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# Mathematics and Data Research Group

## Our Research

The modern world is awash with data. Our ability to store, process, interpret and analyze data arising in real-world applications relies on foundational mathematics and mathematical tools. The interaction between mathematics and data is a fruitful and active area of research. Not only does the analysis of data lead to new mathematical questions and problems, novel mathematical techniques - arising often from seemingly unconnected areas - lead to new and powerful tools in data science.

SFU has an active research group in contemporary applied mathematics and data science, encompassing a wide range of expertise and specialities. Our mathematics research includes: foundations of data science, discrete mathematics, optimization, mathematical modelling, compressed sensing and sparse recovery, neural networks and deep learning. We work on applications in computational biology, epidemiology, evolution and genomics, imaging, cognitive science, and develop data science methods for computational science and engineering.

Our group has collaborations with the Departments of Statistics, Biology, Molecular Biology and Biochemistry, Linguistics, Psychology, the School of Computing Science, and with SFU’s Faculty of Health Sciences. We also collaborate with other researchers throughout the lower mainland, Canada and internationally.

The Department of Mathematics offers a selection of graduate and undergraduate courses in this area. See below for a list.

## People

### Faculty

**Ben Adcock**

Mathematical Data Science, Numerical Analysis, Approximation Theory, Computational Harmonic Analysis

**Cedric Chauve**

Computational Genomics and Paleogenomics

**Caroline Colijn**

Canada 150 Research Chair in Mathematics for Evolution, Infection and Public Health

#### Jessica Stockdale

Infectious disease modelling, statistics

**Tamon Stephen**

Operations Research

**Paul Tupper**

Infectious Disease Modelling and Estimation, Cognitive Science, Metric Spaces, Phylogenetics

### Postdoctoral Fellows & Visitors

- Elisha Are
- Amy Langdon

### PhD Graduate Students

- Niloufar Abhari
- Juan Cardenas
- Omid Gheysar Gharamaleki
- Fatih Karaoglanoglu
- Aniket Mane
- Sebastian Moraga
- Nicola Mulberry
- Baraa Orabi
- Yexuan Song
- Kurnia Susvitasari
- Alice Yue

### MSc Graduate Students

- Piyush Agarwal
- Saimon Islam
- Maksym Neyra-Nesterenko
- Hannah Sutton

## Recent Research

**Publications:**

B. Adcock, S. Brugiapaglia and C. G. Webster

Sparse Polynomial Approximation of High-Dimensional Functions

SIAM, 2022

www.sparse-hd-book.com

B. Adcock and S. Brugiapaglia

Is Monte Carlo a bad sampling strategy for learning smooth functions in high dimensions?

arXiv 2208.09045, 2022

B. Adcock, J. M. Cardenas and N. Dexter

CAS4DL: Christoffel Adaptive Sampling for function approximation via Deep Learning

arXiv:2208.12190, 2022

B. Adcock and M. Neyra-Nesterenko

Stable, accurate and efficient deep neural networks for inverse problems with analysis-sparse models

arXiv:2203.00804, 2022

B. Adcock, J. M. Cardenas and N. Dexter

An adaptive sampling and domain learning strategy for multivariate function approximation on unknown domains

arXiv 2202.00144, 2022

J. Barnes, M. R. Blair, R. C. Walshe and P. F. Tupper

LAG-1: A dynamic, integrative model of learning, attention, and gaze

PLOS One 17(3):e0259511, 2022

S. Brugiapaglia, M. Liu and P. Tupper

Invariance, encodings, and generalization: learning identity effects with neural networks

Neural Computation 34(8):1756-1789, 2022

C. Colijn, D. J. D. Earn, J. Dushoff, N. H. Ogden, M. Li, N. Knox, G. Van Domselaar, K. Franklin, Kristyn, G. Jolly and S. P. Otto

Genomic surveillance of SARS-CoV-2

Preprint, 2022

G. Ebrahimi, B. Orabi, M. Robinson, C. Chauve, R. Flannigan and F. Hach

Fast and accurate matching of cellular barcodes across short-reads and long-reads of single-cell RNA-seq experiments

iScience 25(7):104530, 2022

M. Hayati, L. Chindelevitch, D. Aanensen and C. Colijn

Deep clustering of bacterial tree images

Philosophical Transactions of the Royal Society B 377(1861):20210231, 2022

F. Karaoglanoglu, C. Chauve and F. Hach

Genion, an accurate tool to detect gene fusion from long transcriptomics reads

BMC Genomics 23(1):129, 2022

P. Liu, P. Biller, M. Gould and C. Colijn

Analyzing Phylogenetic Trees with a Tree Lattice Coordinate System and a Graph Polynomial

Systematic Biology (in press), 2022

J. Sielemann, K. Sielemann, B. Brejová, T. Vinař and C. Chauve

plASgraph - using graph neural networks to detect plasmid contigs from an assembly graph

bioRxiv 2022.05.24.493339, 2022.

B. Sobkowiak, K. Kamelian, J. Zlosnik, J. Tyson, A. G. da Silva, L. Hoang, N. Prystajecky and C. Colijn

Cov2clusters: genomic clustering of SARS-CoV-2 sequences

medRxiv 2022.03.10.22272213, 2022

A. Yue, C. Chauve, M. Libbrecht and R. R. Brinkman

Automated identification of maximal differential cell populations in flow cytometry data

Cytometry A 101(2):177-184, 2022

P. Tupper, K. W. Leung, Y. Wang, A. Jongman and J. A. Sereno

The contrast between clear and plain speaking style for Mandarin tones

The Journal of the Acoustical Society of America 150(6):4464-4473, 2021

**Talks:**

C. Colijn

Genomic epidemiology in SARS-CoV-2: new tools and challenges

Artificial Intelligence for Pandemics (AI4PAN) seminar, The University of Queensland, June 2022

B. Adcock

Deep learning for scientific computing: Two stories on the gap between theory and practice*
*Alan Turing Institute workshop on Interpretability, Safety, and Security in AI, December 2021

C. Colijn

Modelling and policy in the COVID-10 pandemic*
*Biostatistics-Biomedical Informatics Big Data (B3D) Seminar series, Harvard University, May 2021

B. Adcock

Deep learning for scientific computing: (closing) the gap between theory and practice*
*The AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physics Sciences, April 2021

B. Adcock

The troublesome kernel: instabilities in deep learning for inverse problems*
*One World Mathematics of INformation, Data, and Signals (OW-MINDS) Seminar, June 2020

C. Colijn

Genomic epidemiology with TransPhylo: methods, applications and limitations

Phyloseminar.org seminar, January 2020

P. Tupper

Fitting a Stochastic Model to Eye Movement Time Series in a Categorization Task

Distributed Data for Dynamics and Manifolds, BIRS Oaxaca, September, 2017

T. Stephen

Two pairs of Boolean functions in biology*
*Fields Institute Industrial Optimization Seminar, December 2016

Recent Theses

Y. Song

Account for sampling bias in ancestral state reconstruction

MSc thesis, 2022

E. Haghshenas**
**Computational methods for analysis of single molecule sequencing data

*PhD thesis, 2020*

M. King-Roskamp

Global guarantees from local knowledge: Stable and robust recovery of sparse in levels vectors*
*MSc thesis, 2020

## Recent Courses

#### Fall 2022:

APMA 920 – Numerical Linear Algebra

MATH 895 - Infectious Disease Modelling in Populations and Within Hosts

#### Spring 2022:

MATH 775 - Mathematical Topics in Data Science

#### Fall 2021:

APMA 923 - Numerical Methods in Continuous Optimization

MATH 709 - Numerical Linear Algebra and Optimization

#### Summer 2021:

APMA 940 - Mathematics of Data Science

#### Fall 2020:

APMA 920 – Numerical Linear Algebra

#### Fall 2019:

APMA 923 - Numerical Methods in Continuous Optimization

MATH 709 - Numerical Linear Algebra and Optimization

## Recent visitors

- Melanie Chitwood (Yale) - Fall 2022
- Tomas Vinar (Comenius University) - Spring/Summer 2022
- Brona Brejova (Comenius University) - Spring/Summer 2022