2025 CMS Summer Meeting
Quebec City, June 6 - 9, 2025
[PDF]
- TANJIMA AKHTER, University of Alberta
RSV Seasonal Outbreak Projections in Alberta: A Mathematical Modeling Study [PDF]
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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 aim is to develop a mathematical model to analyze the transmission dynamics of RSV. This study also aims to assess whether mathematical models can accurately predict RSV's epidemic peak magnitude, peak duration, peak timing and intensity. A five-age group mathematical model, based on the standard SIR framework, was developed to capture the complex transmission dynamics of RSV, incorporating heterogeneous contacts across the entire population. The model is calibrated using Bayesian inference and Diffusive Nested Sampling in MATLAB. Key challenges include nonidentifiability and computational complexity arising from a higher-dimensional system of equations and parameters. We used advanced calibration algorithms with multiple data sets and informed parameter priors to address challenges. RSV case counts for Alberta in the 2024–2025 season are projected using the model and validated against real-time data to enhance accuracy and reliability. The model projects a peak week magnitude of 568 RSV cases, closely matching the confirmed case count of 562. The model accurately captured the rise to the peak, with the peak week occurring within the predicted range. Projections from the model provide essential recommendations for health authorities to prepare for RSV outbreaks and guide targeted prevention and management efforts, strengthening public health resilience and informing policies to reduce the RSV burden.
- MARIE-ANNE BOURGIE, Université Laval
Quasi-frises [PDF]
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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]
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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.
- HAYATO NASU, Kyoto University, Research Institute for Mathematical Sciences
Double categories of relations relative to factorization systems [PDF]
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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]
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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]
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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.