagrammatic approach for determining the braid index of alternating links
With Yuanan Diao, Claus Ernst and Gábor Hetyei
To appear in Journal of Knot Theory and Its Ramifications
Preprint, arXiv:1901.09778
Invited Conference Talks
- A diagrammatic approach for determining the braid index of alternating links
The Geometry and Topology of Knotting and Entanglement in Proteins, CMO-BIRS Workshop, Oaxaca, Mexico.
November 2017 - The braid index of reduced alternating links
AMS Sectional Meeting, University of Saint Thomas, Minneapolis, MN.
October 2016 - The HOMFLY polynomial of links in closed braid form
Workshop on Graphs and Knots, Xiamen University, Xiamen, China.
June 2016