2025 CMS Summer Meeting

Quebec City, June 6 - 9, 2025

Submission Form Plenary, Prize and Public Lectures By session By speaker Posters

AARMS-CMS Student Poster Session
[PDF]

TANJIMA AKHTER, University of Alberta Seasonal RSV Projections in Alberta: A Mathematical Modeling Study [PDF]

Respiratory Syncytial Virus (RSV) has become a significant global concern, causing respiratory illness in infants, children, older adults, and immunocompromised individuals. According to the WHO, RSV causes 3.6 million hospitalizations and 100,000 deaths annually worldwide in children under five. My research aimed to develop a mathematical model to analyze RSV transmission dynamics. It also assessed whether such models could accurately predict the magnitude, duration, timing, and intensity of RSV infection peaks during the respiratory viral season. A five-age-group model based on the SIR framework was developed to capture the complex transmission dynamics of RSV, incorporating heterogeneous contacts across the population. The model was calibrated using a Bayesian inference framework with Diffusive Nested Sampling algorithm implemented in MATLAB. Key challenges included non-identifiability and computational complexity arising from a high-dimensional system of equations and parameters. We used advanced calibration algorithms, multiple data sets, and informed parameter priors to address these challenges. RSV case counts for Alberta in the 2024–2025 season were projected using the model and validated against observed data to enhance accuracy and reliability. The model projected the peak week of RSV cases with a magnitude that closely aligned with confirmed cases. It precisely captured the rising trajectory leading to the peak, with the peak’s timing falling within the predicted range. Model results aid health authorities in planning for seasonal RSV surges by anticipating the timing and intensity of cases. It also supports resource allocation and informs targeted prevention and response strategies to minimize the impact of RSV on vulnerable populations.

RUCHITA AMIN, Westren University Complex Dynamics and Bifurcation Analysis of a Virotherapy Model [PDF]

Recent progress in genetic engineering has led to a new way to treat cancer called virotherapy. It uses modified viruses that attack and kill cancer cells while leaving healthy cells unharmed. Oncolytic virotherapy utilizes viruses to partic- ularly target and destroy cancer cells, offering a novel and increasingly studied cancer treatment approach. The mathematical model describing the interaction among un- infected tumor cells, virus-infected cells, and virus particles is formulated as a system of nonlinear ordinary differential equations and analyzed in the following work. The model captures essential biological processes such as logistic tumor growth, virus- mediated infection, cytolysis, and viral clearance. We perform a comprehensive bifur- cation analysis to understand the system’s dynamic behavior under varying biological parameters. Using center manifold theory and normal form analysis, we identify con- ditions for a codimension of Hopf bifurcation, revealing the emergence of stable limit cycles that represent sustained oscillatory dynamics between tumor cells and viral populations. Our results provide theoretical insights into the origins and nonlinear mechanisms that govern successful virotherapy, offering valuable guidance for the op- timization of treatment procedures in clinical and experimental settings.

MARIE-ANNE BOURGIE, Université Laval Quasi-frises [PDF]

En 2015, Dupont et Palesi [DP01] ont publié un article où ils définissent les algèbres quasi-amassées. Avant cette publication, Fomin, Shapiro et Thurston [FST01] avaient montré que plusieurs algèbres amassées peuvent être étudiées à travers les triangulations de surfaces orientables. Dupont et Palesi [DP01] ont généralisé ces travaux en étendant les idées de Fomin, Shapiro et Thurston aux triangulations de surfaces orientables et non-orientables.

Parmi les objets combinatoires auxquels on peut associer des triangulations de surfaces orientables figurent les frises d'entiers positifs. Ce sont les seules frises finies qui sont associées aux triangulations de surfaces orientables, les $n$-polygones convexes. Ces frises nous permettent, par leurs propriétés, de mieux comprendre les algèbres amassées liées aux triangulations de polygones convexes.

Mon projet de recherche consistait à définir et à étudier les propriétés des quasi-frises, l'analogue des frises d'entiers positifs pour les triangulations de rubans de Möbius. Ce nouvel objet combinatoire nous permet de mieux comprendre les algèbres quasi-amassées. Nous présenterons comment construire une quasi-frise, son lien avec les algèbres quasi-amassées ainsi que ses plus importantes propriétés.

BERKANT CUNNUK, University of Manitoba Using computer vision to analyze R-loop imaging data [PDF]

R-loops are three-stranded nucleic acid structures containing a DNA:RNA hybrid and an associated single DNA strand. They are usually created during the process of transcription. Although their presence can be beneficial in cellular processes, an excessive formation of these objects is commonly associated with instabilities. As such, it is important to identify and classify different R-loop architectures. This task has been previously accomplished through manual classification. In this poster, we use computer vision to develop a computational pipeline to analyse AFM (atomic force microscopy) imaging data of R-loops and show some preliminary results.

WILLIAM FORGET, Bishop's University Evaluating Neural Networks Through the Lens of Topology: A Persistent Homology Approach [PDF]

The goal of this project is to study formal methods to analyse a neural network’s performance metrics. To do so we use a compact “knowledge matrix”, which captures the relationships among learned features across all layers. The idea is to treat this matrix as a point cloud in a high-dimensional feature space, and apply topological data analysis (more precisely persistent homology) to extract its multi-scale topological features such as connected components, loops and voids that persist across filtration levels. Our investigation follows two complementary paradigms. In Experiment 1, we fix a trained (or untrained) network and compute knowledge matrices for every input in our dataset; we then either vectorize these matrices or analyse them directly via persistent homology, comparing topological invariants against accuracy, robustness and generalisability. In Experiment 2, we fix a single input and trace its evolving knowledge matrix at successive training epochs, revealing how topological structure emerges and stabilizes during learning. To assess resilience, we introduce adversarial and corruption-based attacks into both paradigms and compare the resulting homological features to those of the unperturbed network.

LEA LAVOUÉ, Université de Sherbrooke Equivalence between brick-finite and representation-finite property for skew-gentle algebras [PDF]

Skew-gentle algebras, introduced by C. Geiss and J.A. de la Peña in 1999, generalize gentle algebras, extending some of their combinatorial and geometric properties. They admit geometric models in terms of marked surfaces with orbifold points, enabling the study of their algebraic properties via the combinatorics of the surface. This perspective connects skew-gentle algebras to tagged triangulations and cluster algebras, and provides an effective combinatorial framework for analyzing their derived categories. A notable feature of these algebras is that all indecomposable modules can be classified combinatorially.\Bricks are modules that have a local endormorphism ring, and thus are indecomposable. In 2017, L. Demonet, O. Iyama, and G. Jasso showed that the study of bricks is essential for $\tau$-tilting theory. In this context, whether the number of bricks is finite or not is a crucial question. When the algebra is gentle, P. Plamondon showed that being representation-finite, that is, having finitely many indecomposable representations, is equivalent to having finitely many bricks.\In this poster, we study the generalization of this result to skew-gentle algebras. We show that any skew-gentle algebra of infinite representation type admits a minimal band of one of four types, that we explicitly describe. By analyzing the associated subalgebras, we construct an infinite family of brick modules, thus showing that, for a skew-gentle algebra, being representation-finite is equivalent to being brick-finite.

SAMUEL LEBLANC, Université de Sherbrooke Multiplicity of the Interval Module [PDF]

Given a finite and connected poset $\mathcal{P}$ and a pointwise finite-dimensional persistence module $M : \mathcal{P} \to \mathrm{vect}_K$, we are interested in finding the number of copies, or the multiplicity, of the interval module in the decomposition of $M$ into indecomposable summands. More precisely, we give necessary and sufficient conditions for a subposet to be such that the restriction of $M$ along it preserves the multiplicity of the interval module. In addition, we characterize the minimal subposet where these conditions are satisfied.

HAYATO NASU, Kyoto University, Research Institute for Mathematical Sciences Double categories of relations relative to factorization systems [PDF]

Double categories generalize ordinary categories by incorporating two distinct kinds of morphisms. A prototypical example is the double category of functions and binary relations as the two kinds of morphisms. Using the notion of factorization systems, one can construct a broader class of examples of double categories in a similar manner. In this poster talk, we will present an axiomatic approach to characterizing this class of double categories. This talk is based on joint work with Keisuke Hoshino (Kyoto Univ).

RAHUL PADMANABHAN, Concordia University Deep Learning Approximation of Matrix Functions: From Feedforward Neural Networks to Transformers [PDF]

Deep Neural Networks (DNNs) have been at the forefront of Artificial Intelligence (AI) over the last decade. Transformers, a type of DNN, have revolutionized Natural Language Processing (NLP) through models like ChatGPT, Llama and more recently, Deepseek. While transformers are used mostly in NLP tasks, their potential for advanced numerical computations remains largely unexplored. This presents opportunities in areas like surrogate modeling and raises fundamental questions about AI's mathematical capabilities.

We investigate the use of transformers for approximating matrix functions, which are mappings that extend scalar functions to matrices. These functions are ubiquitous in scientific applications, from continuous-time Markov chains (matrix exponential) to stability analysis of dynamical systems (matrix sign function). Our work makes two main contributions. First, we prove theoretical bounds on the depth and width requirements for ReLU DNNs to approximate the matrix exponential. Second, we use transformers with encoded matrix data to approximate general matrix functions and compare their performance to feedforward DNNs. Through extensive numerical experiments, we demonstrate that the choice of matrix encoding scheme significantly impacts transformer performance. Our results show strong accuracy in approximating the matrix sign function, suggesting transformers' potential for advanced mathematical computations.

XUEMENG WANG, Simon Fraser University Christoffel Adaptive Sampling in Sparse Random Feature Models for Function Approximation [PDF]

Random feature models have become a powerful tool for approximating high-dimensional functions and solving partial differential equations (PDEs) efficiently. The sparse random feature expansion (SRFE) enhances traditional random feature methods by incorporating sparsity and compressive sensing principles, making it particularly effective in data-scarce settings. In this work, we integrate active learning with sparse random feature approximations to improve sampling efficiency. Specifically, we incorporate the Christoffel function to guide an adaptive sampling process, dynamically selecting informative sample points based on their contribution to the function space. This approach optimizes the distribution of sample points by leveraging the Christoffel function associated with a chosen function basis. We conduct numerical experiments on comparing adaptive and non-adaptive sampling strategies within the sparse random feature framework and examine their implications for function approximation. Furthermore, we implement different sparse recovery solvers, including Orthogonal Matching Pursuit (OMP) and Hard Thresholding Pursuit (HTP) to reconstruct target function. Our results demonstrate the advantages of adaptive sampling in maintaining high accuracy while reducing sample complexity, highlighting its potential for scientific computing.

This is joint work with Ben Adcock and Khiem Can.

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