Monday, 8:30-9:15,

Biosciences 1101 (Aud)

Plenary: Jeff Calder

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8:30-9:15

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PDE theory and applications in graph-based learning

Jeff Calder

(University of Minnesota)
## Abstract

This talk will overview recent work using partial differential equation (PDE) theory to analyze graph-based semi-supervised learning algorithms, with the goal of designing new algorithms with performance guarantees. Graph-based semi-supervised learning is a field within machine learning that uses both labeled and unlabeled data with an underlying graph structure for classification and regression tasks, and is especially useful for problems with very few labeled examples. We will explain how PDE continuum limits for graph-based learning can be used to understand why some algorithms perform poorly, and to design several new algorithms using the p-Laplacian, higher order Laplacians, re-weighted Laplacians, and Poisson equations. We will focus our attention on a recent algorithm called Poisson learning, and show how provable guarantees require studying the convergence rates for Green's functions on random geometric graphs.

Monday, 10:00-12:00,

Chernoff Hall 117

Advancing Scientific computing through recent High-Performance Computing paradigms

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10:00-10:30

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Leveraging the Actor Model for Improving Performance in Scientific Computing

Mohammad Mahdi Moayeri

(University of Saskatchewan)
## Abstract

Scientific computing is increasingly facing challenges related to scalability and complexity, particularly with the growing demand for simulations across heterogeneous architectures. Traditional parallel programming frameworks often require developers to handle complex low-level details, which complicates efficient software development on modern high-performance computing (HPC) systems. The actor model of concurrent computing offers a promising alternative by simplifying the expression of concurrency and managing the complexities of scientific computing applications through its resilience, dynamic workloads, and overlapping of communication and computation. In this presentation, I will explore the improvements in computational performance, resource utilization, and usability that actor-based programming brings, specifically through its application to a hydrological model called SUMMA. This method not only makes development more straightforward but also enhances fault tolerance, efficiency, and resource management in scientific simulations.

10:30-11:00

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Challenges in Optimizing Local Time Stepping Schemes for Earthquake Simulations on GPUs

David Schneller

(Technical University of Munich)
## Abstract

We consider the earthquake simulation software SeisSol which simulates linear hyperbolic PDEs (e.g., the linear elastic wave equation) on unstructured tetrahedral meshes to capture complex geometries, coupled with the simulation of (non-linear) fault dynamic rupture behavior. For the wave propagation, the software uses the ADER Discontinuous Galerkin method and a Local Time Stepping (LTS) scheme which clusters mesh cells by their maximum allowed timestep to enable an efficient parallelization, while taking advantage of the numerical properties of the mesh. On GPUs, the LTS scheme requires careful treatment to maintain a good strong scaling behavior: for small LTS cell clusters, the launch overhead yields worse performance on the GPU than on the CPU.
In this talk, we present two approaches to counteract this problem: firstly, we use a tasking scheme to execute many LTS time clusters in parallel, when possible. Secondly, we consider a CPU-GPU hybrid approach to the LTS scheme—that is, to execute latency-bound clusters on the CPU, while throughput-bound clusters run on the GPU.

11:00-11:30

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Domain decomposition preconditioners, solvers and software for PDEs intrinsic to surfaces

Ronald Haynes

(Memorial University)
## Abstract

The solution of surface intrinsic PDEs using the closest point method will be proposed. For efficiency we have designed and analyzed domain decomposition solvers and preconditioners to solve the resulting discrete system of equations. Numerical results for model test examples will be presented

11:30-12:00

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A fast and friendly shallow water model in Oceananigans.jl

Francis Poulin

(University of Waterloo)
## Abstract

Oceananigans.jl is a new library written completely in the julia language that can simulate oceanic flows with different degrees of realisim. It can run on CPUs, GPUs, in serial or in parallel using MPI. There is a shallow water model in this library that is designed to make it easy for researchers to get started in doing simulations and enable them to study scientific problems efficiently. There are options in this model for time stepping, advection, closure schemes, grids, the formulation of the model equations and much more. Using an immersed boundary method it allows for the inclusion of irregular coastlines that enables us to study more realistic oceanic dynamics. In this talk we present various tests that we have developed to validate this model, one of which is to do a near global simulation with realistic winds, coastlines and bathymetry.

Monday, 10:00-12:00,

Chernoff Hall 211

Exponential integrators for differential equations

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10:00-10:30

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Efficient computation of linear combination of the $\varphi$ functions.

Siqi Wei

(University of Saskatchewan)
## Abstract

Exponential time integrators rely on the computation of the matrix exponential and related matrix functions, generally referred to as $\varphi$ functions. The computation of these $\varphi$ functions contributes to the main cost of an exponential integrator. In most cases, the matrices in question are large and sparse. Accordingly, one can use matrix-free strategies that evaluate the action of a matrix function on a vector without computing the matrix itself. Several adaptive time-stepping methods using Taylor series expansions or Krylov subspaces have been developed for computing $\varphi$ functions. Alternatively, computing a linear combination of the $\varphi$ functions is equivalent to solving a linear ODE. In this talk, we explore the use of embedded Runge—Kutta methods that exploit the linear, constant-coefficient structure of the ODE to achieve an efficient evaluation of the $\varphi$ functions, resulting in more efficient exponential integrators.

10:30-11:00

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Schur Decomposition and Robust Embedded Exponential Integrator Pairs for Stiff Differential Equations

John Bowman

(University of Alberta)
## Abstract

A quantitative definition of numerical stiffness is proposed.
Exponential integrators are designed to solve
linearly stiff systems of differential equations efficiently. However,
they become expensive when the linear coefficient is a matrix,
especially when the time step is adapted to maintain a prescribed
local error. We show that a Schur decomposition avoids the need for
computing matrix exponentials, while still circumventing linear
stiffness. We also symbolically solve the Hochbruck--Ostermann
stiff-order conditions, expressing the Runge--Kutta weights as unknown
linear combinations of $\phi$ functions. Embedded exponential pairs
that efficiently generate high- and low-order estimates are needed to
support dynamic adjustment of the time step.
A key requirement is that the pair be robust: if the nonlinear
source function has nonzero total time derivatives, the order of the
low-order estimate should never exceed its design value. Robust
exponential Runge--Kutta (3,2) and (4,3) embedded pairs that are
well-suited to initial value problems with a dominant linearity
are constructed.
This work was done in collaboration with Thomas Zoto.

11:00-11:30

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A new class of exponential integrators for stiff systems

Vu Thai Luan

(Mississippi State University)
## Abstract

This talk focuses on the construction, analysis, and derivation of a new class of exponential methods, so-called two-derivative exponential Runge--Kutta methods (TDEXPRK), for stiff reaction-diffusion problems. Interestingly, while TDEXPRK methods employ a fixed linearization of the vector field, they require much less order conditions than conventional exponential Runge--Kutta methods, thereby enabling the derivation of high-order efficient schemes with only a few stages. Numerical examples for both one-and two-dimensional problems are provided to validate the accuracy and efficiency of TDEXPRK schemes.
This work is a collaboration with my student, Nguyen Van Hoang.

11:30-12:00

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Irksome: Automated Runge-Kutta methods and monolithic multigrid for time-stepping PDEs

Scott MacLachlan

(Memorial University of Newfoundland)
## Abstract

Irksome is a library based on the Unified Form Language (UFL) that enables automated generation of Runge-Kutta methods for time-stepping with finite element spatial discretizations of partial differential equations. Allowing users to express semidiscrete forms of PDEs, it generates UFL for the stage-coupled variational problems to be solved at each time step. The Firedrake package then generates efficient code for evaluating these variational problems and allows users a wide range of options to deploy efficient algebraic solvers in PETSc. We will survey some of the features of Irksome, and then address the major challenge facing practitioners of fully implicit RK methods -- solution of the stage-coupled algebraic system. Many strategies that scale well with respect to mesh parameters and the number of stages are being explored in the literature, and we will present a "monolithic" framework for stage-coupled multigrid that appears quite promising. As an example, we will demonstrate this preconditioning strategy for the Navier-Stokes equations, comparing fully implicit integrators with diagonally implicit schemes.

Monday, 10:00-12:00,

Chernoff Hall 213

Delay Differential Equations and Their Applications

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10:00-10:30

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Time Delays, Symmetry and Hopf Bifurcation in Neural Networks

Sue Ann Campbell

(University of Waterloo)
## Abstract

We consider networks of oscillator nodes with time delayed, global circulant coupling. We first study the existence of Hopf bifurcations induced by coupling time delay, and then use symmetric Hopf bifurcation theory to determine how these bifurcations lead to different patterns of phase-locked oscillations. We apply the theory to a variety of systems inspired by biological neural networks to show how Hopf bifurcations can determine the synchronization state of the network. Finally we show how interaction between two Hopf bifurcations corresponding to different oscillation patterns an induce complex torus solutions in the network.

10:30-11:00

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Transient Oscillations in Immune Response to Viral Infections due to Delay and Functional Forms

Michael Li

(University of Alberta)
## Abstract

I will show some data on immune responses that exhibits robust and finite-time oscillations. We will examine models with different functional forms of response function and incorporation of time delay to identify mechanisms that can lead to transient oscillations.

11:00-11:30

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Lyapunov functionals for Disease Models with Delayed Vector Transmission

Connell McCluskey

(Wilfrid Laurier University)
## Abstract

Lyapunov functions, used in the global stability analysis of dynamical systems, are notoriously difficult to find, even for ODEs. Nevertheless, Lyapunov functions have been found for many dynamical systems, giving a ``library" of pairs:
\[
\Bigl( \text{dynamical system}, \text{Lyapunov function} \Bigr).
\]
This library can be drawn upon when exploring the stability of a dynamical system that is similar to a system for which a Lyapunov function is known.
When studying a delay differential equation (DDE), there is typically an associated ODE that can be obtained by setting the delay equal to zero. If the associated ODE appears in the library, then this can give a good starting point for finding a Lyapunov function for the DDE.
In this talk, we will apply these ideas to compartmental models of infectious disease for which there is vector-style transmission with delay, similar to $\beta S(t) I(t-\tau)$.
This is joint work with Julian Christopher.

11:30-12:00

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Recent advances in the initial value problems for first order differential equations

Kunquan Lan

(Toronto Metropolitan University)
## Abstract

In this presentation, I shall present the basic theory on the existence and uniqueness of solutions and local solutions
for initial value problems of first order ordinary differential equations with $L^{p}$-Carathéodory nonlinearities that are not necessarily continuous based on the following paper:
Kunquan Lan, A basic theory for initial value problems of first order ordinary differential equations with $L^{p}$-Caratheodory functions and applications, Journal of Differential Equations, 386 (2024), 368-403.

Monday, 10:00-12:00,

Chernoff Hall 250 (Aud)

Financial Mathematics

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10:00-10:30

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On the relation between discrete and continuous-time affine option pricing models

Alexandru Badescu

(University of Calgary)
## Abstract

This article studies the weak convergence of discrete-time GARCH and stochastic volatility option pricing models that allow for fat tails, multi-component volatilities, and non-monotonic pricing kernels. We introduce a general affine framework that enables the simultaneous derivation of new diffusion limits for Gaussian and inverse Gaussian GARCH models based on distributional invariant parametric convergence rates. When restricted to one-component specifications, our limits yield non-degenerate bivariate diffusions, generalizing the existing results in the affine GARCH literature. By using alternative parametric convergence rates, we further provide a comprehensive classification of all possible limits for two new classes of affine and non-affine discrete-time stochastic volatility models. Specifically, we show that the canonical affine classes of models popularized in discrete and continuous time are not analogous to one another. Our theoretical results are supported by a series of numerical experiments that investigate the impact of parametric scaling assumptions and model features on the convergence of European option prices. Overall, we find that the new limiting diffusions produce option prices that are closest to their discrete-time counterparts sampled at daily frequency.

10:30-11:00

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A simulation and empirical study of the behaviour of the maximum likelihood estimator for stochastic volatility jump-diffusion models

Jean-François Bégin

(Simon Fraser University)
## Abstract

We investigate the behaviour of the maximum likelihood estimator (MLE) for stochastic volatility jump-diffusion models commonly used in financial risk management. A simulation study shows the practical conditions under which the MLE behaves according to theory. In an extensive empirical study based on nine indices and more than 6,000 individual stocks, we nonetheless find that the MLE is unable to replicate key higher moments. We then introduce a moment-targeted MLE—robust to model misspecification—and revisit both simulation and empirical studies. We find it performs better than the MLE, improving the management of financial risk.

11:00-11:30

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Optimal Robust Reinsurance with Multiple Insurers

Silvana Pesenti

(University of Toronto)
## Abstract

We study a reinsurer who faces multiple sources of model uncertainty. The reinsurer offers contracts to $n$ insurers whose claims follow compound Poisson processes representing both idiosyncratic and systemic sources of loss. As the reinsurer is uncertain about the insurers’ claim severity distributions and frequencies, they design reinsurance contracts that maximise their expected wealth subject to an entropy penalty. Insurers meanwhile seek to maximise their expected utility without ambiguity. We solve this continuous-time Stackelberg game for general reinsurance contracts and find that the reinsurer prices under a distortion of the barycentre of the insurers’ models. We apply our results to proportional reinsurance and excess-of-loss reinsurance contracts, and illustrate the solutions numerically. Furthermore, we solve the related problem where the reinsurer maximises, still under ambiguity, their expected utility and compare the solutions.

11:30-12:00

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What income to expect in retirement: A case study

Kristina Sendova

(University of Western Ontario)
## Abstract

To ensure a comfortable post-retirement life and the ability to cover living expenses, it is of utmost importance for individuals to have a clear understanding of how long their pre-retirement savings will last. In this research, we employ a ruin-theory approach to model the inflows and the outflows of retirees' portfolios. We track all transactions within the portfolios of retired clients sourced by a registered investment provider to Canada's Financial Wellness Lab at Western University. By utilizing an advanced ruin model, we calculate the mean and the median time it takes for savings to be exhausted, the probabilities of exhaustion of funds within the retirees' expected remaining lifetime while accounting for the observed withdrawal rates, and the deficit at ruin if a retiree has used up all of their savings. We also account for gender as well as for the risk tolerance of retired clients using a K-Means clustering algorithm. This allows us to compare the financial outcomes for female and male retirees and to enhance some findings in the literature. In the final phase of our study, we compare the results obtained by our methodology to the 4% rule which is a widely used approach for post-retirement spending. Our results show that most retirees can withdraw safely more than they currently do (around 2.5%). A withdrawal rate of about 4.5% is proved to be safe, but it might not provide sufficient income for most retirees since it yields approximately 20,000CAD per year for male retirees in the highest risk tolerance group who withdraw about 4.5% annually.

Monday, 10:00-12:00,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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10:00-10:30

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Instability, three-dimensionalization and mixing in late winter lakes

Marek Stastna

(University of Waterloo)
## Abstract

Water has the unique feature that its solid state floats, or in other words water achieves its largest possible density at a temperature above 0 Centigrade (around 4 degrees for distilled water). In late winter and early spring lakes are typically below 4 degrees, and many have a complete or nearly complete iced cover. As the solar insolation increases, even lakes that have iced over begin to be heated by radiation through the ice cover and a family of novel fluid phenomena can occur. I will survey work from my group over the past several years that outlines how the processes of instability, three-dimensionalization and mixing occur in this regime. I will outline both theoretical and computational challenges, showing that even though the under ice regime is relatively quiet compared to open water hydrodynamics during the warm season, it still yields puzzles for the theoretician and fluid structures that may have profound implications for lake ecology.

10:30-11:00

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Inertial instability and how it depends on eddy viscosity

Francis Poulin

(University of Waterloo)
## Abstract

There are many different mechanisms of shear instability in geophysical flows. The two that have received the most attention are barotropic and baroclinic instabilities, which are classified as global instabilities. Examples of local instabilities are gravitational, inertial/centrifuglal and symmetry. Unfortunately, there is not a consensus as to the nomenclature of these types of instabilities.
In this talk we present the results of a linear stability analysis for a range of Reynolds numbers, which depicts different strengths in eddy viscosities. It is revealed that at very high Reynolds numbers, inertial instability tends to dominate over barotropic or baroclinic instabilities. This is in contrast to small Reynolds numbers where the barotropic and baroclinic instabilities dominate. We also present the results from numerical simulations in Oceananigans.jl, which shows how the growth rates and spatial structures of the inertial instability can vary quite dramatically on the Reynolds number.

11:00-11:30

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Resonant sloshing in a shallow annular tank

David Amundsen

(Carleton University)
## Abstract

The resonant sloshing of fluid in a closed tank provides a fundamental basis for the study of resonant behaviour in a range of physical contexts. Extending upon past studies for a rectangular geometry, we consider the case of resonant radial waves in a cylindrically symmetric, shallow annular tank. In the absence of characteristic structure, we investigate and characterize the impact of the geometric effects through an underlying spectral decomposition. For weak curvature we find the associated extended solvability criteria for an appropriately truncated modal expansion. As expected, this limits to a single mode response for high curvature and a fully commensurate (fKdV) response in the limit that the geometric effects vanish. For comparison and further insight these analytic approximations are further supplemented by numerical simulations based on the underlying equations of motion and nonlinear surface conditions. Joint work with Benjamin Cheng.

11:30-12:00

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Long-time dynamics of a heavy solid with a fluid-filled cavity

Anirban Dutta

(Queen's University)
## Abstract

In this talk, we consider the dynamics of a heavy rigid body constrained to rotate around a frictionless, fixed point, and with an interior cavity entirely filled with a Navier-Stokes fluid. Examples of such a fluid-solid system include fluid-filled spinning tops or fluid-filled spherical pendulums. Through a nonlinear spectral stability analysis, we show that for a large class of fluid-solid configurations and for any initial data (corresponding to the system having finite initial mechanical energy), there exists a time after which each distributional solution to the governing equations approaches a steady state at an exponential rate.

Monday, 10:00-12:00,

Stirling Hall 401

Mathematical Modelling of Behaviour

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10:00-10:30

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Asymptotic limits of fear in a behaviour-modified disease model

Iain Moyles

(York University)
## Abstract

We explore a mathematical model of disease transmission with a fearful compartment. Susceptible individuals become afraid by either interacting with individuals who are already afraid or those who are infected. Individuals who are afraid take protective measures via contact reductions to reduce risk of transmission. Individuals can lose fear naturally over time or because they see people recovering from the disease. We consider two scenarios of the model, one where fear is obtained at a slower rate than disease spread and one where it is comparable. In the former we show that behavioural change cannot impact disease outcome, but in the latter, we observe that sufficient behavioural intervention can reduce disease impact. However, response to recovery can induce a bifurcation where contact reduction cannot mitigate disease spread. We identify this bifurcation and demonstrate its implication on disease dynamics and final size.

10:30-11:00

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Coupled disease and fear dynamics can lead to significant bifurcations in final size

Rebecca Tyson

(University of British Columbia Okanagan)
## Abstract

Effective management of epidemics requires not only modeling the disease itself but also the population's fear respons to both the disease and the vaccine. These fear responses can be modeled as contagions that occur alongside that of the disease itself. Here we take an existing model of these three contagions (disease, fear of disease, and fear of vaccine) and extend it to include a double-fear compartment for individuals who are simultaneously fearful of both the disease and the vaccine. We show that there is a trade-off between the rates of fear acquisition and fear loss that, in certain ranges, can result in bifurcations in final epidemic size. The direction of each bifurcation (from small to large epidemic size or vice versa) varies as the rate of fear acquistion increases. We show that these transitions are linked to whether the epidemic consists of one or two infection waves.

11:00-11:30

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Mathematical modelling for HIV-ZIKV co-infections

Bouchra Nasri

(Université de Montréal)
## Abstract

In this talk, we examine the dynamics of HIV and ZIKV and their interactions. We begin by exploring the qualitative behaviour of each model separately. Next, we analyze the dynamics of the co-infection model using thresholds and outcomes defined separately for each model. We then propose control interventions and study their impact on the spread of these viruses. This work is carried out in collaboration with J. P. Romero-Leiton, J. Arino and I. Sekkak.

11:30-12:00

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Vaccination, NPIs, and collective action under social norms

Bryce Morsky

(Florida State University)
## Abstract

Social dynamics are an integral part of the spread of disease affecting contact rates as well as the adoption of pharmaceutical and non-pharmaceutical interventions (NPIs). When vaccines provide waning immunity, efficient and timely uptake of boosters is required to maintain protection and flatten the curve of infections. How then do social dynamics affect the timely uptake of vaccines and adoption of NPIs and thereby the course of an epidemic? To explore this scenario, behavioural-epidemiological models are explored that feature a tipping-point dynamics for the uptake of vaccines or adoption of NPIs that combines the risk of infection, perceived cost of the vaccine/NPI, and social payoffs for deviating from the decision making of others. The social payoffs are derived from a social norm of conformity, and they create a collective action problem. A key finding driven by this dilemma is that waves of vaccine uptake and infections can occur due to inefficient and delayed uptake of boosters. This results in a nonlinear response of the infection load to the transmission rate: an intermediate transmission rate can result in greater prevalence of disease relative to more or less transmissible diseases. Further, global information about the prevalence of the disease and vaccine/NPI uptake increases the infection load and peak relative to information restricted to individuals' contact networks. Thus, decisions driven by local information can mitigate the collective action problem across the population. Finally, the optimal public policy program to promote disease mitigating behaviours is shown to be one that focuses on overcoming social inertia at the start of an epidemic.

Monday, 10:00-12:00,

Stirling Hall 414

Advancing Health and Medicine through Scientific Computing: Mechanistic Modelling, Machine Learning, and Quantitative Systems Pharmacology

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10:00-10:30

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Learning Chemotherapy Drug Action with Universal Physics-Informed Neural Networks

Mohammad Kohandel

(University of Waterloo)
## Abstract

Quantitative systems pharmacology (QSP) serves as a vital tool for evaluating drug efficacy and toxicity pre-clinically. However, constructing a QSP model necessitates extensive manual curation of literature, parameter fitting, and simplifying assumptions. In this study, we leverage Universal Physics-Informed Neural Networks (UPINNs) to learn unknown components within differential equations that govern chemotherapy pharmacodynamics. Specifically, we employ UPINNs to elucidate the mechanisms underlying three commonly utilized chemotherapeutic drug actions using synthetic data. We also demonstrate the capability of UPINNs to simultaneously fit parameters for multiple datasets. While our analyses are based on simplified examples, our findings underscore the potential of UPINNs in uncovering unknown terms within pharmacodynamic and pharmacokinetic models.

10:30-11:00

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Tumour-associated macrophages are immunotherapy targets in glioblastoma

Morgan Craig

(Sainte-Justine University Hospital Azrieli Research Centre / Université de Montréal)
## Abstract

Glioblastoma is a deadly brain and central nervous system cancer for which standard-of-care (SOC) only moderately extends survival. Immune checkpoint blockade (ICB) has been intensively studied to improve treatment outcomes, but improvements to overall survival are limited to a subset of patients and overall, ICB has failed in glioblastoma with and without standard-of-care therapy. New immunotherapeutic approaches are required to prolong patient survival. Our previous work showed that the limited recruitment and penetration of CD8+ T cells within glioblastomas hampers ICB success. To study putative treatment options for glioblastoma, we developed a comprehensive, mechanistic mathematical model of SOC and ICB that describes tumour-immune interactions within the tumour microenvironment. Our results suggest that tumour-associated macrophages/microglia (TAMs) are compelling targets to improve treatment outcomes. Our study lays the framework for continued experimental work developing TAM-targeting therapies for glioblastoma.

11:00-11:30

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Data driven QSP modeling of cancer: a step toward personalized treatment

Leili Shahriyari

(University of Massachusetts Amherst)
## Abstract

One of the common approach for predicting the cancer patients response to treatments is the adaptation of a mechanistic model informed by quantitative systems pharmacology (QSP), a computational method with potential in drug response analysis. One of the notable challenges in QSP modeling is the accurate calibration of model parameters, which traditionally rely on broad data sources that may not account for individual patient variability. Our approach seeks to contribute to this field by focusing on individual patient data to refine model parameters, aiming for a more personalized digital twin representation. Through sensitivity analysis and uncertainty quantification, we attempt to understand the complex interactions within the model, striving to improve the reliability of our predictions. This effort to personalize the QSP model, while still in its early stages, is driven by a desire to better understand the intricate network of cellular and molecular interactions in cancer and to provide insights that may eventually support more tailored treatment strategies. Our work represents a cautious step forward in the pursuit of personalized medicine in oncology, acknowledging the vast complexities and challenges that lie ahead.

11:30-12:00

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Practical Parameter Identifiability and Handling of Censored Data with Bayesian Inference in Models of Tumour Growth

Kathleen Wilkie

(Toronto Metropolitan University)
## Abstract

Mechanistic mathematical models are a powerful tool to help us
understand and predict the dynamics of tumour growth under various
conditions. In this work, we use five models with an increasing number of
parameters to explore how certain (often overlooked) decisions in
estimating parameters from data affect
the outcome of the analysis. In particular, we propose a framework
for including tumour volume measurements that fall outside the upper
and lower limits of detection, which are normally discarded. We
demonstrate how excluding censored data results in an overestimation
of the initial tumour volume and the model-predicted tumour volumes
prior to the first measurements, and an underestimation of the
carrying capacity and the predicted volumes beyond the
latest measurable time points. We show how the choice of
prior for the model parameters can impact the posterior distributions,
and illustrate that reporting the most likely parameters and their
95\% credible interval can lead to confusing or misleading
interpretations. We hope this work will encourage others to carefully
consider the choices made in parameter estimation and to consider
adopting the approaches discussed in this talk.
This is joint work with
Jamie Porthiyas, Daniel Nussey
(Department of Mathematics, Toronto Metropolitan University, Toronto, CAN);
Catherine A. A. Beauchemin, Christian Quirouette
(Department of Physics, Toronto Metropolitan University, Toronto, CAN); and
Donald C. Warren (Florida Institute of Technology, Melbourne, USA).

Monday, 10:00-12:00,

Stirling Hall A

Infectious disease modelling for small jurisdictions

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10:00-10:30

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Modeling and Prospects to Support Small Jurisdiction Public Health in Canada

Michael Li

(Public Health Agency of Canada)
## Abstract

Mathematical modeling has been critical in supporting public health initiatives, providing valuable insights into disease dynamics, intervention strategies, and resource allocation. While modeling played an important role in the COVID-19 pandemic response and has had many successes, there is still much to be done, especially as we transition out of the pandemic into the new norm. In particular, many regional heterogeneity effects and challenges from small jurisdictions were masked by the larger jurisdictions. In this talk, I will discuss prospects working towards supporting small-jurisdiction public health.

10:30-11:00

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Applied Public Health Modelling Software: macpan2

Steven Walker

(McMaster University)
## Abstract

The McMasterPandemic model and software package was created for COVID-19 forecasting. However, the pressure to provide regular forecasts hindered software development. The macpan2 project aims to build a more general public health modelling tool, incorporating lessons learned from the pandemic. macpan2 streamlines modelling for small jurisdictions, where modellers juggle multiple roles, enhancing efficiency without sacrificing rigor. Instead of building models from scratch, applied modellers can use macpan2's library of predefined models as starting points. macpan2 allows for flexible modification of predefined models to adequately address new public health situations. macpan2 encourages targeted model modifications for direct comparison with relevant data, using a standard data format designed to work well with standard data prep tools. macpan2 uses formal mathematical optimization for efficient calibration of model parameters to data, even when these parameters change over time. In this presentation, I'll demonstrate macpan2 usage with Covid-19, Mpox, and Measles examples, highlighting demographic stochasticity modifications important for small jurisdictions (source code will be shared). I'll conclude by discussing macpan2 alternatives like epiverse-trace and stan, comparing their pros and cons.

11:00-11:30

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Dynamic Response to Omicron Spread Under Structured Alert Levels: A Compartmental Analysis of Newfoundland and Labrador's Public Health Strategy

Francis Anokye

(Memorial University of Newfoundland)
## Abstract

Severe acute respiratory syndrome coronavirus (SARS-CoV-2) started spreading to all provinces across Canada in March 2020. Newfoundland and Labrador implemented stringent nonpharmaceutical interventions (NPIs) effectively keeping transmission rates lower compared to other provinces. However, the emergence of the highly transmissible, Omicron variant (SARS-CoV-2 B.1.1.529) in December 2021 posed new public health challenges. The province responded swiftly by modifying its existing system of COVID-19 measures called alert levels (categorized into five distinct levels) that corresponded to the progressive tightening or relaxation of restrictions. As of now, the level of transmission of the Omicron variant under these alert levels remains unclear. To address this, we created the SEARCH-ID compartmental model, analyzing the epidemic dynamics from December 2021 to June 2022 using two primary data streams: reported cases adjusted for underreporting, which provide near real-time insights but are limited by testing capacity and eligibility; and seroprevalence, which offers comprehensive exposure data but with a delay. This approach allowed us to assess the real-time versus retrospective views of the outbreak's progression under the different alert levels. Our approach ensures a detailed assessment of Omicron's progression under the provincial alert levels, revealing critical insights into the effectiveness of public health measures. Our analysis emphasizes the need for adaptable and responsive public health policies to successfully manage evolving epidemic scenarios, highlighting the importance of continuous adaptation and assessment of policy measures.

11:30-12:00

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Airborne Transmission Model for SARS-CoV-2 in Northern Remote Canadian Households

Shokoofeh Nourbakhsh

(Public Health Agency of Canada)
## Abstract

Current population-level respiratory disease modelling practices often overlook the influence of indoor environmental factors on the accumulation of infectious aerosols and airborne transmission within enclosed spaces. Recognizing the significance of individual infection risk heterogeneity due to indoor air quality parameters becomes particularly crucial when modelling disease transmission for small communities with drastic differences in their geographical location and housing structure as opposed to major urban centers. Our study presents an airborne transmission model tailored to household settings in remote northern communities, characterized by prolonged winter seasons (e.g., resulting in longer time spent indoors) and larger-than-average household sizes compared to the Canadian norm. Our findings illustrate the interconnectedness of indoor environmental conditions (e.g., ventilation, temperature, humidity) and crowding in shaping cumulative exposure to viral-laden droplets and transmission risk in northern Inuit households. This modelling endeavour holds promise for integration into population-level disease transmission models, offering insights to guide epidemic curve projections within the community using indoor environmental properties.

Monday, 10:00-12:00,

Stirling Hall B

Celestial Mechanics: Old and New in Dynamical Systems

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10:00-10:30

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Completely parabolic and total colliding trajectories are the basic representatives of a large class of asymptotic motions

Alessandro Portaluri

(University of Turin)
## Abstract

In this talk we sketch the construction of an index theory for such classes of motions. Both problems suffer from a lack of compactness and can be brought in a similar form of a Lagrangian system on the half (time) line by a regularizing change of coordinates which preserves the Lagrangian structure. We introduce a Maslov-type index which is suitable to capture the asymptotic nature of these trajectories as half-clinic orbits and we develop the relative index theory by proving the relation with the Morse index of these trajectories as critical points of the Lagrangian action functional. If time permits, we discuss asymptotic estimates for the growth of the Morse index for such classes of solutions as well as possible applications of non-action minimization methods in the Newtonian N-body problem. This talk is based on a recent joint work with Barutello, Hu and Terracini.

10:30-11:00

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Mountain pass frozen planet orbits in the helium atom model

Stefano Baranzini

(University of Turin)
## Abstract

We study a one dimensional model for the Helium atom in which the two electrons and the nucleus are collinear and subject to electric attraction/repulsion. The nucleus is fixed at the origin and the system is governed by two coupled non-linear singular ODEs.
Using a mountain pass type argument and a suitable smoothing of the action functional, we show the existence of a particular family of periodic solutions called frozen planet orbits, for all negative values of the energy. For energy close to zero, they are qualitatively characterized by the fact that one electron keeps collapsing into the nucleus whereas the outer one oscillates very slowly and far off.
This is a joint work with G. Canneori and S. Terracini.

11:00-11:30

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The N-centre problem on surfaces: complex and chaotic behaviours

Gian Marco Canneori

(University of Turin)
## Abstract

In this talk I will state a generalised version of the $N$-centre problem of Celestial Mechanics, where the motion of a test particle takes place on a punctured surface $(M\setminus\{c_1,\ldots,c_N\},g)$ and the leading potential $V$ has the following prescribed behaviour close to the centres
\[
V(q)\sim C_j d_{g}(q,c_j)^{-\alpha_j},\quad \text{when}\ q\in\mathcal{U}(c_j),
\]
for a positive constant $C_j$ and $\alpha_j\geq 1$. I will show how to construct many periodic solutions in distinct homotopy classes, avoiding collisions with the centres. As a result, I will identify an invariant set for the system which is semi-conjugated with the Bernoulli shift. After that, I will recognise some situations in which the topological relation is actually a conjugation, and thus a chaotic map acts on the invariant set. For instance, this is possible when the curvature of $g$ is negative and the mechanical energy is above some threshold. This is a joint work with Stefano Baranzini.

11:30-12:00

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Morse Index Theory for Periodic Trajectories in Billiards

Henry Kavle

(Maine School of Science and Mathematics)
## Abstract

In a billiard table with $C^2$ boundary, trajectories are critical points of the negative length functional on the space of admissible paths in the table. We will discuss Morse theory for periodic trajectories, including a geometric interpretation of the Morse index, a Morse index criterion for linear stability of periodic trajectories, and a sufficient condition expressed in terms of the evolute of the boundary for a billiard to have a linearly stable period-2 trajectory.

Monday, 10:00-12:00,

Stirling Hall C

Modelling heterogeneity in ecology, epidemiology, and evolution

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10:00-10:30

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Microbial Competition in the Self-Cycling Fermentation Process

Tyler Meadows

(Queen's University)
## Abstract

Self-cycling fermentation is an industrial process used for the cultivation of microorganisms, which has found use in wastewater treatment systems and pharmaceutical production. The process is comprised of two stages: a batch stage in which the microbes consume the nutrients and grow, and a decanting stage in which the reactor is partially emptied and refilled with fresh nutrient. We analyze an impulsive differential equation model for the competition between an arbitrary number of species for a single nutrient and show that, unlike in continuous culture models, multiple species are able to coexist. We establish criteria for the coexistence of two species in the form of a periodic solution, as well as for competitive exclusion.

10:30-11:00

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Heterogeneity in mutation rate and spectrum

Lindi Wahl

(University of Western Ontario)
## Abstract

In evolutionary modelling, both the mutation rate (how many mutations occur) and the mutation spectrum (what types of mutations occur) are often assumed constant. I will highlight several research projects in which we have relaxed these assumptions, demonstrating how heterogeneity does (or does not) change key qualitative predictions. Recent experimental evidence demonstrates that microbial populations frequently experience episodes of elevated mutation rates, and that these changes in mutation rate are coupled with changes in mutation spectrum. Thus understanding this heterogeneity has important implications for pathogen evolution.

11:00-11:30

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Modelling the impact of precaution on disease dynamics and its evolution

Tianyu Cheng

(York University)
## Abstract

In this talk, by introducing the notion of practically susceptible population, which is a fraction of the biologically susceptible population, and assuming that the fraction depends on the severity of the epidemic and the level of precaution of the public, we propose a general framework model with the response level involving the epidemic. We study how behaviour response evolves with epidemics and the impact of such evolution on the response. We verify the well-posedness and confirm the disease’s eventual vanishing for the framework model under the assumption that the basic reproduction number \(R_0 \lt 1\); For \(R_0 \gt 1\) when the precaution level is taken to be the instantaneous best response function, the endemic dynamic is shown to be the dynamic of converging to the endemic equilibrium, while when the precaution level is the delayed best response, the endemic dynamic can be either convergence to the endemic equilibrium, or convergence to a periodic solution. Our derivation offers a justification/explanation for the best response used in some literature. By replacing ``adopting the best response" with ``adapting toward the best response", we also explore the adaptive long-term dynamics.

11:30-12:00

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Cell Entrainment in a Mechano-Chemical Model of Collective Cell Migration

Andreas Buttenschoen

(University of Massachusetts Amherst)
## Abstract

Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics also play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both chemical and mechanical cues, but also to be spatially and temporally heterogeneous. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration. Motivated by recent one-dimensional experiments (e.g. micro-channels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations).
Using this framework, we build cell migration models of both loose (mesenchymal) and cohering (epithelial) tissues. We use numerical simulations, and analysis tools, such as bifurcation and local perturbation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration. We show how feedback from mechanical tension to GTPase activation lead to a variety of dynamics, including collective and individual cell migration phenotypes.

Monday, 13:30-15:30,

Chernoff Hall 117

Advancing Scientific computing through recent High-Performance Computing paradigms

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13:30-14:00

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Transforming Sparse Matrix Computation

Kazem Cheshmi

(McMaster University)
## Abstract

Sparse computations are a crucial category of algorithms characterized by minimal interaction between system components. These algorithms are essential for various scientific simulations, including computer graphics, weather forecasting, data analytics, and machine learning. The effectiveness of these simulations heavily relies on the efficient execution of sparse computations. However, irregular memory access patterns and the inherent nature of sparse computations limit their ability to fully utilize high-performance computing systems.
In this presentation, I will address the fundamental question of how to optimize complex sparse codes and algorithms for practical applications. I will introduce innovative strategies for automating and redesigning sparse linear algebra computations by decoupling the symbolic information from the numerical manipulations within sparse calculations. I will demonstrate how these novel approaches in symbolic decoupling can automatically generate high-performance code that significantly outperforms even highly-tuned code from state-of-the-art linear solvers and numerical optimization libraries.

14:00-14:30

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Parallel Sparse Polynomial Multiplication on Chiplet-Based CPUs

Alexander Brandt

(Dalhousie University)
## Abstract

Chiplets are small integrated circuits which are packaged together to act as a single integrated circuit. The use of chiplets in CPU architectures is motivated by practical and economic considerations in the manufacturing process as well as the continued demand for increased computational performance. Chiplet-based CPUs promise to offer more cores per socket and better per-core performance than is possible with the traditional monolithic design. What is limiting performance now is software's ability to effectively exploit this new architectural paradigm.
In this talk we will examine sparse multivariate polynomial multiplication as an illustrative example of designing and implementing high-performance parallel algorithms for chiplet-based architectures. A key consideration will be the partitioned L3 cache which leads to on-chip Non-Uniform Memory Access (NUMA). Particular attention will be given to data locality, inter-core communication, and thread cooperation. We will also discuss hardware topology, cache hierarchies, and thread pinning.

14:30-15:00

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Leveraging nonlinear approximation and random sampling in scientific computing

Simone Brugiapaglia

(Concordia University)
## Abstract

Techniques based on nonlinear approximation and random sampling are two essential mathematical pillars of modern data science and machine learning. On the one hand, nonlinear approximation techniques such as neural networks and sparse polynomials can reproduce extremely complex function classes. On the other hand, random sampling is at the core of reconstruction methods able to perform well in the data-scarce regime such as classical and generative compressive sensing. Notably, random sampling techniques such as Monte Carlo sampling are also "embarrassingly parallelizable".
Motivated by the success of nonlinear approximation and random sampling in data science, in this talk we will show their benefits in the context of scientific computing. We will review recent progress on numerical methods for high-dimensional function approximation, surrogate modelling, signal reconstruction and PDE solution, focusing on techniques accompanied by rigorous theoretical guarantees.

15:00-15:30

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Informed Normalized Gradient Flow Method for Parameterized Schroedinger Operator

Emmanuel Lorin

(Carleton University)
## Abstract

We are interested in the numerical computation of the point spectrum of parameterized Schroedinger operators, including operators with spectral gaps. We propose a neural network-based normalized gradient flow algorithm, allowing dissolution-free computation of the point spectrum. Additionally, we provide a rigorous accuracy analysis under proper conditions. Among the fundamental applications, we consider computations of edge states and their dynamics in photonic graphene, corresponding to eigenvalues of parameterized Schroedinger operators with non-constant coefficients which are periodic in a given direction. The convergence is proven, and numerical computations are presented.

Monday, 13:30-15:30,

Chernoff Hall 211

Recent Progress on the Intersections of Nonlinear Dynamics, Control, Learning, and Optimization

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13:30-14:00

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Dynamic Global Feedback Stabilization: why do the twist?

Mohamed-Ali Belabbas

(University of Illinois, Urbana-Champaign)
## Abstract

We investigate global dynamic feedback stabilization from a topological viewpoint. In particular, we consider the general case of dynamic feedback systems, whereby the total space (which includes the state space of the system and of the controller) is a fibre bundle, and derive conditions on the topology of the bundle that are necessary for various notions of global stabilization to hold. This point of view highlight the importance of distinguishing trivial bundles and twisted bundles in the study of global dynamic feedback stabilization, as we show that dynamic feedback defined on a twisted bundle can stabilize systems that dynamic feedback on trivial bundles cannot.

14:00-14:30

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Nonparametric Steady-state Learning for Robust Output Regulation of Nonlinear Output Feedback Systems

Shimin Wang

(Massachusetts Institute of Technology)
## Abstract

This article addresses the nonadaptive and robust output regulation problem of the general nonlinear output feedback system with error output. The global robust output regulation problem for a class of general output feedback nonlinear systems with an uncertain exosystem and high relative degree can be tackled by constructing a linear generic internal model provided that a continuous nonlinear mapping exists. Leveraging the presented nonadaptive framework facilitates the conversion of the nonlinear robust output regulation problem into a robust nonadaptive stabilization endeavour for the augmented system endowed with Input-to-State Stable dynamics, removing the need for constructing a specific Lyapunov function with positive semidefinite derivatives. To ensure the feasibility of the nonlinear mapping, the approach is extended by incorporating the nonparametric learning framework. Moreover, the introduced nonparametric learning framework provides the ability to learn the dynamics of the steady-state/input behaviour from the signal generated from the internal model only using the output error feedback. As a result, the nonadaptive/nonparametric approach can be advantageous by guaranteeing convergence of the estimation and tracking error even when the underlying controlled system dynamics are complex or poorly understood. The effectiveness of the theoretical results is illustrated for a controlled duffing system and a continuously stirred tank reactor

14:30-15:00

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An extremum seeking control approach for data driven control of uncertain nonlinear systems

Martin Guay

(Queen's University)
## Abstract

The complexity of system dynamics can often be an obstacle in the development of reliable dynamical models. In classical control engineering methodologies, the knowledge of the system’s dynamics has always been a key element in the design, testing and implementation of control systems. Since the development of reliable dynamical models is often restrictively onerous and fraught with technical and experimental difficulties, the access of high-quality dynamical models is often limited. The last ten years has seen a tremendous amount of research activity on the development of model free control techniques. One leading technique is extremum-seeking control (ESC). This technique has been applied extensively in many application areas such as biomedical engineering, aerospace engineering, automotive, biotechnology and process control. In this study, we seek to review some of the new developments on the generalization of extremum seeking control as a data-driven controller design technique. It is shown how one can apply this technique to design reliable control systems that require only limited knowledge of the system dynamics. Several applications are presented to demonstrate the versatility of this technique.

15:00-15:30

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Resonantly Forced ODEs and Repeated Roots

Allan R. Willms

(University of Guelph)
## Abstract

We present a little-known method for finding particular solutions to resonantly forced linear ordinary differential equations, which was recently published in SIAM Review . The method is much simpler than the method of variation of parameters and is also applicable to the case of repeated linear operators. We illustrate the method on a number of examples.

Monday, 13:30-15:30,

Chernoff Hall 213

Topics in Cell Biology

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13:30-14:00

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From Forces to Functions: Modelling Biological Condensates

Aiden Huffman

(University of Waterloo)
## Abstract

This talk introduces tools and techniques for modelling biological condensates, which are liquid-liquid phase separations comprised of biological materials. These condensates behave similarly to oil droplets in water and are part of the broader category of active droplets, including Janus droplets and microcapsules. To enhance our understanding of their biological functions and potential industrial applications, we employ a diffuse-interface method for simulation. This method handles topological changes, such as droplet fusion and breakup, without the need for heuristics often employed in interface tracking methods or volume of fluid methods. These heuristics are necessary to manage node additions or removals or for interface reconstruction.
Our simulations capture the mobility of active droplets driven by variations in chemical concentrations, which arise from changes in reaction rates or pathways between the bulk and droplet phases. To demonstrate these abilities, we present a toy model that captures the essential phenomenological properties of real condensate systems. Throughout the simulation, spatial variations in chemical concentrations, which subsequently affect surface tension, produce flows. These flows enable the droplets to spontaneously navigate through the fluid as observed in some experiments. Time permitting, we will use these tools to investigate the efficacy of mobile biological condensates in regulating and promoting chemical reactions.

14:00-14:30

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Bayesian Mapping of Molecular Diffusion.

Ilhem Bouderbala

(University of Alberta)
## Abstract

Developing mechanistic models and employing statistical methods to unravel biological complexities have become rapidly advancing research areas. We aim to understand the intricacies of cytosolic crowding within the cellular environment by analyzing nanoparticle diffusion patterns. We hypothesize that changes in nanoparticle movement directly relate to distinct physiological processes influenced by varying crowding gradients. Assuming uniform initial diffusion coefficients across all particles, we explore the impact of a heterogeneous medium on diffusion dynamics, focusing on how spatially dependent diffusion is affected by varying crowding levels. Areas with increased crowding show a dampening effect on diffusion coefficients, while regions with lower crowding densities exhibit increased diffusion coefficients. We apply a Bayesian inference approach using a counting measurement process that quantifies the number of particles crossing a boundary with a mean proportional to the flux of particles across the boundary. We developed an algorithm combining Gibbs sampler and Hamiltonian Monte Carlo algorithm (GHMC) to perform particle tracking and mapping the molecular diffusion, offering valuable insights into the movement and behaviour of nanoparticles within the cellular environment.

14:30-15:00

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Spatial organization of T cell surface receptors: implications on ligand discriminability and the design of nanoparticle therapies.

Louis Richez

(McGill University)
## Abstract

T cells demonstrate a remarkable sensitivity and specificity in the binding of their T cell receptors (TCR) towards antigen peptide-Major Histocompatibility Complex (pMHC) molecules. This characteristic feature of the TCR is essential for the proper functioning of the adaptive immune response, yet how exactly these T cells are able to achieve near perfect discrimination of pMHC ligands remains incompletely understood. Most modelling efforts of early T cell activation, such as McKeithan’s kinetic proofreading model, focus primarily on the downstream signalling network. Less emphasis has been placed on how the spatial organization of surface TCRs may contribute to preferential ligand binding and cooperativity. Using dynamic Monte Carlo simulations of various TCR configurations on the cell surface, we show that receptor clustering can substantially contribute to ligand discrimination in polyvalent binding interactions. We investigate the implications of these results on the design of nanoparticle-based T cell therapies and identify key geometrical features required for nanoparticle-induced T cell activation. In this talk, I will provide an overview of these findings.

15:00-15:30

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Operon dynamics modeled with threshold state-dependent delays

Zhao (Wendy) Wang

(McGill Univeristy)
## Abstract

Time-delays arise naturally in biological systems involving transport processes. Mathematical models of operon dynamics incorporating constant transcriptional and translational delays have been developed and show similar dynamics to models without delay. We derived an extended model taking into account the effect of cell growth and variable delays that depend on the state of the system. We develop techniques to make the model numerically tractable and we find that inclusion of threshold state-dependent delays lead to expanded possible operon dynamics. Because of the complexity of the model, we also consider a reduced model which is a scalar differential equation with one threshold state-dependent delay and systemically study the various cases when feedback and transport velocity are described by increasing or decreasing (or constant) Hill functions of the state variable. We also examine the stability and bifurcations of the steady states in a limiting case where the Hill function turns into a piecewise constant function. The dynamics with variable transport velocity is more interesting and complex due to the existence of high dimensional bifurcations of the steady states as well as periodic orbits. The steady state could undergo fold-Hopf bifurcation and Bogdanov–Takens bifurcation, which were inferred to occur but not explicitly detected in the full model. We also find signs of Shilnikov-type homoclinic bifurcation in the reduced model which was hinted to exist in the full model. Understanding the dynamics of the reduced scalar model may help to locate regions where interesting dynamics could occur for the full model.

Monday, 13:30-15:30,

Chernoff Hall 250 (Aud)

Financial Mathematics

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13:30-14:00

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Deep hedging under imperfect liquidity

Frédéric Godin

(Concordia University)
## Abstract

This work explores the optimization of hedging strategies for financial options in the presence of imperfect liquidity for the underlying asset. A deep reinforcement learning approach is used to obtain the solution to the problem of minimizing global hedging losses risk under a given illiquidity market impact model. Numerical investigations reveal that the discrepancies between the optimal policy and delta hedging benchmarks are complex and materially driven by various interacting (and sometimes competing) parameters and state variables, such as market depth and impact resilience parameters, the underlying asset drift, the hedging portfolio value, time-to-maturity and past hedging positions. Such complexity highlights the need to rely on sophisticated optimization schemes such as deep reinforcement learning to uncover the optimal policy.

14:00-14:30

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Generative Ornstein–Uhlenbeck Markets via Geometric Deep Learning

Cody Hyndman

(Concordia University)
## Abstract

We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of solves this problem without having prior assumptions on the market’s “clipped” log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.

14:30-15:00

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Analyzing Retirement Preparedness: A Study of a Canadian Investment Data Set

Yang Miao

(Western University)
## Abstract

Having a financially sound retirement plan is crucial to a person's overall financial wellness. It is of great research interest to assess whether a population is well prepared for their retirement. To this end, we obtain an investment data set from a registered Canadian investment provider. We analyze the financial instruments of the clients, as well as their investment behaviours. After building models for both components, the investor's wealth at retirement is projected, which is then compared with the commonly used retirement savings goals. Finally, we compare the results with the existing literature and comment on the retirement preparedness of the client cohort.

15:00-15:30

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Neural Operators Can Play Dynamic Stackelberg Games

Anastasis Kratsios

(McMaster University and Vector Institute)
## Abstract

We show that the solution map to broad range of dynamic Stackelberg games can be approximated by neural operators, depending on polynomially many parameters. The approximation is uniform on compact subsets of an infinite-dimensional space of predictable processes.

Monday, 13:30-15:30,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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13:30-14:00

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Recent Advances in Polymer Viscoelasticity From General Rigid Bead-Rod Theory

Jeffrey Giacomin

(University of Nevada Reno)
## Abstract

One good way to explain the elasticity of a polymeric liquid, is to just consider the
orientation distribution of the macromolecules. When exploring how macromolecular
architecture affects the elasticity of a polymeric liquid, we find general rigid bead-rod theory
to be both versatile and accurate. This theory sculpts macromolecules using beads and rods.
Whereas beads represent points of Stokes flow resistances, the rods represent rigid
separations. In this way, how the shape of the macromolecule affects its rheological behavior
in suspension is determined. Our work shows the recent advances in polymer viscoelasticity
using general rigid bead-rod theory, including the discovery of the first new materials
functions from general bead-rod theory since the first, the complex viscosity of Hassager
(1974). These include the steady shear material functions, large-amplitude oscillatory shear
flow material functions, and the steady uniaxial, biaxial and planar extensional viscosities.
We find each of these material functions to depend upon the same molecular feature: the
ratio of the macromolecular moment of inertia about the molecular axis to that about the
axes transverse to the molecular axis. We then use these new material functions to bridge
the Oldroyd 8-constant framework (and thus all of its many special cases) to general bead-rod theory.

14:00-14:30

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Rotational Taylor dispersion of passive and active Brownian particles

Zhiwei Peng

(University of Alberta)
## Abstract

Transport and mixing of active particles in the presence of fluid flows are important for various physical, biological, and industrial processes. In contrast to the extensive study of the long-time effective transport of active or passive particles in position (linear) space, the dynamics and transport of active particles in orientation space remains relatively less developed. In this work, we develop a rotational Taylor dispersion theory that characterizes the long-time orientational dynamics of both active and passive Brownian particles in unbounded linear and bounded quadratic (Poiseuille) flows. We show that at long times the net orientational distribution satisfies an effective rotational advection diffusion equation. We show that in Poiseuille flow, the effective rotational dispersion of a passive Brownian particle (zero swim speed) is enhanced compared to the bare rotational diffusivity of the particle. Compared to the rotational dispersion of passive Brownian particles, activity (i.e. self-propulsion) reduces the long-time rotational dispersion. To elucidate the swimming-induced reduction in dispersion, weak-swimming asymptotic analysis is considered. Our findings may be useful for the understanding of the coupling between flow-induced rotations and Brownian motion.

14:30-15:00

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Modeling and Simulation of Viscoplastic Fluid Transport in Grooved Channels

Seyed Mohammad Taghavi

(Université Laval)
## Abstract

We study the transport of viscoplastic fluids through channels with grooved superhydrophobic walls. To this end, we employ a comprehensive modeling approach and high-resolution numerical simulations and, in particular, consider longitudinal, transverse, and oblique orientations of the grooves. We use the perturbation theory to derive semi-analytical and closed-form solutions for the velocity fields, whose results are validated against our numerical simulations. Finally, we highlight the strong nonlinear effect of viscoplastic rheology and analyze the stabilizing/destabilizing effects of slip conditions on the flow.

15:00-15:30

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Improved vane-in-cup rheometry of yield-stress fluids

Emad Chaparian

(University of Strathclyde)
## Abstract

A computational analysis is presented to qualify traditional and fractal vane-in-cup geometries for accurate rheometry of yield-stress fluids with and without slip within and around vane tools with $N=3$ to $24$ arms for a wide range of Bingham numbers (i.e. the ratio of the yield stress over the characteristic viscous stress). This allows for accurate calculations of the velocity and stress fields around vanes with various geometries, as well as direct comparison to experimental observations of the output torque measured by a rheometer, revealing sources of variation and error. We describe the impact of the vane structure on the fluid velocity field, from few-arm cruciform vanes ($N\leq6$) that significantly perturb the flow away from ideal azimuthal kinematics, to many-arm fractal vanes ($N\geq12$) in which the internal structural features are successfully “cloaked” by a yield surface. This results in the shearing of an almost-circular ring of viscoplastic fluid that is indistinguishable from the annular ring of fluid deformed around a slip-free rotating cylindrical bob and leads to more accurate rheometric measurements of the material flow curve. Moreover, in direct comparison with data from previous literature, we show that slip conditions on the vane surface do not impact the velocity field or measured overall torque, whereas slip conditions on the smooth outer wall have significant impact on data, even when using a vane geometry. Rheo-PIV measurements are conducted using Carbopol and $\kappa$-Carrageenan gels to further validate the numerical results.

Monday, 13:30-15:30,

Stirling Hall 401

Mathematical Modelling of Behaviour

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13:30-14:00

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Bayesian Paramterization of Coupled Behaviour-Disease Models

Sefah Frimpong

(University of Waterloo)
## Abstract

Mathematical models have been widely used to understand the dynamics of diseases from infectious diseases to oncology. Many infectious disease models have generally helped to understand the behaviour of diseases and in making predictions. However, recent data shows that the dynamics of these diseases are influenced by the behaviour of the host population. With evidence of imitation dynamics amongst the host population affecting the transmission of the disease. This work establishes that coupled behaviour-disease models give more information about the disease and improve the predictive powers of the models. We illustrate this concept by applying a formulated coupled behaviour-disease model for the first year of the COVID-19 virus from selected countries and cities while parameter estimation is performed using an Approximate Bayesian Computation (ABC) approach. We examine the predictive power of a conventional deterministic SIR model and a coupled behaviour-disease model which takes into account the seasonality of the COVID-19 virus. Using an adjusted AIC statistical measure for model performance, we obtained a similar performance for both models with respect to fitting but observed the coupled model outperformed the disease model. Also, the peak magnitude and duration for the second peak within the prediction period had the coupled model match closely with the data unlike the disease model.

14:00-14:30

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A PDE model of social distancing applied to the COVID-19 pandemic

Zahra Khanzad

(York University)
## Abstract

Many disease ODE models use dynamic contact structures by allowing flow through compartments, but it is necessary to clarify the number of compartments needed. In this talk, we present a SIR model with compartmental physical distancing. We assess how social distancing affects disease burden by varying the number of compartments. We then connect dynamic contact structures in the ODE model and continuum distance. We create an equivalent PDE model by taking the distancing continuum limit to transition to a distancing continuum. Comparing ODE and PDE models sheds light on the scenarios where the PDE model offers advantages over the ODE counterpart, highlighting its potential for capturing continuous behaviors in disease dynamics.

14:30-15:00

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Effect of Homophily on Coupled Behavior-Disease Dynamics Near a Tipping Point

Zitao He

(University of Waterloo)
## Abstract

Understanding the interplay between social activities and disease dynamics is crucial for effective public health interventions. Recent studies using coupled behavior-disease models assumed homogeneous populations. However, heterogeneity in population, such as different social groups, cannot be ignored. In this study, we divided the population into social media users and non-users, and investigated the impact of homophily (the tendency for individuals to associate with others similar to themselves) and online events on disease dynamics. Our results revealed that homophily hinders the adoption of vaccinating strategies, hastening the approach to a tipping point after which the population converges to an endemic equilibrium with no vaccine uptake. Furthermore, we found that online events can significantly influence disease dynamics, with early discussions on social media platforms serving as an early warning signal of potential disease outbreaks. Our model provided insights into the mechanisms underlying these phenomena and underscored the importance of considering homophily in disease modeling and public health strategies.

15:00-15:30

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Multiplex Network Modeling for the Impact of the Opinion and Behavior of Mask- wearing on the Spreading and Control of COVID-19

Sanaz Gholizadeh

(York University)
## Abstract

We propose a network model to find out how and to what extent the level of people's behavior
and opinion toward protection measures will affect the spread and transmission of a disease, such
as the SEAIRS model of COVID-19. We have demonstrated how two simultaneous spreading
processes, such as disease spreading and behavior-changing propagation, work together and
impact each other within the same population group by utilizing a multiplex network. For
studying people's attitudes toward behavior changing, we specifically consider the case of mask-
wearing protection measures. Our model quantifies behavior change as a combination of two
factors. The first is the act of matching attitudes and the influence pressure of others, which is
known as the threshold model. The second is the fear of the increasing number of confirmed
cases, known as the fear effect. These two behavior effects may occur via media, virtual
networks, and communication between friends. Then, by using the Micro Markov Chain method,
we show all the system's possibilities and transition probabilities. Our results show that different
levels of people's adherence to mask-wearing as a protection measure can influence disease
spreading and vice-versa. Our research reveals periodic solutions that indicate a reciprocal
relationship between disease spread and behavior change.
Keywords: COVID-19; fear effect; opinion; mask-wearing behavior; multiplex network models;
Markov chain; threshold model; transmission

Monday, 13:30-15:30,

Stirling Hall 414

Computational Neuroscience

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13:30-14:00

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Defining neural heterogeneity based on their intrinsic and extrinsic properties

Anmar Khadra

(McGill University)
## Abstract

Neurons ubiquitously display heterogeneities in spiking activity even within a given cell type. To date, the relative contributions of extrinsic mechanisms (e.g., synaptic bombardment) and intrinsic mechanisms (e.g., conductances, cell morphology) towards determining spiking activity remain poorly understood. We have recently addressed this important question using a novel approach that combines biophysical techniques, in which extracellular in vivo recordings of electrosensory pyramidal cells within weakly electric fish, are combined with computational modeling. Specifically, we explored how varying parameters of a Hodgkin-Huxley type model successfully reproduced the highly heterogeneous spiking activities seen experimentally. Model parameters that varied the most were then used to gauge the relative contributions of extrinsic vs. intrinsic mechanisms. Overall, extrinsic synaptic input was predicted to be the main factor accounting for spiking heterogeneities. We tested this prediction experimentally by performing two different manipulations: i) pharmacologically inactivating feedback; ii) applying the neuromodulator serotonin. Our model predicted that feedback inactivation should reduce while serotonin application should increase spiking heterogeneities. Experiments corroborated these predictions. Importantly, for serotonin application, increased heterogeneity occurred despite a strong reduction in intrinsic membrane conductance, further demonstrating that extrinsic synaptic input is the primary determinant of spiking heterogeneities in vivo. In this talk, I will provide an overview of these findings.

14:00-14:30

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Influence of heterogeneous myelination patterns on axonal conduction and vulnerability to demyelination

Afroditi Talidou

(University of Ottawa)
## Abstract

Axons of the mammalian brain display significant variations in their myelination motifs. Far from being regular and uniform, the distribution patterns of myelin sheaths vary significantly between axons, and across brain areas. To explore the influence of such variability on axonal conduction, we developed an axon model based on a system of PDEs, exhibiting myelin distributions mirroring those observed experimentally in different regions of the central nervous system of mice. We also examined how varying myelination patterns predispose axons to failure. Our study shows such variability significantly impacts axonal conduction timing and reliability. Action potential propagation was found to be highly sensitive to the specific arrangement and ordering of myelinated and/or exposed segments along axons, indicating that axonal conduction is non-linear and path-dependent. Furthermore, properties of axonal conduction were found to differ between cortical and callosal axons, influencing their vulnerability to demyelination, while shaping both conduction time and predisposition to failure. Our analysis indicates that callosal axons are particularly sensitive to myelin changes, especially after damage. These findings highlight the crucial role of myelination profiles in brain function and disease.

14:30-15:00

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Mean-Field Description for Spiking Neural Networks with Calcium-Dependent Short-Term Synaptic Plasticity

Liang Chen

(University of Waterloo)
## Abstract

We introduce a network model for a population of heterogeneous quadratic integrate-and-fire (QIF) neurons with presynaptic short-term plasticity (STP). This model captures calcium-dependent synaptic dynamics and integrates various forms of short-term synaptic plasticity, including facilitation, depression, and mixed effects, in a relatively simple mathematical form. Following the theoretical framework of Ott-Antonsen mean-field theory for the phase model or the equivalent Lorentzian ansatz for the QIF model, we derive a macroscopic description for such a neural network, valid in the limit of infinitely many neurons in the network. Furthermore, we investigate the effect of STP on collective dynamics, particularly the effect of muscarinic activation at inhibitory synapses using the parameters fitted for the PV BC-pyramidal cell in the CA1 region of the hippocampus. Our numerical simulations demonstrate satisfactory agreement between the neural network and the derived mean-field model. The introduction of muscarine results in a decreased postsynaptic response, leading to an extended transient oscillating process towards stationary states and an increased possibility of the emergence of collective oscillations in the inhibitory network. For the excitatory network, it may have a decreased tendency to oscillate. To our knowledge, our mean-field system represents the first macroscopic description derived from spiking neural networks with synaptic kinetics. It is important to investigate the contribution of physiologically defined STP processes to neural networks through experimentally measurable models. Our models reflect biophysical properties, have direct functional implications, and support analysis and comparison with experiment data. In addition, muscarine is important in the regulation of numerous physiological processes, and its modulation is of great interest in the fields of pharmacology and medical research. Our mean-field framework will greatly facilitate understanding of its effects in networks and its relevance to normal and abnormal brain functions.

15:00-15:30

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Mathematical Modeling of Neurodegenerative Prion Diseases in One-Dimensional Neuronal Networks

Joel Williams

(University of Texas Rio Grande Valley)
## Abstract

This presentation introduces a mathematical model to simulate the progression of prion diseases in the brain. We model neurons as they interact with normal and misfolded (scrapie) proteins. The model uses a delay differential equation to describe changes in protein concentrations and neuronal viability, using various parameters to regulate protein degradation, misfolding rates, and the spread between interconnected neurons. Neurons are modeled in a one-dimensional space with various connectivity distributions to mimic different types of neuronal networks. We visualize how neurodegenerative diseases propagate through the neuronal network over time and even account for how different brain regions permit their spread.

Monday, 13:30-15:30,

Stirling Hall A

Infectious disease modelling for small jurisdictions

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13:30-14:00

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Emerging infectious disease modelling to support the needs of both small and large jurisdictions

Amy Hurford

(Memorial University)
## Abstract

Emerging infectious disease models support jurisdictions by synthesizing information, estimating key quantities, defining relationships, quantifying and managing uncertainty, presenting information intuitively and visually, and aiding in communicating with the public. Yet, common modelling approaches are often applicable only when community spread is continuously occurring, and may not be suitable for jurisdictions that experience long periods between community outbreaks or with novel socio-demographic and geographic features, which can frequently be small jurisdictions. Inspired by invasion biology, we develop epidemiological theory to meet the modelling needs of both small and large jurisdictions to respond to the threat of emerging infectious diseases. We develop models that can estimate the risk of disease establishment during periods between community outbreaks, and simulate counterfactual scenarios and fit to data for both sporadic or continuously occurring outbreaks. This modelling bridges existing gaps, and builds towards a unified theory to recommend the full range of public health measures and support the needs of both small and large jurisdictions.

14:00-14:30

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Changing contact patterns in Newfoundland and Labrador in response to public health measure during the COVID-19 pandemic

Renny Doig

(Simon Fraser University)
## Abstract

Between March 2020 and December 2021, Newfoundland and Labrador (NL) implemented a containment strategy as a part of its COVID-19 response. Contact tracing was a key component of this strategy; the relatively low incidence in NL during this period resulted in contact networks containing most or all of the contact individuals. In this project we use these complete contact networks to directly approximate the number of secondary cases as well as visualize contact patterns in the population. These contact patterns were compared under varying levels of stringency of public health measures. We observed heterogeneity in the contact patterns, becoming more pronounced with increasing stringency. Additionally, we found that the public health measures were successful in regulating the spread of the disease, keeping the average number of secondary cases around 1.

14:30-15:00

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Time of Infection on a Finite Network

Junling Ma

(University of Victoria)
## Abstract

An SI model for infectious disease transmission on a finite weighted digraph is exactly solvable. However, the solution becomes difficult to obtain as the size of the network increases, because the dimensionality of the underlying Markov chain to increases exponentially with the size. We propose a novel method to yield the exact solution to the time of infection for any node. Applying to networks of farms or cities, this method can be used to calculate the time distribution for disease importation. In this framework, the latent stage and the time of symptom onset (or time of observing the first case in a city or farm) with realistic wait time distributions can be modelled by introducing extra nodes in the graph.

15:00-15:30

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Effects of COVID-19 NPIs on seasonal infections

Matthew Betti

(Mount Allison University)
## Abstract

Non-pharmaceutical Interventions (NPIs) put in place to combat COVID-19 had a significant impact on other respiratory illnesses. We fit an SIR model with historical influenza data to determine which epidemiological parameters (attack rate, effective population size, reproduction number) were most affected by NPIs. We study these parameters on a national and provincial level to determine how larger and smaller provinces differ in the effectiveness of NPIs on endemic respiratory illnesses.

Monday, 13:30-15:30,

Stirling Hall B

Celestial Mechanics: Old and New in Dynamical Systems

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13:30-14:00

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Minimization and Hyperbolicity

Daniel Offin

(Queen's University)
## Abstract

The application of the global variational method has had a spectacular list of achievements in the search and understanding of periodic orbits in Hamiltonian systems. We investigate the relationship
between strict locally minimizing properties of the Lagrangian action
and hyperbolicity of the Euler-Lagrange flow on compact invariant
subsets of the energy surface $\mathcal E^{-1}(k)$. As an application of our main
result we invesigate the nonintegrability of generic perturbations of
the mathematical pendulum equation with periodic forcing. This is
joint work with Gonzalo Contreras of CIMAT, Mexico.

14:00-14:30

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Moser Transformation of a Stochastically Perturbed Kepler Problem

Archishman Saha

(University of Ottawa)
## Abstract

We consider a stochastic Kepler problem perturbed by a Hamiltonian noise affecting the angular momentum vector. We show that while the angular momentum and the Laplace-Runge-Lenz vectors are not conserved, their norms satisfy the usual deterministic dynamics. This allows us to determine the set of initial conditions leading to collisions. Further, in a procedure similar to Moser's regularization, we transform the stochastic Kepler problem to obtain its dynamics as a stochastic geodesic flow on a 3-sphere.

14:30-15:00

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Data-driven summaries of qualitative dynamics with Dynamic Mode Decomposition

Tanya Schmah

(University of Ottawa)
## Abstract

Various data-driven methods have been applied to the problem of summarising qualitative features of a dynamical system. We apply a version of Dynamic Mode Decomposition to the Circular Restricted Three Body Problem, leading to a low-dimensional linear approximation to the global dynamics, which we use to produce a classification of orbits.
Joint work with Cristina Stoica and Narmeen Oozeer.

15:00-15:30

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Triple-collision in the isosceles three-body problem

Cristina Stoica

(Wilfrid Laurier University)
## Abstract

The isosceles three-body problem may be considered as the simplest non-trivial case study of the more complicated classical N-body problem. In this talk we present some results related to the behaviour near the triple collision singularity in isosceles three body problems with modified Manev- and Schwarzschild-type potentials. In particular, we answer (positively to) a question posed by Diacu in 1993 related to the existence of non-zero angular momenta orbits ejecting/tending asymptotically to triple collision.

Monday, 13:30-15:30,

Stirling Hall C

Modelling heterogeneity in ecology, epidemiology, and evolution

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13:30-14:00

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A mathematical model between keystone species: bears, salmon, and vegetation

Xiaoying Wang

(Trent University)
## Abstract

We study an ecosystem of three keystone species: salmon, bears, and vegetation. Bears consume salmon and vegetation for energy and nutrient intake but the food quality differs significantly due to the nutritional level difference between salmon and vegetation. We propose a stoichiometric predator-prey model that not only tracks the energy flow from one trophic level to another but also nutrient recycling in the system. Analytical results show that bears may coexist with salmon and vegetation at a steady state but the abundance of salmon may differ under different regimes. Numerical simulations reveal that a smaller vegetation growth rate may drive the vegetation population to extinction whereas a large vegetation growth rate may drive the salmon population to extinction. Moreover, a large vegetation growth rate may stabilize the system where the bear, salmon, and vegetation populations oscillate periodically.

14:00-14:30

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Critical Gap Size for Stable Populations in Patchy Environments

Ali Beykzadeh

(University of New Brunswick)
## Abstract

This study explores the persistence of a population within a single patch with hard boundaries, such as a lake, implying that no disperser exits the habitat. A centrally located gap, like a fishing zone, divides the population within the patch. We present a method to calculate the maximum size of this gap for which the non-zero state is stable. The population’s life cycle is modeled by a one-dimensional domain integrodifference equation (IDE). This approach separates the reproduction phase from the dispersal phase in the species’ life cycle. For selected parameter values, we found that when individuals are more likely to settle in the fishing zone, or when they move slower in it and spend more time there, the fishing area must be shorter, and the no-take length must be larger to maintain the population in the lake.
The relationship between the reproduction rate of the species in the no-take area and the optimal length of the fishing zone indicates that a longer fishing zone requires a higher reproduction rate in the no-take area to sustain the total population in the lake. This ensures that the no-take sides of the lake can support each other and prevent population collapse.

14:30-15:00

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The Effect of Climate Change Fluctuations on Population Abundance and Range Size

Jane Shaw MacDonald

(Simon Fraser University)
## Abstract

Climate change causes temperature isoclines to shift poleward or upward in altitude, consequently jeopardising many species’ persistence ability as they attempt to keep pace with their shifting thermal niche. Through mathematical modelling and averaging the speed of climate change by studying constant shifting speeds, we have gained a general understanding of the impact of the velocity of climate change on species persistence outcomes, and on population abundance and range-size. With a computational approach applied to a reaction-diffusion model, we explore the impacts of fluctuations in the shifting speed on these metrics. We examine two scenarios of fluctuating speeds: one where the thermal niche size remains constant, and another where it varies. For each case, we analyse how the amplitude and frequency of the environmental fluctuations affect population abundance and range size. By fixing population dynamics, we differentiate between long-lived species and short-lived species through relative scales between life-cycle and frequency of environmental fluctuations. We find that the species’ life cycle duration relative to the frequency of fluctuations yields varying outcomes in population abundance and range size; for example, in scenarios where the thermal niche size varies, our model predicts that short-lived species can show stronger responses to fluctuations, taking advantage of their thermal niche when and where it appears in times of habitat expansion, yet in times of habitat contraction this same strong response leaves them more susceptible to extinction.

15:00-15:30

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Stage-structured discrete-time population model of snow crab

Sophie Léger

(Université de Moncton)
## Abstract

The snow crab fishery is one of Canada's most profitable fisheries and is a significant economic driver in coastal communities in Atlantic Canada and Quebec. As snow crabs are generally considered to be a stenothermic species, with juvenile crabs being more sensitive to water temperature than adult crabs, the change in water temperature due to climate change is becoming worrisome. Population models are a helpful tool to better understand and predict how biological populations will change over time. These models can also help predict population responses to environmental changes by studying the effect of certain parameters on the population. As snow crab has a complex life cycle, developing an adequate population dynamics model for this species is challenging. Limiting the complexity of the model, at first, is therefore helpful to assess how life-history characteristics affect the population level. In this talk, we present a discrete-time population model for snow crab based on three developmental stages (i.e. immature, adolescent and mature) for each gender. The model, which is being developed to study the snow crab population in the southern Gulf of St. Lawrence, takes into consideration density-dependent intercohort processes (i.e. cannibalism), but predation is neglected as it is not believed to be an important factor in this region. We investigate the role of cannibalism and variability in recruitment in promoting cyclic population dynamics. Bifurcation analysis are performed to provide a more complete and comprehensive understanding of the dynamics of the population and numerical examples are presented.

Monday, 16:15-17:00,

Biosciences 1101 (Aud)

Plenary: Susanna Terracini

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16:15-17:00

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Chaotic behaviours in Celestial Mechanics

Susanna Terracini

(Università di Torino)
## Abstract

We show some examples of controlled chaotic trajectories in relevant models of Celestial Mechanics, investigating the mathematical mechanisms that lead to trajectories that are indeed complex, but visit given sets of configurations in a prescribed manner.

Monday, 17:30-18:30,

Biosciences 1101 (Aud)

NSERC Session

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Monday, 17:30-18:30,

Biosciences 1120

Contributed Session I

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17:30-17:45

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Modelling West Nile virus transmission in Canada using a cellular automata approach for multiple hosts (birds and humans) in heterogeneous landscape

Baki Cisse

(Public Health Agency of Canada)
## Abstract

Introduction: West-Nile virus (WNV) represents a growing public health risk in Canada, particularly in the context of climate change and increasing urbanization. Its periodic re-emergence is difficult to predict and seems to be related with infected migratory birds and the survival of infected mosquito vectors during winter. The main aim of this work was to explore the relative importance of these hypotheses, which have not yet explored in a spatially distributed model, on local WNV transmission.
Methods: We developed a compartmentalized and spatialized SEIRDS-SEI (Susceptible, Exposed, Infected, Recovered, Dead) WNV transmission model using a Cellular Automata (CA) approach. We introduced heterogeneity within bird populations by dividing our study area into two parts: Low Habitat Suitability (LHS) cells and High Habitat Suitability (HHS) cells for birds and then humans. We used 2010-2021 bird data from the eBird project and 2010-2019 mosquito data from Ontario Public Health to calibrate the model. In MATLAB software, we performed simulations and characterized the resulting epidemics in bird, mosquito, and human populations in time and space and compared the relative importance of the re-emergence scenarios.
Results/Discussion: With heterogeneous bird populations, we showed that the increase in the proportion of infected migratory birds in spring or the overwintering infectious mosquitoes, will likely amplify WNV transmission in human populations. We also established for the ‘infected bird simulations’, epidemics will be larger when infectious birds arrive in the LHS cells for birds, relative to HHS cells.
Conclusion: The arrival of infected birds in spring and the overwintering of infected mosquitoes has a similar impact on the local transmission of WNV, and are associated to the periodic re-emergence of the disease. Our research offers policymakers and health officials valuable insights into spatial-temporal frameworks to help prevention WNV transmission in southern Canada.
Keywords: West Nile virus, Modelling, Cellular automata, birds, mosquito, Canada

17:45-18:00

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A Distributed Delay Differential Equation Model to Study the Effect of Repeated Blood Donations on Hemoglobin and Storage Iron

Shaza Alsibaai

(McGill University)
## Abstract

Several experimental studies have shown that iron deficiency is common among regular blood donors. Indeed, the recommended inter-donation interval of 56 days (8 weeks) in the United States and Canada is based on old studies investigating only hemoglobin recovery after blood donation. Recent experimental studies, which measure other iron parameters after blood donation, have shown that this interval is very short to prevent iron deficiency in frequent blood donors. In this talk, we will present a mathematical model that we propose for erythropoiesis and iron metabolism and apply it to this problem. The model consists of seven coupled delayed differential equations (DDEs). The first equation describes the dynamics of mature erythrocytes in circulation. The following four equations track iron during erythropoiesis, including the hemoglobin iron within erythrocytes, iron in recycling macrophages, iron in circulating plasma, and iron in storage. The last two equations describe the dynamics of the principal regulating hormones: hepcidin and erythropoietin (EPO). Mathematically, including delays in our model has the advantage of minimizing the number of variables to circumvent issues with parameter identifiability that arise in ODE many-compartment models. Distributed delays allow us to capture the effect of the regulating hormone on the erythroid precursor cells. Our model is a system of DDEs with discrete and distributed delays; however, there is no available off-the-shelf computer package capable of directly solving this system of equations as an initial value problem. We show how to reformulate the distributed DDEs so that solutions can be simulated using a standard MATLAB solver. We present numerical simulations of our model for single and multiple blood donation scenarios. We reveal how repeated blood donations result in a significant iron storage depletion. We demonstrate the impact of lengthening the inter-donation interval and giving iron supplementation on the recovery of hemoglobin and storage iron. We also show the severe effect of having dietary iron intake below the recommended daily amount.

18:00-18:15

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Stability analysis of a new differential-difference model applied to the Pre-Exposure Prophylaxis (PrEP) effect on the spread of HIV

Gregoire Ranson

(York University)
## Abstract

In this research, an examination is conducted on a model derived from the inquiry into the efficacy of HIV Pre-Exposure Prophylaxis (PrEP) within high-risk populations. To achieve this objective, we employ an SI model coupled with an age-structured equation to delineate the dynamics of individuals under PrEP protection, incorporating an infected-dependent rate of new users recruited from the susceptible population. This nonlinear term is contingent upon a factor dedicated to the political or economic context of a government. Local asymptotic stability for both disease-free and endemic equilibria is established, and global asymptotic stability for the disease-free steady-state is demonstrated. To address the system's behaviour, a reduction of the partial differential equation is undertaken, presenting it as a coupled system of differential equations and a delayed difference equation. Lastly, persistence is substantiated when the endemic equilibrium is realized.

18:15-18:30

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Lyapunov Functions for Compartmental Disease Models with Added on Groups

Kaylee Devries

(Wilfrid Laurier University)
## Abstract

Previous work has shown that many compartmental disease models have a positive equilibrium for $\mathcal{R}_0 \ge 1$, which can be shown to be globally asymptotically stable through the use of a Lyapunov function. Many of these Lyapunov functions are similar, suggesting a pattern.
We compare the Lyapunov calculation for the standard $SEI$ model to the corresponding calculation for an $SEIT$ model where a treatment group $T$ has been added. Based on this analysis, we refine the calculations into a general result, finding algebraic conditions under which the Lyapunov function for one model extends to be a valid Lyapunov function for a related model that has been obtained by adding an additional group.
The method is then applied repeatedly to a multi-group $SI$ model leading to a general result for when a model is modified by adding several groups.

Monday, 17:30-18:30,

Biosciences 2109

Contributed Session II

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17:30-17:45

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Effects of heterogeneous distribution of resources and toxins on movement strategies

Lin Wang

(University of Ottawa)
## Abstract

In this talk, we explore the optimal movement strategies for organisms in characterized by varying distributions of resources and toxins. Our investigation is inspired by recent experiments on C. elegans movement in the environments with heterogeneously distributed food and toxins. The authors found that when resources and toxins overlap spatially, fast diffusion was beneficial for the population, whereas when they were in different locations, slow diffusion was better. We model the experimental system using reaction-diffusion-advection equations with a stage-structured population. We analyze how the principal eigenvalue of the linearized system depends on the diffusion and advection parameters, to identify the best combination between random motion (seeking resources) and directed motion (moving away from toxins, avoiding danger). Our main result is to determine the conditions under which the principal eigenvalue is monotonic with respect to diffusion or advection parameters, which will clarify whether larger or smaller diffusion or advection are beneficial. Specifically, we identify limiting scenarios in which diffusion and advection are very small or large. These theoretical insights deepen our comprehension of optimal movement strategies in heterogeneous environments and provide a theoretical basis for interpreting experimental observations.

17:45-18:00

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Life-history evolution in periodic environments

Rebekah Hall

(Simon Fraser University)
## Abstract

Life-history traits such as those determining an organism’s capacity for reproduction (the parameter '$r$') and ability to compete for resources (the parameter '$K$') demonstrate unique eco-evolutionary feedback loops due to their direct relationship to determining the fitness of a population. Classic theory holds that in a constant environment, evolution will maximise a population’s competitive ability in high-density environments. However, many environments undergo seasonal changes which may alter these evolutionary pressures. In this talk, I will present a competitive Lotka-Volterra model for life-history evolution under three different types of seasonal perturbations: fluctuating death rates, fluctuating resource levels, and repeated, sudden population crashes. Using asymptotic approximations and Floquet analysis on the long-term periodic solutions, we show that fluctuating resources cannot change the evolutionary outcome, but that under sufficiently harsh population crashes or fluctuating death rates, an environment will favour a high rate of reproduction over competitive ability.

18:00-18:15

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Predicting invasion probability of mutators

Marwa Tuffaha

(Western University)
## Abstract

Mutation rate and spectra changes, among other factors, are fundamental in shaping adaptive trajectories of asexual organisms, such as pathogenic bacteria and viruses. The distribution of fitness effects of mutations that are accessible to the organism also plays an important role in its evolution and ability to compete with other species. We examine the interaction between these three factors (mutation rates, mutation spectra, and the distribution of fitness effects) by simulating bacterial wildtype-mutator competition experiments and develop a mathematical model that estimates the invasion probability of the mutator. We show that mutation rates and spectra are not enough to predict the invasion probability; the detailed distribution of fitness effects should be taken into consideration as well. These theoretical predictions have been tested in laboratory competition experiments in bacteria, confirming our analyses and simulations.

18:15-18:30

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Modeling and analysis of a time-switching mosquito population suppression model

Yining Chen

(York University)
## Abstract

In this talk, we formulate and study a time-switching mosquito population suppression model with a Beverton-Holt form of offspring survival probability. Assuming that sterile mosquitoes are released impulsively and periodically. We introduce release waiting period $T$ and sexual lifespan $\bar T$ of sterile mosquitoes, and
consider three cases. When $T$ equals to $\bar T$, we explore the existence and stability of equilibria. When $T $ is larger than $\bar T$ or $T$ is smaller than $\bar T$, the model evolves into two switching equations. We confirm that when there is no periodic solutions, the origin is globally asymptotically stable; when there is a unique periodic solution, the unique periodic solution is globally asymptotically stable or semi-stable; when there are exact two periodic solutions, one is stable and the other is unstable. The periodic dynamics of the model are verified through numerical simulations. This research has theoretical and practical significance for in-depth understanding of mosquito population dynamics and the development of relevant prevention and control measures.

Monday, 18:30-19:30,

Biosciences Atrium

Poster Session

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18:30-19:30

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P1. Measles in Reykjavik, Iceland during the Pre-Vaccine Era: A Case Study

Anthony Pasion

(Queen's University)
## Abstract

As computational power advances, there is a growing trend toward developing mechanistic models to explain physical and biological phenomena. In this work, we evaluate the merits and limitations of a Continuous Time Markov Chain (CTMC) Susceptible-Exposed-Infected-Recovered (SEIR) measles model with seasonally varying transmission rates, cohort effects, and demographic and extra-demographic stochasticity on how well the model fits pre-vaccine era data in a small and isolated population. We present demographic information along with disease incidence data from Reykjavik, Iceland. By treating the population sizes and birth rates in this community as covariates, we perform parameter fitting using the maximization via iterated filtering algorithm. Finally, we discuss the outcomes of the simulations generated. (Joint work with FMG Magpantay)

18:30-19:30

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P2. EVOLUTIONARY STABILITY OF BACTERIAL PERSISTER CELLS

Chongming Li

(Queen's University)
## Abstract

I model the switching process of bacteria between antibiotic dormant features and normal active replication using an integro-reaction-diffusion-advection partial differential equation (PDEs). The PDE captures the impacts of epigenetic inheritance of metabolic state by implementing a non-local term that models a birth jump process. I prove the well-posedness of the non-local PDE model followed by the corresponding stability analysis on the positive steady-state solutions. Of primary interest will be to extend the model to a wider scenario of biological evolution by examining the evolutionarily stable strategies (ESSs) of persister cells. The idea is that genetic mutations will occasionally occur, and these mutations can alter any of the parameters describing the persister cell dynamics. We are most interested in exploring the effects of periodic application of antibiotics on the nature of the ESSs.

18:30-19:30

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P3. MODELLING ARCTIC CLIMATE RESPONSE TO PERMAFROST MELT

Tonima Datta chaity

(University of Guelph)
## Abstract

The effect of melting permafrost on the Arctic climate is investigated. A simple Energy Balance model consisting of a set of differential equations describing the temperatures of air, land, and water, the concentration of carbon dioxide and methane, and the carbon stores in the soil is developed. In addition, the model incorporates seasonal variation of the solar forcing. The model uses projected carbon dioxide and methane concentrations from the Representative Carbon Pathways published by the Intergovernmental Panel on Climate Change, along with additional carbon sourced from the melting permafrost. Through analysis of the model, it is determined whether melting permafrost significantly affects climate change in the Arctic.

18:30-19:30

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P4. Integrating dynamic model with deep learning to simulate multiple waves of COVID-19 outbreaks

Mengqi He

(York University)
## Abstract

Since the end of 2019 the COVID-19 repeatedly surges with most countries/territories experiencing multiple
waves, and mechanism-based epidemic models played important roles in understanding the transmission
mechanism of multiple epidemic waves. However, capturing temporal changes of the transmissibility of COVID-
19 during the multiple waves keeps ill-posed problem for traditional mechanism-based epidemic compartment
models, because that the transmission rate is usually assumed to be specific piecewise functions and more
parameters are added to the model once multiple epidemic waves involved, which poses a huge challenge
to parameter estimation. Meanwhile, data-driven deep neural networks fail to discover the driving factors
of repeated outbreaks and lack interpretability. In this study, aiming at developing a data-driven method to
project time-dependent parameters but also merging the advantage of mechanism-based models, we propose
a transmission dynamics informed neural network (TDINN) by encoding the SEIRD compartment model into
deep neural networks. We show that the proposed TDINN algorithm performs very well when fitting the
COVID-19 epidemic data with multiple waves, where the epidemics in the United States, Italy, South Africa,
and Kenya, and several outbreaks the Omicron variant in China are taken as examples. In addition, the
numerical simulation shows that the trained TDINN can also perform as a predictive model to capture the
future development of COVID-19 epidemic. We find that the transmission rate inferred by the TDINN frequently
fluctuates, and a feedback loop between the epidemic shifting and the changes of transmissibility drives the
occurrence of multiple waves. We observe a long response delay to the implementation of control interventions
in the four countries, while the decline of the transmission rate in the outbreaks in China usually happens once
the implementation of control interventions. The further simulation show that 17 days’ delay of the response to
the implementat

18:30-19:30

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P5. From process to structure of EWS

Francisca Olajide

(University of Ottawa)
## Abstract

The emergence of infectious diseases remains a huge challenge to public health. Early detection of outbreaks using early warning signals (EWSs) offers an invaluable opportunity for effective preparedness and disease management. In this study, we seek to understand the structure of these signals using a mechanistic model that captures epidemic and social processes. We analyzed the simulated time series for change points and EWSs (autocorrelation and variance). All time series showed the expected delay in that the detected change point occurred significantly after the parameter passed the bifurcation point. These early warning signals exhibited a stronger response after the threshold for disease emergence had been exceeded. Assessing different disease progression and intervention models will help determine the most effective signals for use in public-health settings.

18:30-19:30

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P6. Functional Koopman Analysis of Phase Mixing in Collisionless Systems

Keir Darling

(Queen's University)
## Abstract

We study solutions of the collisionless Boltzmann equation (CBE) in a functional Koopman representation. This facilitates the use of spectral techniques characteristic of the analysis of linear differential equations. For illustrative purposes, we first consider the classical phase mixing of a non-interacting CBE solution, $f$, subject to a quartic potential. Solutions are determined perturbatively relative to a harmonic oscillator. We impose a form of coarse-graining by choosing a finite dimensional basis to represent $f$ and its time evolution operators. We observe a relationship between the dimension of the representation and the algebraic multiplicity of the harmonic oscillator eigenvalues. The quartic potential splits the degenerate eigenvalues, which drives mixing in $f$. We then add a simple self-interaction modeled by a quadratic potential that tracks the distribution's center of mass. We study the effect of self-interaction on the mixing process by time-series analysis of the basis expansion coefficients for $f$. Mixing rate decreases in proportion to self-interaction strength in a manner qualitatively consistent with expectations from numerical simulations, but the present treatment offers quantitative insights. This work facilitates understanding the mechanism of phase mixing with and without mutually interacting particles, which appear in both gravitational and electromagnetic contexts. Questions about the representation of Hamiltonian systems obeying the CBE, and connections to dynamic mode decomposition and neural network based applications are discussed.

18:30-19:30

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P7. Regularity of solutions to the Navier equations with mixed boundary conditions

Jerin Tasnim Farin

(Queen's University)
## Abstract

In this poster, I will present some regularity results for solutions to the partial differential equations, the so-called Navier equations of linear elasticity, modelling the deformation of an elastic solid. We impose mixed (Dirichlet and Neumann-type) boundary conditions on the solid’s boundary. More precisely, we assume that the boundary of the solid is constituted by two disjoint components: an “interior” one subject to a non-zero displacement (a Dirichlet boundary condition), and an “exterior” one subject to a traction-free boundary condition (a Neumann-type condition). We will show existence and uniqueness of the solution to the corresponding initial-boundary value problem, and derive some further regularity of the traction vector on the boundary. Such a regularity result does not follow from the classical energy estimates; it is in the spirit of the “hidden regularity” shown for solutions to the wave equation with Dirichlet boundary conditions.

18:30-19:30

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P8. Effect of Acetylcholine on the formation of CA3 Neural Assemblies

Megha Manoj

(University of Waterloo)
## Abstract

Acetylcholine (Ach), a neuromodulator, has been implicated in the development of neurodegenerative disorders characterized by memory decline. Ach has also been linked to the encoding of new memories and learning. While the influence of Ach has been studied extensively at a single cell level, it remains to be studied at a network level, which is where memory formation is expected to occur. The underlying mechanism proposed here suggests that the activation of Ach receptors in the hippocampal cells, trigger some network level response that could be indicative of encoding a memory.
We explore this theory by investigating the impact of Ach on the dynamics driving ensemble formations within the neuron dense CA3 region of the hippocampal circuit. To capture this impact, we develop a computational model for a network of excitatory pyramidal cells, in which, each cell is supplemented with an additional M current regulated by Ach.
Further, a phase model reduction of a two-neuron system is used to predict the existence of stable clusters for corresponding larger networks equipped with nearest neighbour coupling. Depending on the connectivity between the neurons, in the presence of Ach, we find non-trivial multi-stable clusters in the network which synchronize in its absence. The results of this project could provide an insight into how Ach facilitates specific network transitions in the CA3 region that may be relevant in the process of storing memories. Strengthening our understanding of this effect could contribute to the search for novel therapeutic drugs targeting fatal neurodegenerative disorders like Alzheimer's disease.

18:30-19:30

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P9. A Mean-Field Games Approach to Score-based Generative Modeling

Benjamin Burns

(University of Massachusetts Amherst)
## Abstract

Advancements in diffusion-based generative modeling have made high-performing, image-based generative models, such as Stable Diffusion, accessible to anyone with an internet connection. It was shown early last year that diffusion-based generative models can be formulated in terms of a mean-field game (MFG). For score-based generative modeling (SGM) in particular, this MFG formulation admits alternate characterizations of the SGM based on its optimality conditions, which are a set of coupled nonlinear partial differential equations (PDE). The first PDE is a controlled Fokker-Planck equation which is equivalent to the denoising process in SGM, while the second PDE is a HJB equation that characterizes the optimal controller, whose solution is related to the score function. Based on this mathematically rigorous connection, we develop a PDE-based theory for explaining and understanding the role of latent space in SGM. In addition, we introduce two regularizers, the first based on measuring the discrepancy in the HJB equation, the second based on measuring discrepancy in satisfying the terminal condition. The terminal condition is determined by the training data. By including these regularizers, we are informing the structure of the score function, thereby constraining the search space. This strategy is well-grounded through the theory of mean-field games and HJB equations. Through experiments we will show that the HJB regularizer helps learn the score function in a more stable way, while the terminal condition regularizer is associated with higher quality samples.

18:30-19:30

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P10. Modeling the cytotoxicity of Romidepsin reveals the ineffectiveness of this drug in the "shock and kill" strategy

Qi Deng

(York University)
## Abstract

The "shock and kill" strategy is being widely explored to purge Human Immunodeficiency Virus (HIV) latent reservoirs. Romidepsin, a kind of latency-reversing agents (LRAs), has been shown to induce HIV RNA transcription. However, several clinical trials testing this drug have resulted in limited effect in reducing the HIV latent reservoirs. To understand the mechanisms underlying such limited effect, we develop a multi-scale model that incorporates pharmacokinetics and considers the toxicity of romidepsin to T cells in this paper. By fitting the model to the viral load data from plasma of six patients received romidepsin, we find that the model with T cell toxicity of romidepsin can well explain the clinical data. The dynamics of latently infected cells during romidepsin administration are explored using the best-fit parameter values. The results show that latently infected cells decrease very slowly and remain very stable overall in 4 of the 6 participants under the assumption of T cell toxicity of romidepsin. This implies that the ineffectiveness of romidepsin on latent reservoirs can be explained by its toxicity to T cells. In the remaining 2 participants, however, latently infected cells are quite stable without T cell toxicity of LRAs. It is found that the estimated activation rate of latently infected cells by romidepsin and the estimated elimination rate of romidepsin on immune cells for these two patients are very different from those for the other four patients. Thus we speculate that the heterogeneous response to romidepsin across participants may also be a determining factor of the effectiveness of romidepsin. These results may have significant implications in the search for the control of the infection.

18:30-19:30

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P11. Spatiotemporal Dynamics of the Unfolded Protein Response Mechanism in Prion Diseases

Omar Sharif

(Graduate Research Assistant)
## Abstract

Neurodegenerative diseases (NDs) affect the brain and central nervous system through the spread of toxic proteins. Two very common NDs are Alzheimer’s disease, which makes people lose their memory and ability to do things on their own over time, and Parkinson’s disease, which causes problems with muscle control. Among neurodegenerative diseases (NDs), it is common for the Unfolded Protein Response (UPR) to be activated when toxic proteins induce neuronal stress. The UPR slows or halts protein translation, helping to alleviate toxic load, but its activation may also lead to damage and apoptosis in neurons. We introduce a novel mathematical model to describe spatiotemporal dynamics of UPR in prion diseases. Our model, centered on a single neuron, incorporates heterodimer dynamics of representative proteins P (healthy) and S (toxic). The system comprises nonlinear reaction-diffusion equations with delayed, nonlinear flux for P. We discovered certain sets of parameters that show oscillations in the levels of both P and S proteins. These oscillations are more obvious when the S-diffusivity and S-clearance rates are small in comparison to P-diffusivity and P-clearance rates. Finally, we observe that as the delays in initiating the UPR increase, the UPR activity intensifies.

18:30-19:30

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P12. Modelling long-term security returns

Xinghan Zhu

(Western University)
## Abstract

This research focuses on the concerns of Canadian investors regarding portfolio diversification and preparedness for unexpected risks in retirement planning. It models market crashes and two main financial instruments as independent components to simulate clients’ portfolios. Initially exploring single distributions on mutual funds such as Laplace and t distributions, the research finds limited success. Instead, a normal-Weibull spliced distribution is introduced to model log returns.
The Geometric Brownian Motion (GBM) model is employed to predict and evaluate returns on common stocks using the Maximum Likelihood Estimator (MLE), assuming that daily log returns follow a normal distribution. Additionally, the Merton Jump Diffusion (MJD) model is considered to account for jumps in stock trajectories with an independent
Poisson process term based on the GBM model. Market crashes, defined as a decline of at least 10% in the S&P500 over a maximum of 252 trading days, are modelled using a homogeneous Poisson process. The combined simulation results show that the model is effective in most portfolio predictions.

18:30-19:30

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P13. A new linearization principle for nonlinear evolution equations

Anirban Dutta

(Queen's University)
## Abstract

In this poster, I will present a new linearization principle for the nonlinear stability analysis of equilibria of nonlinear evolution equations in Banach spaces. The two principal features of our evolution equations are that the set of equilibria forms a finite dimensional manifold, and $0$ is an eigenvalue of the relevant linear operator $L$, arising after linearizing the equation about an equilibrium. Classical "linearization principles", inferring that the nonlinear stability (or instability) of the equilibria is determined by the spectral properties of $L$, do not apply in our case. More recent "generalized principles of linearized stability" require strong regularity assumptions on the linearized equations (for example, $L$ must satisfy the property of maximal $L^p$-regularity). We prove a new linearization principle by assuming that $L$ is the generator of an analytic semigroup plus mild assumptions on the structure of the evolution equation. Specifically, we show that if (mild) solutions to our evolution equations exist globally in time and remain “close” to the manifold of equilibria at all times, then the solution must eventually converge to an equilibrium point at an exponential rate. I will also discuss an application of this abstract theory to a physical problem concerning the dynamics of a heavy top filled with a viscous fluid.

18:30-19:30

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P14. Numerical approximation of spike-type solutions to a one-dimensional sub-diffusive Gierer-Meinhardt model with controlled precision

Nehemie Nguimbous

(Thompson Rivers University)
## Abstract

This study focuses on numerically solving the sub-diffusive Gierer-Meinhardt model with controlled precision. We start by defining and explaining basic concepts of reaction diffusion, highlighting the main differences between normal and anomalous diffusion. Sub-diffusion is modelled at continuum level by fractional derivatives replacing regular ones in PDEs. Therefore an important part of our study involves fractional calculus, which provides a solid framework for describing sub-diffusive processes.
We then delve into the well-known Gierer-Meinhardt model, a reaction-diffusion system used to describe pattern formation in biological systems. Leveraging the matched asymptotic expansion technique, which is applicable due to the asymptotic smallness of certain parameters in the
system, we transform the differential Gierer-Meinhardt model into a differential algebraic system. This differential algebraic system contains a fractional operator denoted $\mathcal{D}^{\gamma}_{t}$, which involves the integral of a complicated function impossible to determine analytically. This operator depends on multiple parameters, and the number of subdivisions needed for numerical computation varies significantly with these parameters and the desired precision. To address this challenge, we have developed a program capable of precalculating the required number of subdivisions before computation, thus saving significant computation time. All elements in place, we use these tools to study the dynamics of the obtained solutions.

18:30-19:30

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P15. Applications of Scale-Varying Functional Data Analysis to Biological Species Distribution Modelling

Allan Roberts

(McMaster University)
## Abstract

Functional data analysis considers situations where at least some observations can be regarded as functions; moreover, the functions that are observed will often not be of a known parametric form. Types of functional data that are particularly relevant to ecological modelling are functional observations that attempt to capture time-varying or distance-varying phenomena; for example a habitat characteristic may be observed as being a function of time (e.g. temperature observed as a function of day of the year), or as being a function of spatial scale (e.g. an index of a local landscape attribute observed as a function of distance). Such situations are often handled by identifying a single spatial or temporal scale at which to represent an explanatory variable; however, an alternative is to use a functional data approach that allows habitat characteristics to be regarded as functions of scale, rather than as values observed at a single particular scale. One way to model datasets that include functional observations is with generalized additive models (GAMs). A GAM is a type of statistical model that allows the concurrent estimation of response curves for multiple environmental predictor variables and is a tool that is commonly used for modelling the distribution of biological species. Although there is available software that allows functional terms to be included in GAMs, scale-varying functional terms seem to be used rather infrequently in ecological modelling. Potential benefits of using scale-varying functional terms in species distribution models implemented with GAMs include improved interpretability and prediction accuracy; however, the increase in model complexity associated with the use of scale-varying functional terms will tend to increase computational expense, and could perhaps result in decreased prediction accuracy in cases where a model becomes overly complex. For instance, we might expect that an overly complex model could result from the use of observations of a predictor variable at a scale that is not biologically informative. This poster will report the results of fitting simulated datasets with generalized additive models including a scale-varying functional term; a goal of the simulations is to explore tradeoffs between model complexity, computational expense, and prediction accuracy.

18:30-19:30

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P16. Phase portrait control for a two patch reaction-diffusion equation

Romain Gérard

(Ecole Nationale des Ponts Paritech)
## Abstract

We consider a control problem for the dynamics of a single species in a one-dimensional heterogeneous environment. Specifically, we study the following two-patch reaction-diffusion model with boundary control:
\begin{equation*}
\begin{cases}
u_{t}=d_{l}u_{xx}+f_{l}(u)&\ t \gt 0,\ x\in (L,0),\\
u_{t}=d_{r}u_{xx}+f_{r}(u)&\ t \gt 0,\ x\in (L,0),\\
u(0,x)=u_{0}(x)&\ x\in [L,R],\\
u(t,L)=u(t,R)=a&\ t \gt 0,\\
u_{x}(t,0^{-})=\sigma u_{x}(t,0^{+})&\ t \gt 0.
\end{cases}
\end{equation*}
Here $u:\mathbb{R}_{\geq 0}\times (L,R)\to [0,1]$ represents the density of population which satisfies in the left and right patch $(L,0)$, $(0,R)$ two reaction-diffusion equations with different diffusion coefficient ($d_l$ and $d_r$) and rates of reproduction ($f_l$ and $f_r$). Both the rates of reproduction can be of monostable or bistable type.
We investigate whether the system can be steered to extinction (steady state 0) or invasion (steady state 1) in finite or infinite time by appropriately choosing the Dirichlet control $a$ at $x=L$ and $x=R$. This is an extension to the heterogeneous case of the analysis carried out in [Pouchol, Trelat, Zuazua, 2019].

18:30-19:30

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P17. Optimization of a Bullet

Sieon Kim

(Seoul International School)
## Abstract

We optimize the shape of a bullet given by the rotation of a polynomial curve under certain physical constraints with respect to air-resistance, using tools from calculus of variations in the general case. We produce a complete solution of the simpler case where the curve determining the radially generated bullet is quadratic. A potential method for generating air-resistance minimizers in the general case of smooth curves is provided, and a discussion of the physical feasibility of the analysis is then conducted.

18:30-19:30

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P18. Uncertainty quantification for the random HIV dynamical model driven by drug adherence

Dingding Yan

(York University)
## Abstract

In HIV drug therapy, the high variability of CD$4^+$ T cells and viral loads brings uncertainty to the determination of treatment options and the ultimate treatment efficacy, which may be the result of poor drug adherence. We develop a dynamical HIV model coupled with pharmacokinetics, driven by drug adherence as a random variable, and systematically study the uncertainty quantification, aiming to construct the relationship between drug adherence and therapeutic effect. Using adaptive generalized polynomial chaos, stochastic solutions are approximated as polynomials of input random parameters. Numerical simulations show that results obtained by this method are in good agreement, compared with results obtained through Monte Carlo sampling, which helps to verify the accuracy of approximation. Based on these expansions, we calculate the time-dependent probability density functions of this system theoretically and numerically. To verify the applicability of this model, we fit clinical data of four HIV patients, and the goodness of fit results demonstrate that the proposed random model depicts the dynamics of HIV well. Sensitivity analyses based on the Sobol index indicate that the randomness of drug effect has the greatest impact on both CD$4^+$ T cells and viral loads, compared to random initial values, which further highlights the significance of drug adherence. The proposed models and qualitative analysis results, along with monitoring CD$4^+$ T cells counts and viral loads, evaluate the influence of drug adherence on HIV treatment, which helps to better interpret clinical data with fluctuations and makes several contributions to the design of individual-based optimal antiretroviral strategies.

18:30-19:30

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P19. A nonlocal reaction-diffusion-advection model with free boundaries

Yaobin Tang

(York University)
## Abstract

A nonlocal diffusion single population model with advection and free boundaries is considered. Our aims is to discuss how the advection rate affects dynamics behaviors of species under the case of small advection. Firstly, the well-posed global solution is obtained. Secondly, we apply the eigenvalue problem of integro-differential operator to obtain the dichotomy and sharp criteria for persistence or extinction, which is determined by initial habitat and initial density. Further, the asymptotic spreading speed of species is estimated when spreading happens. Namely, we get the exact asymptotic spreading speed, and find that if kernel function satisfies certain conditions, then the leftward asymptotic spreading speed is less than the rightward one due to the impact of advection rate. Meanwhile, we also observe that accelerated spreading happens if certain conditions do not be satisfied.

18:30-19:30

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P20. Nestled Allies: Richardson’s Ground Squirrels and Artificial Burrows in the Conservation of Burrowing Owls

Tim Rogalsky

(Canadian Mennonite University)
## Abstract

Recent data indicate a critical decline in the Burrowing Owl (Athene cunicularia) populations across Canada's Prairie Regions, partially due to habitat loss driven by the culling of Richardson’s Ground Squirrels (Spermophilus richardsonii) through agricultural control. These squirrels provide essential burrows that the owls use for protection against predators and environmental extremes. In response, our study develops an ordinary differential equation framework to investigate the dynamics of this commensal relationship and the potential for artificial burrows to aid conservation efforts. The mathematical model encapsulates the population dynamics of both species under natural and anthropogenic pressures, including intrinsic growth rates, natural carrying capacities, the unidirectional benefit of squirrels to owls through burrow provision, the impact of agricultural culling on the squirrel population, and the effects of artificial burrows. Stability and bifurcation analysis was used to assess how variations in the artificial burrow effectiveness and squirrel culling rates affect population equilibria. Our analysis suggests that a substantial increase in the number of artificial burrows, by approximately threefold, is required to mitigate the risk of extinction for the Burrowing Owls. This study highlights the effectiveness of mathematical models in crafting and supporting conservation strategies, offering quantitative insights that can inform practical interventions and policy decisions that balance the dual needs of wildlife conservation and sustainable food production.

18:30-19:30

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P21. Study of skeleton muscle in cylindrical geometries

Harshil Pathak

(Simon Fraser University)
## Abstract

Skeletal muscles exhibit large mechanical deformations in a short period of time. Muscle contains fibres which can be non-linearly activated. We are interested in the study of the mechanical behaviour of muscle in cylindrical architecture (eg. earthworms). We will also study the impact of pennation angle in a cuboidal and cylindrical geometry. We use a fully 3-D model of elastic deformation in skeletal muscle, in a quasi-static regime. Our computation are based on Finite Element Method approach. We present numerical results based on it.

18:30-19:30

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P22. Vortex Rossby waves and the beta-gyre effect in a cyclonic vortex

Mingyao Cai

(Carleton University)
## Abstract

We examine the development of a vortex Rossby wave in a cyclonic vortex in a context where the effect of the rotation of the Earth affects the structure of the wave and generates a beta gyre. Vortex Rossby waves occur in the atmosphere in the form of outward-propagating disturbances within cyclonic vortices such as hurricanes. They result from the force due to the radial gradient of the vorticity of the cyclone. The rotation of the Earth contributes to the beta-gyre effect, or beta drift, where there is a secondary dipole circulation and a resulting displacement of the vortex. The vortex Rossby wave development is described by a nonlinear initial-value problem which allows asymptotic analyses and numerical solutions. The balance between the effects of nonlinearity and rotation gives rise to an additional component with wave number one, which causes a secondary spiral motion, consistent with a beta gyre. Joint work with L. Campbell.

18:30-19:30

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P23. Smeared Null Energy Condition Constraints on Dark Energy Equation of State

Elly Moghtaderi

(University of Waterloo, Perimeter Institute)
## Abstract

In general relativity, energy conditions can put a restriction on allowed geometries. One of the most prominent conditions is the classical null energy condition (NEC). However, quantum field theories can violate this condition which prompts the need for quantum null energy conditions (QNEC). The smeared null energy condition (SNEC) is a proposed QNEC, that modifies NEC by averaging it through a real, positive smearing function, and it allows the null energy to be negative over short smearing scales. This can have insightful implications for cosmological theories and dark energy models. Our goal is to apply the SNEC to a flat Friedmann-Lemaître-Robertson-Walker cosmology with pressure-less matter and dark energy as sources and find the imposed constraint on constant equation of state of dark energy and the possible allowance of phantom dark energy models that violate the classical NEC. This analysis can be extended to parameterized non-constant equations of state as well.

Tuesday, 8:30-9:15,

Biosciences 1101 (Aud)

CAIMS Industrial Research Prize Lecture: Huaiping Zhu

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Tuesday, 9:15-10:00,

Biosciences 1101 (Aud)

CAIMS Early Career Prize Lecture: David Del Rey Fernández

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9:15-10:00

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The Summation-by-Parts Framework for Solving PDEs: Past, Present, and, Future

David Del Rey Fernández

(University of Waterloo)
## Abstract

Simulation is essential in modern science and engineering and the numerical methods powering simulation represent crucial components in both. Despite tremendous effort and many successes, the development of efficient numerical methods with mathematical guarantees remains a difficult task, particularly in the context of nonlinear PDEs on complex, potentially moving and deforming, geometries. Nearly 50 years ago, summation-by-parts (SBP) operators were created by Kreiss and Scherer (1974) in order to bring to finite-difference methods the ability to systematically prove stability common in many finite-element approaches. Since those days, the SBP concept has matured into an abstract matrix based approach for analyzing a wide range of existing schemes, the development of novel schemes, and the design-order modification of existing schemes such that the result is provably stable. The matrix point of view gives incredible flexibility in designing and developing schemes. In recent years, these ideas have been extended to the notion of entropy-stability and have resulted in provably-stable schemes for a variety of nonlinear PDEs important in fluid mechanics (e.g., compressible Euler and Navier-Stokes equations). In this talk, I will first recount this evolution, highlighting important contributions to the SBP framework that result in efficient schemes applicable to practical problems. I will then discus current research directions and finish with a perspective on the future of the SBP-framework.

Tuesday, 10:30-11:15,

Biosciences 1101 (Aud)

Plenary: Sebastian Reich

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10:30-11:15

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The Mathematics of Nurturing a Digital Twin

Sebastian Reich

(University of Potsdam)
## Abstract

With the invention of digital computers in the mid 1940's, John von Neumann envisioned numerical weather prediction (NWP) as a revolutionising application of this technology and famously stated in a talk at Princeton in 1950: "All processes that are stable we shall predict. All processes that are unstable we shall control." In today's language, von Neumann had sown the seeds for the modern concept of NWP as a digital twin (DT) of actual weather processes in the atmosphere, its physical twin (PT). Since the days of von Neumann, DTs have found ground breaking applications in science and engineering. Still many challenges remain when considering highly complex multi-scale processes arising from, e.g., aeronautics, cognition, ecology, and pharmacology. Mathematically speaking, a DT can often be described as a partially observed Markov decision process (POMDP). Solving POMDPs computationally constitutes one of the most challenging problems around. Still, tremendous progress has been made in closely related fields such as data assimilation, uncertainty quantification, control and optimisation, and model reduction. A key emerging questions is thus how we can successfully synthesise these advances into a tool broadly applicable to DT. In my talk, I will map out one possible roadway.

Tuesday, 11:15-12:00,

Biosciences 1101 (Aud)

Plenary: Jim Gatheral

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11:15-12:00

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10 years of rough volatility: A current perspective

Jim Gatheral

(Baruch College, CUNY)
## Abstract

The scaling properties of implied volatility smiles with respect to time to expiration, and the corresponding scaling properties of the realized variance time series, which now appear universal, motivate the modeling of volatility as a function of fractional Brownian motion -- leading to what are known as rough volatility models. With an emphasis on recent developments, we give a comprehensive overview of rough volatility. We will explore the scaling properties of volatility and methods for estimating the roughness parameter H. We will also introduce the most popular models in the rough volatility literature and the computational schemes associated with them. Finally, we speculate on potential future developments in rough volatility modeling.

Tuesday, 14:00-15:30,

Chernoff Hall 117

Development of robust high-order methods for partial differential equations

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14:00-14:30

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POD-Galerkin Reduced Order Modeling of El Niño Southern Oscillations

Yusuf Aydogdu

(University of Waterloo)
## Abstract

Many high-dimensional mathematical models described by partial differential equations (PDEs) present challenges in numerical simulations due to their complexity and high-dimensionality. For instance, climate models with high resolution often require expensive computational resources. Therefore, it is crucial to develop fast and robust formulations for simulating such high-dimensional models. Reduced Order Modeling (ROM) aims to mitigate computational complexity by reducing the dimension of the state space. In this study, we demonstrate the efficiency, accuracy, and stability of Proper Orthogonal Decomposition (POD)-Galerkin when applied to the El Niño Southern Oscillation model, which comprises coupled atmosphere, ocean, and sea surface temperature (SST) mechanisms in the equatorial Pacific. Snapshots obtained from Direct Numerical Simulations (DNS) are used to formulate POD bases. Leveraging the unique coupling properties of the model, we propose a novel approach for constructing POD bases and reduced-order equations (ODEs) derived from Galerkin projection. Results are presented using both L2 and H1 (Sobolev) norms, showing that the full-order model can be effectively approximated using a few reduced-order equations and POD modes. Our findings from the reduced model demonstrate overall stable and highly accurate with those obtained from the full-order PDE model.

14:30-15:00

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Convergence Remedies for Option Pricing on Sparse Grids

Ray Wu

(University of Toronto)
## Abstract

The curse of dimensionality refers to the fundamental challenge that in the numerical solution of multidimensional partial differential equations (PDEs), the number of unknowns increases exponentially with dimension, leading to
computational intractability of even moderate dimension problems. On an isotropic grid with $d$ dimensions and $n$ unknowns in each dimension, the number of unknowns is $\mathcal{O}(n^d)$. We use the sparse grid combination
method [Griebel et al, 1992] to alleviate the curse of dimensionality; resulting in $\mathcal{O}(n(\log n)^{d-1})$ unknowns instead. However, the use of the sparse grid combination method for parabolic PDEs comes at a cost of
requiring smooth initial conditions. We demonstrate potential convergence issues that arise from the nonsmooth/discontinuous initial conditions, typical of computational finance problems. We present remedies that restore convergence, emphasizing on appropriate use of coordinate transformation, appropriate application of one-dimensional grid-alignment, as well as on more general techniques. We consider multidimensional American option pricing problems, and problems with digital and/or complex payoffs. We obtain second-order accurate solutions and Greeks.

15:00-15:30

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A Meshfree Method for Eigenvalues of Linear Differential Operators on Manifolds, Including Steklov Problems

Daniel Venn

(Simon Fraser University)
## Abstract

We present a novel technique for investigating the spectra of linear differential operators using symmetric meshfree methods. The technique applies for operators on manifolds as well as for flat domain problems. While much recent work has been completed on using meshfree methods for solving a wide range of partial differential equations (PDEs), the spectra of operators discretized using radial basis functions (RBFs) suffer from the presence of non-physical eigenvalues (spurious modes). This makes many RBF methods unhelpful for eigenvalue problems. Our technique provides a rigorously justified process for finding eigenvalues based on a result concerning the norm of solution in its native space; specifically, only PDEs with solutions in the native space produce solutions with bounded norms as the fill distance approaches zero. The technique we present is high-order and general enough to work for a wide variety of problems, including Steklov problems, where the eigenvalue parameter is in the boundary condition. Meshfree methods are desirable for surface problems due to the increased difficulties associated with mesh creation and refinement on curved surfaces.

Tuesday, 14:00-15:30,

Chernoff Hall 211

Contributed Session III

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14:00-14:20

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Sensitivity, Bifurcation, and Stochastic Analysis of Tuberculosis Progression

Wenjing Zhang

(Texas Tech University)
## Abstract

Mycobacterium tuberculosis infection features various disease outcomes: clearance, latency, active disease, and reactivation of latent tuberculosis infection (LTBI). Identifying the decisive factors for disease outcomes and progression is crucial to elucidate the macrophage-tuberculosis interaction and provide insight into therapeutic strategies. To achieve this goal, we first model disease progression as a dynamical shift among different disease outcomes, which are characterized by various steady states of bacterial concentration. The causal mechanisms of steady-state transitions can be the occurrence of transcritical and saddle-node bifurcations, which are induced by slowly changing parameters. Based on these two steady-state transition mechanisms, we carry out two sample-based sensitivity analyzes on transcritical bifurcation conditions and saddle-node bifurcation conditions. The results of the sensitivity analysis suggest that the rate of macrophage apoptosis is the most significant factor that affects the transition in disease outcomes. This
result agrees with the discovery that programmed cell death (apoptosis) plays a unique role in the complex microorganism-host interaction. In addition, bifurcation analysis unfolds various disease outcomes induced by the variation of macrophage apoptosis rate, which depend on the number of bacteria engulfed and released by macrophages. We then develop an Ito SDE model, which considers demographic variations at the cellular level to study stochastic fluctuations at the cellular level.

14:20-14:40

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A multilocus perspective on the evolutionary dynamics of multistrain pathogens

David McLeod

(Université de Montréal)
## Abstract

Many human pathogens, including malaria, dengue, influenza, Streptococcus pneumoniae, and cytomegalovirus, coexist as multiple genetically distinct strains. Understanding how these multistrain pathogens evolve is of critical importance for forecasting epidemics and predicting the consequences of vaccination. One factor believed to play an important role is naturally acquired immunity. Consequently, a large body of research has sought to predict how acquired immunity molds the genomics of pathogen populations (i.e., what shapes pathogen strain structure). However, the diversity and specificity of existing models has resulted in conflicting evolutionary predictions. This has led to an ongoing debate about which predictions are most broadly applicable. Here, we adopt a multilocus population genetics perspective that unifies the predictions of existing models. We identify three key factors that determine the role of naturally acquired immunity in the evolution of pathogen strain structure: (i) the strength and specificity of immune protections, (ii) the dynamic immunological landscape, and (iii) the number of loci coding for the antigens of the pathogen. Isolating and discussing these three factors clarifies the relationship among previous models of multistrain dynamics, and establishes a solid theoretical foundation for the study of the evolutionary epidemiology of multistrain pathogens.

14:40-15:00

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A Neuron-Centered Spatiotemporal Model of the Unfolded Protein Response in Prion Diseases

Mike Lindstrom

(The University of Texas Rio Grande Valley)
## Abstract

Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this talk, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P (healthy) and S (toxic) interacting with heterodimer dynamics. The model takes the form of a coupled system of nonlinear reaction-diffusion equations with a delayed, nonlinear flux for P. Through the delay, we find parameter regimes that exhibit oscillations in the P- and S-protein levels. We also consider quasi-realistic clinical parameters to understand how possible drug therapies can alter the course of a prion disease.

15:00-15:20

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On the exponential stability of a stochastic model for transmission dynamics of antimicrobial-resistant infections

Woldegebriel Assefa Woldegerima

(York University)
## Abstract

In this research, a comprehensive stochastic model was developed to analyze the transmission dynamics of methicillin-resistant Staphylococcus aureus (MRSA) in both hospital-acquired and community-acquired contexts. The study explored the existence and uniqueness of solutions and established the presence of a global solution. The investigation focused on assessing the boundedness, extinction, and persistence of MRSA strains in terms of their means. The analysis of the model revealed a noteworthy phenomenon known as competitive exclusion, where the community-acquired MRSA strain gradually out-competes the hospital-acquired strain within hospital settings. In conclusion, effective interventions, and preventive measures, such as improving hand hygiene compliance, implementing decolonization strategies, and enhancing disinfection rates, emerge as critical factors in controlling the transmission of these strains within hospital environments.

Tuesday, 14:00-15:30,

Chernoff Hall 213

Topics in Cell Biology

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14:00-14:30

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Applied mathematics in cell bioengineering: Elucidating design principles for engineered cellular reprogramming and control.

Mads Kaern

(University of Ottawa)
## Abstract

This talk describes how simulation and analysis of differential equations have been used for more than two decades to identify design principles for gene network engineering, and to predict how engineered gene networks behave inside living cells. It covers case studies irrefutably demonstrating the value of applied math in cell bioengineering and describes a roadmap towards the engineering of CRISPR-based gene networks for disease research and cell-based therapeutics.

14:30-15:00

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Analysis of M. smegmatis morphological features from Long-Term Time-Lapse Atomic Force Microscopy

Clément Soubrier

(University of British Columbia)
## Abstract

Atomic Force Microscopy (AFM) is a quantitative scanning technology enabling the investigation of cell surface mechanical properties. Recent advances in coupling AFM-based nanoscale spatial resolution with continuous Long-Term Time-Lapse (LTTL) imaging has allowed to observe the dynamics of cellular morphology at an unprecedented scale, and study associated mechanisms of control. Yet, computational tools are still needed to automate the processing of LTTL-AFM data, mitigate measuring artifacts and fully quantify these dynamics over a cell population. In this talk, we present our automated pipeline for analyzing single cell trajectories from LTTL-AFM, that includes several modules for segmentation, alignment, tracking of cells and extraction of morphological features. We apply this pipeline to investigate the morphology of Mycobacterium smegmatis, that is a non pathogenic bacterium with the same cell membrane structure as M.tuberculosis, and is thus used as a model for its study. Upon using our pipeline to reduce the geometry of the cell surface to its center-line and measure height variation along it, we confirm the presence of peaks and troughs along the height profile, as consistent features of the morphology. We also show how these features relate to bi-phasic and asymmetric polar growth dynamics, as well as division site selection. Finally, we introduce a mathematical model of reaction-diffusion dynamics that can reproduce and maintain these features over time.

15:00-15:30

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Inferring Bacterial Conjugation Events with Graph Algorithms

Nat Kendal-Freedman

(University of Waterloo)
## Abstract

Conjugation is a mechanism for horizontal gene transfer which allows microbes to share genetic material with adjacent cells. It plays an important role in the spread of antibiotic resistance in bacteria and is used as a tool for genetic engineering. Understanding what factors affect conjugation frequency is an ongoing challenge due to the stochasticity inherent in cell-cell interactions.
Our group is conducting experiments in which two populations of bacteria grow in a single layer under a microscope, with frequent imaging capturing the state of the bacteria over time. One population has been modified to express genes for fluorescent proteins, resulting in an optical signal after a cell from the other population receives these genes through conjugation. However, the uncertain delay between gene transfer and visible changes requires us to infer the exact timing and location of conjugation events.
A natural way to formalize this problem is using a graph to model the contact network and cell lineages, which can be recreated from our imaging data. We are developing a probabilistic graphical model (PGM) which uses the graph generated from an experiment, individual cell properties, and initial information about fluorescence. It calculates the probabilities of each cell (i) having received the gene and (ii) being fluorescent. The probabilities depend on which governing rules are used in the calculations, so determining rules which produce fluorescence consistent with our experiments gives us insight into the mechanisms that affect conjugation. We will use the governing rules suggested by the PGM to inform a graph algorithm which infers where individual conjugation events occurred in our experiments.

Tuesday, 14:00-15:30,

Chernoff Hall 250 (Aud)

Financial Mathematics

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14:00-14:30

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Portfolio Management for a Household: Modeling Income

Matt Davison

(Western University)
## Abstract

We have long understood how to manage the finances of an agent who, starting with a given endowment of wealth, allocates their money between a risk-free and one or more risky assets, and consumes from their wealth until time of death T with perhaps some assets remaining. We need to specify the stochastic dynamics of the assets, and to give utilities of consumption and of bequest. This gives some beautiful HJB equations, solved by Merton in the 1970s. We can add random time horizons T with little conceptual difficulty. If transaction costs are added to the mix things get harder, but we conceptually still know how to move forward.
However such a model appears to apply only to retirees or, perhaps, to PJ Wodehouse novel characters. The rest of us finance most of our life from our jobs. As such, employment income must also be modelled as a stochastic process. I will describe work done with the exceptionally rich Stats Can Longitudinal Administrative Database to understand the elements of such a model. I will link these observations to a better understanding of the financial resilience of Canadian households.

14:30-15:00

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Predicting Stock Returns Using Financial News Sentiments

Roman Makarov

(Wilfrid Laurier University)
## Abstract

Financial news contains valuable information that can help investors make informed decisions. To predict stock returns using sentiment extracted from financial news, we build various statistical machine learning (SML) models. We use multi-category models to classify stock returns relative to fixed thresholds and develop option-based trading strategies. To assess multi-category classification models, new performance metrics are proposed. In addition to that, we consider dynamic models that aim to predict the market regime and stock returns over time. Our approach combines SML, Markov switching, and time-series models with sentiment scores obtained using the Financial Bidirectional Encoder Representations from Transformers (FinBERT) model, as well as other features extracted from financial news headlines.
This is a collaborative project with students Jake Tuero, Jiawei He, Wenjing Fan, Mostafa Abdolahi Moghadam Salkoye, Pablo Kowalski Kutz and co-supervisors Drs. Zilin Wang, David Soave, and Sunny Wang.

15:00-15:30

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Operator splitting and optimal control of gas storage

Tony Ware

(University of Calgary)
## Abstract

We consider a natural gas storage facility where the gas is to be traded on a mixture of spot and forward markets. The problem of determining the optimal operating and marketing strategy for such a facility, and its associated value, is complicated by the range of potential markets for the gas, and by the physical characteristics of the facility which create state-dependent constraints on the allowable injection/withdrawal rates. In [SIAM JFM 4(1) 427-451, 2013] we proposed an operator-splitting approach for time-discretisation of the associated HJB equation in a simple one-factor spot price model, and proved convergence to the viscosity solution. Here we expand that approach to a multi-factor polynomial process setting, where the application of one of the operators corresponds to a set of intrinsic value-style computations exploiting the structure of the forward curve with injection/withdrawal rates conforming to system constraints. We show how the approach can facilitate the determination of an optimal 'rateable' forward trading strategy.

Tuesday, 14:00-15:30,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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14:00-14:30

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Multi-scale interaction between atmospheric Rossby waves and internal gravity waves

Lucy Campbell

(Carleton University)
## Abstract

We use analytical and numerical methods to study a mathematical problem describing multi-scale interactions between different types of waves in an atmospheric fluid flow, namely baroclinic planetary Rossby waves resulting from the rotation of the earth and internal gravity waves resulting from the gravitational and buoyancy forces. The configuration studied is representative of the situation where a layer of enhanced temperature, called a mesospheric inversion layer, occurs in the middle atmosphere. Our results indicate that the presence of internal gravity waves acts to modify the background wind and cause an increase in temperature. This is consistent with the hypothesis that these waves play a role in the development of mesospheric inversion layer events.
Joint work with A. Alzahrani.

14:30-15:00

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Trapping and release of bubbles in industrial waste

Ian Frigaard

(University Of British Columbia)
## Abstract

Bubbles in viscoplastic gels arise in a variety of contexts that are interesting both as a source of fundamental and challenging questions in fluid mechanics, and in terms of applications. Here we describe interesting features of both static and moving bubbles, motivated by problems associated with greenhouse gas emission mitigation. We explore single bubbles, the interaction of bubbles in clouds and networks, and questions of how elasticity and thixotropy contribute to bubble flows, modifying simplistic visions of the relevant mechanisms. Joint work with Masoud Daneshi, Marjan Zare, Ali Pourzahedi and Emad Chaparian.

15:00-15:30

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Simulated active droplets near no-slip plane boundaries

Henry Shum

(University of Waterloo)
## Abstract

Active particles and droplets exhibit different regimes of behavior individually as well as collectively. As an example, droplets of liquid crystal added to concentrated surfactant solutions generate observable fluid flows and can become self-propelled through a symmetry-breaking instability. We model such droplets as spherical squirmers and study their motion close to a no-slip plane boundary. The behaviors of individual squirmers with different squirming mode strengths are systematically studied using a boundary element method to numerically solve the equations of Stokes flow around the droplets. We characterize the stationary and self-propelling steady states to understand the interplay among squirming modes and gravity.

Tuesday, 14:00-15:30,

Stirling Hall 401

Mathematical Modelling of Behaviour

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14:00-14:30

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Modeling Compliance to Recommended Interventions to Control Outbreaks

Jacques Bélair

(Université de Montréal)
## Abstract

Management of the COVID-19 pandemic required, in its early stages, the deployment of non pharmaceutical interventions (NPIs) [social isolation, physical distancing, mask-wearing, hand-washing] and, in the later phases, and as they became available, administration of repeated doses of vaccine. We explore the consequences, for the dynamics of the disease, of variable adherence to these measures, and the motivation generating the lack thereof, by presenting two classes of models incorporating slightly different approaches. In the first one, we investigate an expanded SEIRS model for post-infection changes in behaviour, in which the population is divided into two classes according to their degree of adherence to the NPIs. In the second one, a model more structurally linked to information and attitude is analysed, with emphasis on fatigue and waning compliance.

14:30-15:00

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Adolescent vaping behaviors: Exploring the dynamics of a social contagion model

Sarah Machado-Marques

(York University)
## Abstract

The rapid increase in e-cigarette usage (or vaping), particularly among adolescents, has often been referred to as an epidemic of public health concern. We draw upon this epidemiological analogy to present a behavioral mathematical model of adolescent e-cigarette smoking. In particular, we consider the effects of (1) socially-driven initiation and relapse, (2) relapse due to nicotine dependency and other non-socially related factors, (3) socially-influenced cessation, and (4) cessation of one’s own volition. We demonstrate that social influences from and on temporary quitters are not important in overall model dynamics. However, the influence of permanent quitters can reduce the size of the smoking population, and aid in inducing recurrent smoking outbreaks before reaching the smoking present equilibrium.

15:00-15:30

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A coupled social-climate model with multiple populations

Amrita Punnavajhala

(University of Waterloo)
## Abstract

Recent work has shown that the inclusion of human behavioural processes in mathematical models of climate change can significantly affect the outcomes predicted by these models. We further work in this area by constructing a coupled social-climate model with social dynamics across multiple real-world populations. The social component of our model is based on evolutionary game theory and parameterized using projections of renewable energy costs and economic damages associated with climate change, along with a description of social norms, informed by region-specific data. This 'social’ model is then coupled to a simplified earth-system model, representing two-way feedback processes between the two sub-components. Through our results we study the impacts of social and behavioural heterogeneity across the world on both mitigation efforts and climate change outcomes.

Tuesday, 14:00-15:30,

Stirling Hall 414

Computational Neuroscience

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14:00-14:30

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Ictal-Related Chirp: A Potential Marker for Identifying the Seizure Onset Zone

Nooshin Bahador

(University Health Network)
## Abstract

The epileptic brain displays chirp-like patterns, marked by narrow-band frequency modulation in electrographic discharges. These chirps have been observed in both rodent and human subjects. Chirp patterns in human manifest earlier in seizure onset zones and can thus serve as potential indicators to differentiate sites of seizure onset from areas of seizure propagation.

14:30-15:00

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The identification and tracking of pathological neural dynamics with the Markovian Neural Barcode

Jordan Culp

(University of Calgary)
## Abstract

Brain activity is highly structured, and the structure of this activity begins to falter in subtle ways early in neuropsychiatric disease and gradually progress with disease severity. The search for sensitive, and more importantly specific, ways of detecting these early activity changes is critical to early detection and tracking the effectiveness of interventions across a range of conditions.
To date, progress using brain imaging to improve outcomes in these populations has been incremental despite the incredible promise of technology that allow us to sample neural dynamics across the whole brain in a living individual or model organism. With this very high dimensional brain imaging data it is possible to understand the structure of brain activity and how this structure evolves over time, effectively understanding the ‘rules’ governing brain activity and how they falter early in disease.
We hypothesize that a new method we have developed will provide much needed novel insight into disease detection, whereby the rules governing how brain states transition from one to another are explained as a continuous Markov process. By succinctly encoding the statistical features of our Markov model in the form of a Markovian Neural Barcode we can readily analyze the inherent dynamics of the spatial-temporal structure of high dimensional neural imaging data. Moreover, we propose to identify pathological signatures in neural dynamics and the possible intervention testing strategies with our Markov model.

15:00-15:30

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Using a feature-based approach to estimate parameters of a conductance-based thalamocortical model associated with childhood absence epilepsy

Maliha Ahmed

(University of Waterloo)
## Abstract

Childhood absence epilepsy (CAE) is a paediatric idiopathic generalized epilepsy disorder with a confounding ability to spontaneously resolve in adolescence in a majority of cases. There have been several factors hypothesized to be mechanisms behind remission, however, there remains an inadequate understanding of some of these factors. According to some functional connectivity studies, there exist pre-treatment connectivity differences between patients who ultimately experience remission and those who do not.
In this study, we have used a feature-based approach to estimate synaptic parameters of a conductance-based model of the thalamocortical circuit consisting of multiple types of single-compartment thalamic and deep layer cortical neurons corresponding to different parts of the cortex. In particular, our model improves on previous well-established models in the literature by incorporating a more comprehensive cortical component. Through our results we aim to gain an understanding of the role of different neuron types, and differences in synaptic connectivity towards generating distinct networks modelling remitting and non-remitting behaviour.

Tuesday, 14:00-15:30,

Stirling Hall A

Pattern formation for novel reaction-diffusion systems in the fully nonlinear regime

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14:00-14:30

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Traveling waves and wave pinning (polarity): Switching between amoeboid and fan-shaped motility of cells

Jack Hughes

(University of British Columbia)
## Abstract

Experimental studies have shown that cells can switch between fan-shaped motility (direction motion) and amoeboid (semi-random) motion. In this presentation, I investigate the non-linear dynamics of a simple three-component reaction-diffusion system that models the chemical species that induce cell motion. I use full numerical PDE bifurcation analysis to characterize the different types of steady state and periodic solution behaviours. By tuning parameters, I will show the existence of a codimension-2 point consisting of a long wavelength Turing bifurcation (direction motion) and a finite wavenumber Hopf bifurcation (semi-random). Through this codimension-2 point, I will show the robust stable coexistence of mesa and travelling wave solutions that lead to fan-shaped and amoeboid motility, respectively. Lastly, I will use some numerical time-dependent simulations to investigate the interaction between these solution types.

14:30-15:00

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Spike patterns for reaction-diffusion systems in a rectangular domain

Arvin Vaziry

(Dalhousie University)
## Abstract

We examine spike patterns within reaction-diffusion systems situated in a rectangular domain, subject to Neumann boundary conditions. A basic steady state is characterized by a stripe of equidistant spikes along the rectangle's centerline. We calculate the instability thresholds for this particular configuration. Our findings indicate that a pattern composed of N spikes can maintain stability, given that the rectangle's length is adequate. As the stripe length approaches infinity, we determine the minimum inter-spike distance required for the spike stripe to remain stable. Contrastingly, for a rectangle with periodic boundary conditions, a single spike stripe exhibits instability. However, the presence of two spike stripes can achieve stability, provided the rectangle is of sufficient length. Additionally, we conduct numerical investigations of more intricate steady states within a square domain.

15:00-15:30

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Pattern formation in thin domains

Theodore Kolokolnikov

(Dalhousie)
## Abstract

We expore pattern formation for the GM model on thin domains. If the domain is sufficiently thin, the pattern consists of a stripes which are nearly one-dimensional. We analyse patterns consisting of one, two or many stripes. We find that a single stripe can be located either at the thickest or thinnest part of the channel, depending on the choice of parameters. In the limit of many stripes, we derive an effective pattern density description of the equilibrium state. The effective density is easily computable as a solution of a first order ODE subject to an integral constraint. Depending on problem parameters, the resulting pattern can be either global spanning the entire domain, or can be clustered near either thickest or thinnest part of the domain. In addition, instability thresholds are derived from the continuum density limit of many stripes. Full two-dimensional numerical simulations are performed and are shown to be in agreement with the asymptotic results.

Tuesday, 14:00-15:30,

Stirling Hall B

Celestial Mechanics: Old and New in Dynamical Systems

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14:00-14:30

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Regularization in the Circular Planar (2+2)-Body Problem

Lennard Bakker

(Brigham Young University)
## Abstract

We investigate applications of regularization techniques to the Circular Planar (2+2)-Body Problem. Of particular interest is in prolonging numerical simulations when two smaller bodies are in proximity with each other, and in analytically and numerically determining the dynamics when the two smaller bodies are in proximity with one of the primaries. This is joint work with Nathan Sill.

14:30-15:00

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On Kite Central Configurations

Gareth Roberts

(College of the Holy Cross)
## Abstract

Central configurations play a key role in understanding solutions of the Newtonian $n$-body problem. From rest, a central configuration (c.c.) will collapse in on itself homothetically; given the correct initial velocity, a planar c.c. rotates rigidly about its center of mass. Any group of bodies heading toward a collision must asymptotically approach a c.c.
We focus on four-body kite c.c.’s, where two of the bodies lie on an axis of symmetry and the other two bodies (of equal mass) are positioned equidistant from that axis. Kites may either form a convex or concave quadrilateral. Inspired by the recent approach of Santoprete for co-circular c.c.’s, we present a new proof that there exists a unique convex kite central configuration for a given choice of masses and a particular ordering of the bodies. The proof uses tools from differential topology (e.g., the Poincare-Hopf Index Theorem) and computational algebraic geometry (e.g., Grobner bases). We are optimistic that the proof technique will extend to the more challenging, open question on uniqueness of general four-body convex c.c.'s. We also consider the linear stability of kite c.c.'s. Preliminary work in the convex case finds that the heaviest body must be at least 25 times larger than the combined masses of the other three bodies in order for the corresponding relative equilibrium to be linearly stable.

15:00-15:30

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On the Uniqueness of Co-circular Four Body Central Configurations

Manuele Santoprete

(Wilfrid Laurier University)
## Abstract

In this talk we consider central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we show that there is at most one co-circular central configuration for each cyclic ordering of the masses on the circle.

Tuesday, 14:00-15:30,

Stirling Hall C

Modelling heterogeneity in ecology, epidemiology, and evolution

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14:00-14:30

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R0 may not tell everything: transient disease dynamics of some SIR models over patchy environments

Xingfu Zou

(University of Western Ontario)
## Abstract

In this talk, I will report some recent results on short-term/transient dynamics of SIR infectious disease models in patch environments in comparison with long term disease dynamics. We employ the concepts of reactivity and amplification rates from ecology to analyze how dispersals/travels between patches, spatial heterogeneity, and other disease-related parameters impact short-term disease dynamics. Our findings reveal that in certain scenarios, due to the impact of spatial heterogeneity and the dispersals, the short-term disease dynamics over a patch environment may disagree with the long-term disease dynamics that is typically reflected by the basic reproduction number. Such an inconsistence can mislead the public, public healthy agencies and governments when making public health policies and decisions, and hence, these findings are of practical importance.

14:30-15:00

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Can we PrEP our way out of the HIV epidemic?

Abba Gumel

(University of Maryland)
## Abstract

The use of pre-exposure prophylaxis (PrEP), where approved antivirals are administered to uninfected high-risk individuals, is universally regarded as a promising strategy to prevent susceptible high-risk individuals from acquiring HIV infection from their infected partners. A number of antiviral drugs (and their combinations) have been developed and are being used as prophylaxis against the HIV/AIDS pandemic globally. I will present a mathematical model for assessing the population-level impact of PrEP in high-risk population(s). The asymptotic stability properties of the equilibria of the model and theoretical conditions for the effective control or elimination of the disease in the population will be discussed.

15:00-15:30

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Modeling Immune Response to HIV Infections among Elite Controllers

Michael Li

(University of Alberta)
## Abstract

HIV elite controllers are HIV patients who have been infected with HIV for a long time (decades) but manage to keep the viral load below detection without taking antiretroviral drug therapies (ART). The current consensus among HIV medical research of elite controllers is that their Cytotoxic Lymphocyte (CTL) response functions are highly active and play a critical role in the sustained control of the viral load. Understanding of which parts of the CTL functions play a key role is still elusive and offers excellent opportunities for mathematical modeling. In this talk, I will present some new results on how patient data and new mathematical models that include several classes of immune cells have yield new insight on functions of CTL in the sustained control of viral load. This research was in collaboration with Dr. Weston Roda and Dr. Christopher Power of University of Alberta.

Tuesday, 16:15-17:00,

Biosciences 1101 (Aud)

Plenary: Alexander Anderson

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16:15-17:00

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Evolutionary Therapy for Metastatic Cancer

Alexander Anderson

(Moffitt Cancer Center)
## Abstract

Our current approach to cancer treatment has been largely driven by finding molecular targets, those patients fortunate enough to have a targetable mutation will receive a fixed treatment schedule designed to deliver the maximum tolerated dose (MTD). Cancers are complex evolving systems that adapt to therapeutic intervention through a suite of resistance mechanisms, therefore whilst MTD therapies generally achieve impressive short-term responses, they unfortunately give way to treatment resistance and tumor relapse. The importance of evolution during both tumor progression, metastasis and treatment response is becoming more widely accepted. However, MTD treatment strategies continue to dominate the precision oncology landscape. Here we discuss evolutionary therapy, a proactive therapeutic approach that changes and evolves with the tumor being treated. Due to the dynamic feedback between changing treatments and the evolving tumor, mathematical models are essential to drive treatment switch points and predict appropriate dosing and drug combinations. We will consider the importance of using treatment response as a critical driver of subsequent treatment decisions, rather than fixed MTD strategies that ignore it. We will also consider using mathematical models to drive treatment decisions based on limited clinical data. Through the integrated application of mathematical and experimental models as well as clinical data we will illustrate that, evolutionary therapy can drive either tumor control or extinction. Our results strongly indicate that the future of precision medicine shouldn’t only be in the development of new drugs but rather in the smarter evolutionary, and model informed, application of preexisting ones.

Tuesday, 17:30-18:30,

Biosciences 1101 (Aud)

EDII Panel

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Tuesday, 18:30-19:30,

Biosciences 1101 (Aud)

Industry Panel

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Wednesday, 8:30-9:15,

Biosciences 1101 (Aud)

[Remote] CAIMS Research Prize Lecture: Hao Wang

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8:30-9:15

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Stoichiometric Theory with its application in Methane Biogenesis

Hao Wang

(University of Alberta)
## Abstract

Stoichiometric principles allow the construction of robust mechanistic, predictive, and empirically testable models via rigorous chemical and physical laws. Experimental and fundamental evidence motivates the application of this microscopic approach to understand macroscopic phenomena. I will introduce some stoichiometric models and their novel dynamics that resolve some biological paradoxes and lead to new insights. The application in methane biogenesis illustrates how this approach contributes to achieving the ambitious goal of carbon neutrality, essential for mitigating global climate change.

Wednesday, 10:00-12:00,

Chernoff Hall 117

Development of robust high-order methods for partial differential equations

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10:00-10:30

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Summation by Parts Discretizations on Curvilinear Grids

Alex Bercik

(University of Toronto)
## Abstract

This talk will consist of two main parts. The first part will serve as an introduction to Summation by Parts discretizations and their advantageous mathematical properties, including provable stability, discrete conservation, geometric flexibility, and equivalent interpretations under both finite difference and discontinuous spectral element frameworks. The second part will explore the applications of these schemes to stationary curvilinear grids. We compare various approaches of calculating the resulting geometric terms, including grid metric terms, metric Jacobians, and boundary normals. Using both structured and unstructured discretizations of the 3D Euler equations, we then discuss the impact these various approaches have on the accuracy, discrete conservation, and dual consistency of the resulting schemes. Theoretical arguments are verified through numerical experiments involving superconverging wall-boundary functionals.

10:30-11:00

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Strongly imposed Dirichlet boundary conditions for high-order SBP operators

Anita Gjesteland

(University of Waterloo)
## Abstract

Summation-by-parts (SBP) operators are widely used in computational fluid dynamics for approximating partial differential equations. In conjunction with proper boundary procedures, they allow for simple stability proofs mimicking the analogous proof for the continuous problem. In this talk, we consider the injection method for imposing Dirichlet boundary conditions strongly. That is, we require the solution at the boundary nodes to satisfy the boundary data exactly. Specifically, we extend the results of [1] where this boundary procedure, together with the $(2,1)$ finite-difference SBP operator, was proven to yield a stable scheme for the compressible Navier-Stokes equations.
Herein, we show that the strong imposition of Dirichlet boundary condition leads to stable schemes when used in combination with different kinds of SBP operators, including high-order operators, operators defined on unstructured grids and tensor-product operators. We consider the linear advection equation as a model problem to introduce the ideas, and show that the methodology also leads to entropy estimates for the compressible Navier-Stokes equations.
[1]: A. Gjesteland and M. Svärd. Entropy stability for the compressible Navier-Stokes equations with strong imposition of the no-slip boundary condition. Journal of Computational Physics, 470, 111572, 2022.

11:00-11:30

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Tensor-Split-Simplex Summation-By-Parts Operators

Zelalem Arega Worku

(University of Toronto)
## Abstract

While nonlinear stability of discretizations of the Euler and Navier-Stokes equations has been realized by satisfying the discrete entropy inequality using the summation-by-parts (SBP) framework, improving efficiency of these discretizations remains an active area of research. The use of two-point fluxes in entropy-stable discretizations presents computational efficiency challenges, particularly for high-order operators on simplices, which typically produce dense matrix operators. Simplicial elements lend themselves well to automatic mesh generation around complex geometries, suggesting significant potential for the development of robust and versatile fluid dynamics solvers. Conversely, tensor-product operators on quadrilateral and hexahedral elements produce matrix operators that are sparse and substantially more accurate than multidimensional SBP operators---if only there is a way to combine the two! In this presentation, we propose a promising method to do just that. We present simplicial elements with tensor-product structure, referred to as tensor-split-simplex (TSS) SBP operators, on triangles and tetrahedra that are constructed by fitting $d+1$ tensor-product operators into the simplex, where $d$ is the spatial dimension. The TSS operators are different from existing methods involving splitting simplicial meshes into tensor-product operators in that they do not have repeated degrees of freedom along the interior edges. Several numerical studies involving both linear and nonlinear problems are presented to illustrate the efficiency gains afforded by the TSS operators.

11:30-12:00

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Efficient entropy-stable discontinuous spectral-element methods in collapsed coordinates for hyperbolic systems on curved triangular and tetrahedral meshes

Tristan Montoya

(University of Toronto)
## Abstract

We present a new approach to the construction of provably entropy-stable spatial discretizations of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. In order to obtain efficient low-storage algorithms at high polynomial degrees, the proposed methods employ sparse tensor-product summation-by-parts operators in collapsed coordinates within a weight-adjusted flux-differencing formulation using a Proriol-Koornwinder-Dubiner modal polynomial basis. Exploiting sum factorization in tensor-product operator evaluation and exploiting sparsity in flux differencing then enables the explicit evaluation of the time derivative in $O(p^{d+1})$ floating-point operations, where $p$ is the polynomial degree of the discretization and $d$ is the number of spatial dimensions. Particularly for higher polynomial degrees, the proposed approach significantly reduces the number of required entropy-conservative two-point flux evaluations relative to entropy-stable formulations of comparable accuracy based on (non-tensor-product) multidimensional summation-by-parts operators, and exhibits the same provable conservation, free-stream preservation, and nonlinear stability properties provided by such existing schemes. In addition to a description and analysis of the algorithmic aspects of the proposed methods, we demonstrate their accuracy and robustness in numerical experiments involving the solution of the compressible Euler equations in two and three dimensions.

Wednesday, 10:00-12:00,

Chernoff Hall 211

Recent Progress on the Intersections of Nonlinear Dynamics, Control, Learning, and Optimization

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10:00-10:30

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From Gradient Descent to Reinforcement Learning

Alex Olshevsky

(Boston University)
## Abstract

Temporal difference (TD) learning with linear function approximation is one of the earliest methods in reinforcement learning and the basis of many modern methods. We revisit the analysis of TD learning through a new lens and show that TD may be viewed as a modification of gradient descent. This leads not only to a better explanation of what TD does but also improved convergence guarantees. In particular, we are able to show that TD learning does well in the limit as the discount factor approaches one. We will also discuss applications to the analysis of actor-critic methods.

10:30-11:00

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Recent advances in constructing convex relaxations for ODE solutions

Kamil Khan

(McMaster University)
## Abstract

In chemical engineering applications such as safety verification of batch reactors, some problems require global optimization of dynamic systems that are modeled as systems of ordinary differential equations (ODEs). Typical methods for deterministic global optimization compute essential lower bounds by minimizing convex relaxations of the original problem. Hence, global dynamic optimization warrants convex relaxations of parametric ODE solutions that are computationally inexpensive, yet are also tight relaxations.
In this presentation, we detail several of our recent advances in constructing effective convex relaxations for ODE solutions. Specifically, we explain how to incorporate known relaxations of the ODE right-hand side into effective ODE solution relaxations, how to compute subgradients of these cheaply and accurately, and how to use constructions from derivative-free optimization to improve efficiency. Implications are discussed, and numerical examples are presented, based on proof-of-concept implementations in Julia.

11:00-11:30

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Scalarizing Multi-Objective Optimization Problems for the Control of Complex Systems

Stephen Smith

(University of Waterloo)
## Abstract

In controlling complex dynamical systems, one often seeks to simultaneously optimize several competing objectives subject to constraints. Linear scalarization is a common approach for solving such multi-objective optimization problems. This approach involves formulating a single cost function made up of the weighted sum of the individual objectives. For each specific vector of weights, the resultant solution is Pareto optimal with respect to the original problem. However, determining the influence of different weight vectors on system behaviour can be complex. To address this, we discuss how to compute a finite set of weight vectors that offer a comprehensive representation of potential system behaviours. Specifically, we determine a set of weight vectors such that any other weight vector has a corresponding set element whose resultant solution is close to the optimal solution.
One limitation of linear scalarization is its lack of Pareto-completeness; there are Pareto-optimal solutions that are not the solution of the scalarized optimization problem for any vector of weights. To overcome this, we introduce an alternate form of scalarization based on a weighted maximum of objectives, which achieves Pareto-completeness. We demonstrate the application of this scalarization in controlling complex systems in both continuous and discrete spaces. We provide examples in robot motion planning showing the utility of these methods in learning user preferences on robot behaviour and in identifying trade-offs between objectives that are not attainable with linear scalarization.

11:30-12:00

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Flexible-step MPC for Switched Linear Systems with No Quadratic Common Lyapunov Function

Annika Fuernsinn

(Queen's University)
## Abstract

In this talk, I will present flexible-step Model Predictive Control (MPC), which is based on the novel notion of generalized discrete-time control Lyapunov functions. For the case of linear control systems, we develop a systematic method for constructing such generalized discrete-time control Lyapunov functions. The main consequence of this construction is that, when combined with flexible-step MPC, we can effectively stabilize switched control systems, for which no quadratic common (classical) Lyapunov function exists.

Wednesday, 10:00-12:00,

Chernoff Hall 213

Delay Differential Equations and Their Applications

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10:00-10:30

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Analysis of a viral infection model with distributed delay

Jacques Bélair

(Université de Montréal)
## Abstract

We present a distributed delay differential equations system modeling the in-host evolution of an HIV infection, describing the interactions between uninfected CD4-T cells, infected cells, virus particles and the immune response.
The asymptotic behavior of the solutions is entirely characterized by the delay, denoted $\tau$, representing the time before an infected cell produces virus particles. We show that for a sufficiently large value of $\tau$ above an explicitly determined threshold $\tau_1$ , the infection dies out since the disease-free steady-state is asymptotically stable. Then, for a delay below this threshold, the infection persists, the disease-free equilibrium being unstable. In this case, the endemic steady-state and a chronic infection stage exchange stability after another threshold $\tau_2$ is crossed. Numerical simulations supporting the analytical conclusions are presented.
[ Joint work with Marc-Antoine Trahan (U de Montréal) ]

10:30-11:00

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Delays in Mathematical Biology

Tony Humphries

(McGill University)
## Abstract

Fads are as common in mathematics as in all ares of life, and topics such as
spurious solutions, exponential attractors, and differential algebraic equations, have blazed into prominence at different times in recent decades before fading into the background like a burned out star. But, as we approach the 50th anniversary of the publication of the Mackey-Glass equation in 1977, the topic of delay differential equations and in particular their applications in mathematical biology and physiology remains as fertile and active as ever. I will use this talk to discuss what (little) I know and think about why this is, illustrated by some recent and not so recent results. Along the way we will discuss the Mackey-Glass equation, the Burns-Tannock cell cycle, periodic hematological diseases, state-dependent, distributed and threshold delays, and the dynamics, analysis, implementation and tractability of such models.

11:00-11:30

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Modeling the fear effect in predator-prey interactions with adaptive avoidance of predators

Xiaoying Wang

(Trent University)
## Abstract

Recent field experiments on vertebrates showed that mere presence of a predator would cause a dramatic change of prey demography. Fear of predators increases the survival probability of prey but leads to a cost of prey reproduction. Based on the experimental findings, we propose a predator-prey model with the cost of fear and adaptive avoidance of predators. Mathematical analyses show that the fear effect can interplay with maturation delay between juvenile prey and adult prey in determining the long term population dynamics. A positive equilibrium may lose stability with an intermediate value of delay and regain stability if the delay is large. Numerical simulations show that both strong adaptation of adult prey and the large cost of fear have destabilizing effect while large population of predators has a stabilizing effect on the predator-prey interactions. Numerical simulations also imply that adult prey demonstrate stronger anti-predator behaviours if the population of predators is larger and show weaker anti-predator behaviours if the cost of fear is larger.

11:30-12:00

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Predicting and separating chaotic signal mixtures using multi-delay feedback loops

Kamyar Tavakoli

(University of Ottawa)
## Abstract

One of the methods for implementing machine learning tasks such as time series prediction and classification is the Reservoir Computing (RC) scheme. Reservoir computing, a brain-inspired computational model, utilizes a densely interconnected network. This approach enables effective training for time series prediction leveraging the network's high-dimensional properties and complex dynamics. It has been demonstrated that this scheme can separate chaotic signals effectively when a mixture of them is fed as the input to the reservoir [1]. Furthermore, a novel approach employing high-dimensional systems, such as delay differential equations, has been introduced for machine learning tasks, which can be implemented both numerically and experimentally [2]. It is widely known that in this class of dynamical equations, presence of time delays can induce intricate and complex dynamics. We have examined the role of multiple delays in enhancing the prediction accuracy of time delay reservoir computing, utilizing an electro-optic time delay system. Previously, it has been demonstrated that the incorporation of multiple delays that are uniformly distributed, enables the suppression of chaotic dynamics by widening the distribution of delays. Specifically, in first-order nonlinear delay differential equations, having only a few delays that are uniformly distributed, increasing the spacing between delays can lead to the emergence of limit cycle behaviors and stable fixed-point regimes [3]. In the context of time delay reservoir computing, our findings reveal that multiple delays enhance the linear memory capacity (the ability to recall past input data) of time-delay reservoir computing, leading to an improvement in the overall efficacy of the system. We present results for time delay reservoir computing with various architectures, focusing on the classification and simultaneous prediction of signals when the input is the mixture of signals.
\[\]
[1] - S. Krishnagopal, M. Girvan, E. Ott, and B. R. Hunt, "Separation of chaotic signals by reservoir computing," Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 30, no. 2, p. 023123, 2020.
\[\]
[2] L. Appeltant, M. C. Soriano, G. Van Der Sande, J. Danckaert, S. Massar, J. Dambre, B. Schrauwen, C. R. Mirasso, and I. Fischer, "Information processing using a single dynamical node as complex system," Nat. Commun., vol. 2, no. 1, p. 468, 2011.
\[\]
[3] S. K. Tavakoli and A. Longtin, "Multi-delay complexity collapse," Phys. Rev. Research, vol. 2, p. 033485, Sep 2020.

Wednesday, 10:00-12:00,

Chernoff Hall 250 (Aud)

Financial Mathematics

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10:00-10:30

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A Dynamic Structural Model for Contingent Convertible Debt

François-Michel Boire

(University of Ottawa)
## Abstract

This paper provides a simple framework to analyze the design of contingent capital for depository
institutions. We consider a debt portfolio composed of straight debt and contingent convertible
(coco) bonds. Coco bonds are automatically written down or converted into equity upon
meeting predetermined capitalization ratio thresholds, thus providing capital loss absorption
mechanisms. The quality of the design of coco bonds (parameterized by write-down/conversion
factors and trigger levels) is gauged with default probabilities at various horizons, shareholder’s
incentive for risk-shifting, and the present value of bankruptcy costs.

10:30-11:00

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Effect of nonsmooth initial conditions on high-order time-stepping schemes for PDEs in finance: analysis and remedies

Christina Christara

(University of Toronto, Depart Computer Science)
## Abstract

Nonsmooth payoff functions are common in
financial contracts and pose difficulties in
obtaining high-order solutions of the contract prices.
In this work, we consider parabolic PDEs
with initial conditions involving various types of nonsmoothness.
We apply a fourth-order finite difference (FD) discretization
on a uniform grid in space, and BDF4 time stepping initialized
with two steps of an explicit third-order Runge-Kutta (RK3) method
and one step of BDF3.
Using Fourier analysis on the discrete system,
we prove that the low-order errors generated by RK3
for nonsmooth data in the high-frequency domain
get damped away by BDF steps,
which prevents spurious oscillations in the solution;
while low-order errors in the low-frequency domain
come from the low-order initial condition discretization.
To achieve globally fourth-order convergence,
we apply fourth-order smoothing to the initial conditions,
and provide explicit formulas of the discretization.
By combining the initial condition smoothing
with the proposed time-stepping scheme,
we mathematically prove and numerically verify
that fourth-order convergence is obtained.
The analysis is easily generalizable to higher order methods.
Numerical examples on the model PDE and various
option pricing problems are also given to
demonstrate the fourth-order convergence of our method.

11:00-11:30

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Joint dynamics for the underlying asset and its implied volatility surface: A new methodology for option risk management

Pascal François

(HEC Montréal)
## Abstract

This paper develops a dynamic joint model of the implied volatility (IV) surface and
its underlying asset which is tractable and seamless to estimate. It combines an asymptotically
well-behaved, parametric IV surface representation with a two-component
variance, and non-Gaussian asymmetric GARCH specification for the underlying asset
returns. Estimated on S&P 500 index return and option data for the 1996-2020
period, the model captures the IV surface movements well and uses them to obtain
an improved fit on index returns. It also proves to be an effective risk management
tool, producing reliable Value-at-Risk estimates for straddle and strangle positions,
and accurate forecasts of the VIX distribution.

11:30-12:00

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A new approach to (option pricing) model calibration

Lars Stentoft

(University of Western Ontario)
## Abstract

Calibrating option pricing models to market data often presents significant numerical challenges, especially when the object of interest (the option price, i.e., a conditional expectation) relies on simulating from the model itself. We proposed a novel calibration method that relies on, essentially, one simulation only and apply this to the problem of calibrating option pricing models with time varying volatility. A distinct advantage of our approach is that the actual option pricing, which requires simulation, can be done "off-line", leaving only a simple optimization to be solved "on-line" in real time. This separation simplifies the calibration procedure enhancing its applicability.

Wednesday, 10:00-12:00,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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10:00-10:30

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Identifying dominant flow structures in a bubbling gas-particle fluidized bed using the spectral proper orthogonal decomposition

Raymond Spiteri

(University of Saskatchewan)
## Abstract

The spectral proper orthogonal decomposition (SPOD) is a
relatively new way to analyze the spatio-temporal characteristics of
a flow. The dominant SPOD modes can be used for prediction, control,
design, optimization, and reduced-order model construction. We
performed an analysis of the flow fields of a bubbling fluidized bed
using SPOD and found there is no singular dominant frequency linked
to the highest energy levels; rather, there is a spectrum of
frequencies. These frequencies are consistent with the natural
frequency of the bed. The SPOD analysis also reveals the presence
of multiple co-existing spatio-temporal patterns in the particle
volume fraction and velocity fields. This analysis can be used to
guide pulsation strategies to enhance mixing quality and
consequently heat and mass transfer properties of the bed.

10:30-11:00

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THREE-DIMENSIONAL, NONLINEAR, INSTABILITY OF THE BURGERS VORTEX

Basak Cakmak

(Ontario Tech University)
## Abstract

Burger's vortex is one of the few analytically known, three-dimensional, vortical solutions to the Navier-Stokes equation. It relies on vortex stretching, thought to be one of the sustaining mechanisms of turbulence. Remarkably, this solution has been shown to be linearly stable. At the same time, there are theoretical indications that families of less symmetric equilibria exist near Burgers’ solution. We explore the phase space around Burgers flow by direct numerical simulations of finite-sized perturbations for low and intermediate Reynolds numbers, relying on the finite element code OOMPH-LIB for time-stepping as well as for the computation and continuation of equilibria and their spectra.

11:00-11:30

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Finite time blow-up of the axisymmetric Euler equations: a numerical investigation

Martin Haddad

(Université de Montréal)
## Abstract

The importance of the formation of singularities in the 3D Euler and NS equations beginning with a smooth divergence-free velocity field cannot be overstated since it would indicate that the governing equations are not well posed and the issue is of great interest to engineering communities because of the possible connection with the onset of turbulence. In 2014, Luo and Hou presented numerical evidence to show that a certain swirling rotationally symmetric flow of an incompressible inviscid fluid in an axially periodic cylinder of finite radius leads to finite time blow-up in the vorticity $\omega$. Numerical methods used by Luo and Hou (2014), Barkley (2020) and Kolluru et al. (2022) used a vorticity-stream function formulation and pseudospectral or B-spline based Galerkin methods in combination with a Runge-Kutta method.
In this talk, we use a Fourier-Chebyshev spectral collocation method and compare both explicit and implicit adaptive Runge-Kutta methods in an investigation of finite time blow-up of the vorticity in the swirling flow proposed by Luo and Hou.

11:30-12:00

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Growth rates for some axisymmetric Euler flows

Stephen Gustafson

(University of British Columbia)
## Abstract

We discuss solutions of the Euler equations of fluid mechanics in three (and higher) dimensions which describe colliding pairs of vortex tubes. We provide rigorous upper and lower bounds for growth rates of the vorticity which generalize and improve on recent estimates of Choi and Jeong. This is joint work with Evan Miller and Tai-Peng Tsai.

Wednesday, 10:00-12:00,

Stirling Hall 401

25th Canadian Symposium on Fluid Dynamics

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10:00-10:30

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On the Maximum Enstrophy Dissipation in 2D Navier-Stokes Flows in the Limit of Vanishing Viscosity

Bartosz Protas

(McMaster University)
## Abstract

We consider enstrophy dissipation in two-dimensional (2D) Navier-Stokes flows and focus on how this quantity behaves in the limit of vanishing viscosity. After recalling a number of a priori estimates providing lower and upper bounds on this quantity, we state an optimization problem aimed at probing the sharpness of these estimates as functions of viscosity. More precisely, solutions of this problem are the initial conditions with fixed palinstrophy and possessing the property that the resulting 2D Navier-Stokes flows locally maximize the enstrophy dissipation over a given time window. This problem is solved numerically with an adjoint-based gradient ascent method and solutions obtained for a broad range of viscosities and lengths of the time window reveal the presence of multiple branches of local maximizers, each associated with a distinct mechanism for the amplification of palinstrophy. The dependence of the maximum enstrophy dissipation on viscosity is shown to be in quantitative agreement with the estimate due to Ciampa, Crippa & Spirito (2021), demonstrating the sharpness of this bound. [Joint work with Pritpal Matharu and Tsuyoshi Yoneda.]

10:30-11:00

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Modelling Aspects of Flow in the Transition Layer

Mohammad Hamdan

(University of New Brunswick)
## Abstract

Recent advances in the study of the mechanics of the transition layer between a Darcy porous layer and a Navier-Stokes’ channel employ a Brinkman’s porous layer with variable permeability, sandwiched between the two flow regiments. Flow in the Brinkman’s layer is governed by the well-known Brinkman’s equation which has been shown to give rise to Airy’s differential equation. Exact solutions of the flow in the transition layer are then given in terms Airy’s functions. This approach continues to be implemented in the study of flow through and over porous layers, and has provided an impetus to the transition zone approach, which initiated a number of novel ideas that include:
1) Introducing and reviving the implementation of classical integral functions in the porous media literature (as witnessed by the use of Airy’s differential equation and the Airy functions in providing an analytical solution to the flow in the transition zone).
2) Introducing new integral functions to facilitate solution to the inhomogeneous Airy’s differential equation. This, in turn, facilitates analysis of other related problems governed by the inhomogeneous Airy’s equation.
3) Initiating non-traditional models of permeability variations in porous media. These complement classical models that use elementary mathematical functions and have served the subject matter well.
The use of special functions in advancing the topic represents a new generation of models the computations of which is no longer a formidable task.
In the current work, modeling aspects of flow through and over porous layers with an embedded transition layer are discussed in order to provide alternative variable permeability models that reduce Brinkman’s equation in the transition zone to equations that complement Airy’s equation. In particular, the interest is to model the flow using generalized Airy’s equation and Weber’s inhomogeneous differential equation, and to provide efficient algorithms for their computations.

11:00-11:30

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Interaction between long internal waves and free surface waves in deep water

Christopher Kennedy

(Queen's University)
## Abstract

We present a study of the two-dimensional water wave problem consisting of a density-stratified fluid composed of two immiscible layers separated by a sharp interface. A goal is to describe the interaction between long, larger amplitude, nonlinear waves on the interface and modulated, smaller amplitude, free wave packets on the surface when the lower fluid is infinitely deep. In the first part, starting from the Hamiltonian formulation of this problem and using techniques from Hamiltonian transformation theory, we describe the resonant interaction of the waves by a system of equations where the internal wave solves a high-order Benjamin-Ono equation coupled to a linear Schroedinger equation for the time evolution of the wave envelope of the free surface. In the second part, we establish a local well-posedness result for the BO-Schroedinger system in the physical regime where the densities of the two fluid layers are close. Neglecting the higher-order coupling terms, we perform a gauge transformation to eliminate the higher-order non-linear terms and reformulate our BO equation, from which our proof follows by a fixed-point argument. This is a joint work with A. Kairzhan and C. Sulem.

11:30-12:00

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Velocity Gradient Dynamics of Atmospheric Turbulence for Wind Farms Over Complex Terrain

Jahrul Alam

(Memorial University of Newfoundland)
## Abstract

Wind energy is rapidly evolving to be the most reliable renewable energy source. Wind farms, particularly those situated over complex terrain and harsh weather conditions, generally present multi-scale challenges of atmospheric turbulence. To the best of our knowledge, past studies have not systematically evaluated the velocity gradient dynamics of atmospheric turbulence for utility-scale wind farms in complex terrain. In the real atmosphere, a role of turbulence is to transport kinetic energy from the free atmosphere to the atmospheric boundary layer, known as entrainment. However, complex terrain itself can quickly generate turbulence within the atmospheric boundary layer. In this study, we consider wavelet-filtered velocity gradient dynamics to encapsulate and model the impact of atmospheric turbulence in wind energy production, where the vortex stretching is regarded as the principal mechanism of energy cascade. Idealized case studies that simulated the impact of complex terrain and turbulence entrainment indicate that the land needed by wind farms in complex terrain may be five times less than that required by offshore wind farms with sustained wind conditions. The study has utilized wind tunnel experiments, field measurements, and the deep learning approach to validate the role of velocity gradient dynamics wind farm design and control. Overall, the study used wavelet-coherence to show that complex terrain is most unlikely to cause fluttering on wind turbine.

Wednesday, 10:00-12:00,

Stirling Hall 414

Computational Neuroscience

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10:00-10:30

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Intrinsic cell-to-cell diversity promotes the resilience of neural circuits

Jeremie Lefebvre

(University of Ottawa)
## Abstract

Heterogeneity is the norm in biology. The brain is no different: Neuronal cell types are myriad, reflected through their cellular morphology, type, excitability, connectivity motifs, and ion channel distributions. While this biophysical variety adds richness to neural system dynamics, it poses a challenge in maintaining the stability and consistency of brain function over time, known as resilience. To better understand the relationship between excitability heterogeneity (cell-to-cell variability in excitability within a population of neurons) and resilience, we analyzed both analytically and numerically a nonlinear sparse neural network with balanced excitatory and inhibitory connections evolving over long time scales. Homogeneous networks demonstrated increases in excitability, and strong firing rate correlations—signs of instability—in response to slowly varying modulatory fluctuations. Excitability heterogeneity tuned network stability in a context-dependent way by restraining responses to modulatory challenges and limiting firing rate correlations, while enriching dynamics during states of low modulatory drive. Excitability heterogeneity was found to implement a homeostatic control mechanism enhancing network resilience to changes in population size, connection probability, strength and variability of synaptic weights, by quenching the volatility (i.e., its susceptibility to critical transitions) of its dynamics. Together, these results highlight the fundamental role played by cell-to-cell diversity in the robustness of brain function in the face of change.

10:30-11:00

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Expressivity of Neural Networks with Random Weights and Learned Inputs

Ezekiel Williams

(Université de Montréal & Mila)
## Abstract

The expressivity of a neural network where all weights are initialized randomly and only constant inputs (biases) are learned is not well-studied and of interest in two domains. In neuroscience, the contribution of inputs from upstream regions–versus local plasticity–to learning in neural circuits, such as the motor cortex, is poorly understood. In artificial intelligence (AI), recent empirical work has shown that fine-tuning biases alone can yield efficient multi-task learning. However, both fields lack a thorough understanding of the limits of input-only learning. Here, we give theoretical and numerical evidence that a wide class of functions and finite trajectories from many dynamical systems can be well approximated by randomly initialized networks where only biases are optimized. These results extend our collective knowledge of neural networks, providing guidance for future methods in AI and for models of circuit-level plasticity in the brain.

11:00-11:30

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Postdoctoral Fellow

Luisa Liboni

(Western University)
## Abstract

We introduce an approach to image segmentation through spatiotemporal dynamics in a recurrent neural network (RNN). We use a specific RNN, where each node’s state is represented by a complex number. This complex-valued RNN (cv-RNN) generates intricate spatiotemporal patterns that can effectively group structures within a scene. By obtaining an exact solution to the network’s dynamics, we can “open the box” and elucidate the underlying mechanism for how this network performs its computation. This analytical approach then motivates a simple but powerful algorithm that segments objects ranging from simple geometric shapes to complex entities in natural scenes. We find that image segmentation can be accomplished by a single set of recurrent weights obtained from training on simple images and then applied to naturalistic scenes, demonstrating the potential generalizability of the algorithm. Taken together, our results provide a new avenue for machine learning that leverages exact solutions to create algorithms that can be understood through precise mathematical expressions. These results also provide potential insights into computations with spatiotemporal dynamics in the biological neural circuits of the visual system.

11:30-12:00

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Distributed Time Delay and Synchronization in a Neural Field Model

Sue Ann Campbell

(University of Waterloo)
## Abstract

We consider a neural field model for a brain network which is a network of Wilson-Cowan nodes with homeostatic adjustment of the inhibitory coupling strength and time delayed, excitatory coupling. Without time delay, the
system has been show to exhibit rich dynamics including oscillations, mixed-mode oscillations, and chaos. We
explore how synchronization of the nodes depends on both the connectivity structure of the network and the
attributes of the distribution of time delays in the connections between nodes. We show that Hopf bifurcations
induced by the excitatory coupling, the connectivity structure and the delay lead to different patterns of phase-locked oscillations, either synchronized or desynchronized. Finally, we study how the mean and variance of the
distribution affect the results.

Wednesday, 10:00-12:00,

Stirling Hall A

Infectious disease modelling for small jurisdictions

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10:00-10:30

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Coupled opinion and disease dynamics during COVID-19: Comparing the Yukon and BC Southern Interior

Rebecca Tyson

(University of British Columbia Okanagan)
## Abstract

Disease dynamics can be controlled by top-down shutdown regulations, but are also affected by spontaneous behaviour change within the population. These changes in behaviour can occur as a result of opinion dynamics, i.e., shifting opinions following ``conversations'' between individuals, where the infuence of prophylactic voices is affected by disease prevalence. Measuring opinion dynamics is challenging, however, and it is unclear to what extent opinion dynamics change the outcome of the disease dynamics. We present a comparative modelling study of the COVID-19 Omicron wave in the Yukon Territory and the Southern Interior of BC. Vaccination rates were similar in the two regions, but our analysis of the data suggest that different opinion dynamics may have been at play.

10:30-11:00

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A mathematical framework to compare the optimality of elimination, suppression and mitigation response strategies

Amin Afshari

(Memorial University of Newfoundland)
## Abstract

During the COVID-19 pandemic, governments implemented non-pharmaceutical interventions (NPI) including self-isolation and testing requirements, to reduce the spread of SARS-CoV-2. These interventions were implemented as strategies, termed elimination, suppression and mitigation, that differ in the strictness and types of NPIs implemented, the conditions for NPI implementation and relaxation, and the resulting epidemiology. Through implementation of NPIs, these strategies reduce infection spread, but they also disrupt the local economy and impact the health care system. Regional factors and disease characteristics determine which strategy is the most cost effective in a jurisdiction. Most existing mathematical models cannot compare elimination, suppression and mitigation strategies, since elimination reduces infection prevalence to zero, and many epidemiological models are systems of ordinary differential equations that cannot achieve this property. We modified the general SIRS model to study the impact of regional factors on the cost-effectiveness of different strategies. We show that the rate that infected travelers spread infections to the local community (the importation rate), and the fraction of infected people that are hospitalized are important factors determining which strategy is optimal. We found that elimination is the best strategy for a small jurisdiction with a relatively high fraction of the population expected to be hospitalized if infected, and a low importation rate. We also found that when a very low fraction of infected individuals become hospitalized due to severe infections, mitigation is the optimal choice. Regions with limited modeling capacity may rely on modeling intended for other jurisdictions, or may make decisions that differ from recommendations made for other regions. Our work aims to support regions with limited modeling capacity by developing models that consider a range of local characteristics, and can recommend either of three pandemic response strategies.

11:00-11:30

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Pandemic planning using urban mobility simulations

Sanjeev Seahra

(University of New Brunswick)
## Abstract

Urban mobility simulations use agent based modelling to estimate the daily activities of individuals within a community. The output from these simulations can be used to generate a detailed synthetic social network that carries information about the duration and venue of all contact events within a city on a given day, as well as the key demographic information (age, occupation, etc) of the participants in each event. We have been working with The Black Arcs, a Fredericton area technology company, to incorporate synthetic social networks generated by their software into network based models of COVID-19 and related diseases. Our goal is to make quantitative predictions about the impact of various public health interventions on disease spread. For example, we are interested in questions like: Is it more effective to shut down schools or retail businesses to control disease spread? What is the effect of different testing strategies and delays on hospitalizations? And, which policies do the best job of protecting vulnerable demographic groups?

11:30-12:00

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Adjusting prevalence estimates for reductions in testing

Steve Guillouzic

(Defence Research and Development Canada)
## Abstract

\[\text{BACKGROUND}\]
In 2020, Defence Research and Development Canada (DRDC) developed a suite of online decision-support tools to help the Canadian Armed Forces (CAF) mitigate the risk of coronavirus disease 2019 (COVID-19) outbreaks. These tools were underpinned by a COVID-19 prevalence model that leveraged case data published openly by public health agencies. For the first one and a half years, we used a compartmented epidemiological model to estimate prevalence. Then, in early 2022, we transitioned to a method developed by Chiu and Ndeffo-Mbah that also considers test positivity. At the request of the Canadian Forces Health Services, we started applying the same prevalence model to other respiratory illnesses, such as influenza, in early 2023 for Canadian provinces and territories.
\[\text{METHOD}\]
The model by Chiu and Ndeffo-Mbah is based on the fact that the case and test-positivity rates respectively provide lower and upper bounds to prevalence. The prevalence estimate is obtained by taking a weighted geometric mean of the two bounds. The main challenge in applying this method is to determine the appropriate averaging weights, as their value is affected by the testing regime.
\[\text{RESULTS}\]
While there was a high test volume during part of the COVID-19 pandemic, it was eventually scaled back to a level similar to other respiratory viruses. In this presentation, we will discuss our efforts in determining appropriate averaging weights for use in our prevalence estimates.
\[\text{CONCLUSION}\]
The DRDC COVID-19 prevalence map provided the CAF and Department of National Defence with critical information for the determination of workplace posture and force health protection measures during the pandemic. Our renewed map with coverage for other respiratory viruses can continue to support medical advisors as they help navigate the annual respiratory illness season year after year.

Wednesday, 10:00-12:00,

Stirling Hall B

AI for Enhancing Public Health and Healthcare in Canada

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10:00-10:30

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AI in Outbreak Situal Awareness

Berry de Bruijn

(National Research Council Canada, Digitial Technologies Research Centre)
## Abstract

The talk provides an overview of Early Warning / Situational Awareness tools for public health, particularly those that leverage public data, and those that detect and track disease outbreaks. The principles behind the Canadian GPHIN system will be highlighted. The (increasing) role of AI will be explored, both for current systems and emerging ones. Some forecasting for future game changers will be presented.

10:30-11:00

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Making Canadian Healthcare Systems "AI Ready": What do we need to build AI-powered Trustworthy Healthcare Solutions?

Sirisha Rambhatla

(University of Waterloo)
## Abstract

With aging population and healthcare worker shortage sending shock waves throughout the healthcare systems in Canada, there is an urgent need to develop and deploy AI-powered healthcare solutions to assist and support our healthcare workers. While AI for healthcare solutions have made tremendous progress in recent years, translating these gains to improve quality of service (QoS) for real-world healthcare systems has been extremely slow despite a widespread interest both from researchers, hospitals, policy-makers. This is primarily because our healthcare systems are not "Artificial Intelligence (AI) Ready". In this talk, I will first outline various ways AI-powered solutions can revolutionize primary healthcare solutions based on my research in liver transplantation and burn surgical candidacy forecasting. Second, via an example of AI-based surgical skill assessment in radical prostatectomy, I will highlight how AI can play a key role in tooling and training our healthcare workforce in highly skilled tasks. Next, I will delve into the data aspect of machine learning for trustworthy and fair AI modeling in healthcare systems and hospitals, followed by a discussion about the current challenges faced by community hospitals in adoption of AI solutions via my current collaboration with Grand River Hospital. I will then discuss some lessons learned from the COVID-19 pandemic, and its impact on policy and healthcare misinformation. I will conclude with a call to bring together hospitals, industry experts, academic researchers, and policy-makers to develop a unified healthcare strategy for building AI ready healthcare systems. This will lead to faster adoption of research results, data transparency initiatives for patients, and provide a blueprint for AI-centric data organization in the health systems in Canada and abroad.

11:00-11:30

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AI for drug discovery and design

Jonathan Stokes

(McMaster University)
## Abstract

Drug discovery is a discipline defined by failure. The cost of developing a new medicine is roughly $2.6 billion and it requires upwards of 12 years of sustained work. However, AI methods are uniquely suited to accelerate the drug discovery and development process, due to their capabilities of exploring truly vast chemical spaces for ideal molecules that satisfy multiple required properties. In this talk, we will explore the utility and limitations of discriminative and generative AI methods applied to novel drug discovery tasks. We will focus on two therapeutic domains: antibiotic discovery and neuro-oncology applications. Our goal is to more thoroughly understand how to optimally leverage AI to increase the rate of drug discovery and development, as well as decrease the associated costs.

11:30-12:00

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Machine learning classification of vaccine-elicited SARS-CoV-2 immunological responses amongst people living with HIV

Chapin Korosec

(York University)
## Abstract

The COVID-19 pandemic caused by SARS-CoV-2 has disproportionately impacted older (aged 50+) people living with HIV (PLWH). Not all PLWH restore their immunity to pre-HIV-infection levels after receiving combination antiretroviral therapy (cART). Further, HIV-mediated immunodeficiency may result in impaired immunological responses to common COVID-19 vaccines, where this effect may be exacerbated in older individuals due to the natural process of immunosenescence. The ability to classify PLWH as immune responders or immune-non-responders based immunological features would be valuable towards treatment plans in an endemic SARS-CoV-2 environment. Recent modelling and clinical work has revealed substantial differences in vaccine-elicited T-cell responses between PLWH and an HIV- age-matched control [1]. In this talk I will discuss our preliminary results of using machine learning classification techniques in order to classify the SARS-CoV-2 vaccine-elicited immunological footprint of PLWH and HIV-negative age-matched individuals.
[1] V. A. Matveev et al., “Immunogenicity of COVID-19 vaccines and their effect on HIV reservoir in older people with HIV,” iScience, vol. 26, no. 10, 2023.

Wednesday, 10:00-12:00,

Stirling Hall C

Modelling heterogeneity in ecology, epidemiology, and evolution

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10:00-10:30

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Predicting population level immune landscapes from individual level immune dynamics.

James Watmough

(University of New Brunswick)
## Abstract

The progression and burden of disease outbreaks, and biological invasions more generally, is complicated by heterogeneities in the host population and its environment. There are two sides to this heterogeneity: the risk of infection or transmission, and the cost of disease. For the particular case of SARS-CoV-2 and CoViD, transmission risk is raised or lowered by host behaviour and by host immune history. Familiar aspects of the former being masking and isolation, and of the latter being the time lapsed since vaccination or past infections. Host behaviour and immune history also affects disease risk as does age (through immunosenescence) and various comorbidities. The main objective of this talk is to present preliminary results from simple compartmental and individual-based models designed to predict population-level disease burden and immune landscapes from host behaviour and within-host virus and immune dynamics.

10:30-11:00

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The 1978 English boarding school influenza outbreak: where the classic SEIR model fails

Daihai He

(Hong Kong Polytechnic University)
## Abstract

Previous work has failed to fit classic SEIR epidemic models satisfactorily to the prevalence data and the attack rate (proportion of children infected during the outbreak) of the famous English boarding school 1978 influenza A/H1N1 outbreak in the children’s pandemic. Thus it is still an open question that whether a biologically plausible model can fit the prevalence data and the attack rate correctly. We used an intentionally very flexible and overfitted discrete-time model to learn the epidemiological features from the data which led us to the design of a susceptible (S) - exposed (E) - infectious (I) - confined to bed (B) - convalescent (C) - recovered (R) model with the feature of time delay in E and I compartments and multistage (dummy subgroups) in B and C compartments. We simultaneously fitted the reported B and C prevalence curves as well as the attack rate. The model is based on delay differential equations and dummy subgroups to reproduced the non-exponential residence times, which was crucial for good fits. The estimates of the generation time and the basic reproductive number appear to be biologically reasonable. Our work not only provided an answer to this open question, but also demonstrated an approach to constructive model-generation.

11:00-11:30

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Heterogeneity in disease transmission in age-structured/risk-structured models with multiple transmission routes

Qing Han

(York University)
## Abstract

In structured models, e.g., age-structured or risk-structured, where there exist heterogeneity in sub-populations’ susceptibility, activity level or transmission risk, these sub-populations may exhibit different R_0’s and thus different capabilities to drive the overall transmission. Furthermore, if there exist more than one possible transmission routes, R_0 can be quantified for each corresponding route, and thereby identifying the dominant transmission path. We will use pertussis and monkeypox as examples to illustrate the ideas.

11:30-12:00

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Disease Spread on Networks using Percolation Methods and Edge-Based Modeling

Sicheng Zhao

(Queen's University)
## Abstract

Bond percolation methods can be used to model disease transmission on complex networks and accommodate social heterogeneity while keeping tractability. Here we review the seminal works on this field by Newman (2002, 2003, 2010), and Miller, Slim & Volz (2011) and present a more clear and systematic discussion about the theoretical background, assumptions, derivation and development of the percolation method. We also present a new R package based on these results that take epidemic and network parameters as input and generates estimates of the epidemic trajectory and final size. Such theoretical framework and calculation tools allow us to apply the edge-based percolation model to solving real world public health emergencies. With syphilis rates continue rising in Ontario at an alarming rate, an ongoing project is collaborating with KFL&A public health to model Syphilis transmissions within the underserved high-risk community from data. The analysis and prediction of the model could provide scientific evidence to optimize implementation strategy based on community structure, thus help public health professionals to better response to the urgent crisis.

Wednesday, 13:00-13:30,

Stirling Hall 301D (Aud)

[Remote] CAIMS Doctoral Dissertation Award Lecture: Razan Abu-Labdeh

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13:00-13:30

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Monolithic multigrid methods for high-order discretizations of time-dependent PDEs

Razan Abu-Labdeh

(Memorial University)
## Abstract

Currently, a growing interest is seen in developing solvers that couple high-fidelity and higher-order spatial discretization schemes with higher-order time stepping methods for various time-dependent fluid and plasma models. These problems are famously known to be difficult to solve, requiring either very short time steps for explicit schemes, or expensive implicit time-stepping schemes with certain stability properties to be used. One of the most powerful choices is the family of implicit Runge-Kutta (IRK) methods. However, these are multi-stage schemes, often producing a very large and nonsymmetric system of equations that needs to be solved at each time step. Consequently, there have been several recent efforts to develop efficient and robust solvers for these systems. We have accomplished this by using a Newton-Krylov-multigrid approach that applies a multigrid preconditioner monolithically, preserving the system couplings, and uses Newton's method for linearization wherever necessary. We show robustness of our solver on the single-fluid viscoresistive magnetohydrodynamics (MHD) model, along with the (Navier-)Stokes and Maxwell's equations. For all these, we couple IRK with higher-order (mixed) finite-element (FEM) spatial discretizations. In the Navier-Stokes problem, we further explore achieving higher-order approximations by using nonconforming mixed FEM spaces with added penalty terms for stability. For the Maxwell problem, we focus on the more difficult E-B form needed to model plasma flows and overcome the difficulty of using FEM on curved domains by using an elasticity solve on each level in the non-nested hierarchy of meshes to improve mesh quality for the multigrid method.

Wednesday, 13:30-15:30,

Chernoff Hall 117

Development of robust high-order methods for partial differential equations

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13:30-14:00

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Mapping algorithm accuracy for computational multi-physics

David Brown

(Ansys Inc.)
## Abstract

Mapping, in a multi-physics context, is the problem of transferring data from the source to target side of a geometric interface of two physics solvers. Accurate and robust mapping technology is critical to any multi-physics coupling engine. In this presentation we develop the conditions for mapping algorithms to preserve the overall order of accuracy of the discretizations of the participating physics solvers, for both volume and surface mapping, and including the case of non-conformal surfaces.
The presentation also explores the use of radial basis functions for mapping and investigates several numerical pathologies encountered when using radial basis functions, as well as solutions to these problems.

14:00-14:30

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Optimal Runge-Kutta Projection Method with High-Order Methods

Mohammad R. Najafian

(Concordia University)
## Abstract

The exact solution of the governing equations of physical phenomena often enforces auxiliary admissibility criteria, e.g., conservation of entropy or conservation of energies. Often referred to as invariants, these auxiliary admissibility criteria are typically not enforced via conventional discretization techniques. Ultimately, this leads to non-physical solutions, loss of accuracy, and loss of
stability.
Over the past several decades, significant attention has been placed on low-order entropy or kinetic
energy conservative spatial discretizations. These frameworks then have been extended to high-order discretizations, including discontinuous Galerkin (DG) and flux reconstruction (FR). For example, see the work of Chan (2018). However, less attention has been given to the role of time integration in conserving invariants.
Recently, Ketcheson (2019) demonstrated relaxation Runge-Kutta (RRK) schemes can be used to enforce energy conservation, subsequently extended to entropy conservation by Ranocha et al. (2020). These introduce a time step relaxation parameter to enforce global conservation. In contrast, Calvo et al. (2006) showed that entropy conservation can be obtained without relaxing the step size by using embedded RK methods to define a more arbitrary projection direction. However, with either RRK or the method of Calvo et al. stability issues may arise and the order of accuracy may decrease.
Here, we indicate the constraints in defining the search direction to project the RK prediction to the conservative manifold, and then we present a unified projection framework that behaves superiorly in terms of stability and accuracy. We demonstrate invariant conservation for a range of example applications, and propose that the novel technique is a suitable replacement for the RRK and method of Calvo et al., alleviating the limitations of both previously proposed approaches.

14:30-15:00

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Space-Time Spectral Methods for PDEs on Irregular Domains

Chandramali Piyasundara Wilegoda Liyanage

(University of Manitoba)
## Abstract

One major drawback of classical spectral methods is their inability to handle irregularly shaped domains, which is why they have only been used sparingly in many engineering problems. Spectral element methods can handle complex geometry, but they are more difficult to implement. There have been many attempts to use classical spectral methods for elliptic PDEs in irregular domains, but only a few studies on spectral collocation methods for time-dependent PDEs in complex geometries. Here, we propose a numerical method to approximate the solution of PDEs in irregular domains using space-time spectral collocation methods.
The main idea here is to embed the irregular domain in a regular one and apply Fourier extension. We use Fourier and Chebyshev spectral methods to solve PDEs on regular geometries. Here we assume that the non-homogeneous term is only known in the physical domain and perform a periodic extension to the extended domain. We implemented Boyd's technique for this Fourier extension and observed super-algebraic convergence only. Then we apply the method introduced by Huybrechs to extend the non-homogenous term of the PDE from the physical domain to the regular domain with exponential accuracy and have solved steady and unsteady PDEs.

15:00-15:30

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Numerical approximation of spike-type solutions to a one-dimensional sub-diffusive Gierer-Meinhardt model with controlled precision

Nehemie Nguimbous

(Thompson Rivers University)
## Abstract

This study focuses on numerically solving the sub-diffusive Gierer-Meinhardt model with controlled precision. We start by defining and explaining basic concepts of reaction diffusion, highlighting the main differences between normal and anomalous diffusion. Sub-diffusion is modelled at continuum level by fractional derivatives replacing regular ones in PDEs. Therefore an important part of our study involves fractional calculus, which provides a solid framework for describing sub-diffusive processes.
We then delve into the well-known Gierer-Meinhardt model, a reaction-diffusion system used to describe pattern formation in biological systems. Leveraging the matched asymptotic expansion technique, which is applicable due to the asymptotic smallness of certain parameters in the
system, we transform the differential Gierer-Meinhardt model into a differential algebraic system. This differential algebraic system contains a fractional operator denoted $\mathcal{D}^{\gamma}_{t}$, which involves the integral of a complicated function impossible to determine analytically. This operator depends on multiple parameters, and the number of subdivisions needed for numerical computation varies significantly with these parameters and the desired precision. To address this challenge, we have developed a program capable of precalculating the required number of subdivisions before computation, thus saving significant computation time. All elements in place, we use these tools to study the dynamics of the obtained solutions.

Wednesday, 13:30-15:30,

Chernoff Hall 211

Recent Progress on the Intersections of Nonlinear Dynamics, Control, Learning, and Optimization

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13:30-14:00

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Event-triggered stabilization of time-delay systems using Halanay-type inequalities

Kexue Zhang

(Queen's University)
## Abstract

Event-triggered control provides an efficient way to update feedback control signal at a sequence of discrete-time moments, and these discrete times are determined by a certain event that occurs only when the measurement of system states violates a predesigned threshold. The advantage of this control paradigm is that it improves the efficiency of control implementations while still guaranteeing the desired performance level of the control system. In this talk, we present an event-triggered control method for the stabilization of linear time-delay systems. Based on two Halanay-type inequalities, the global asymptotic stability of the event-triggered control system can be guaranteed, and a lower bound of the inter-event times, the intervals between successive control updates, can be derived to ensure the practical implementation of the proposed event-triggering condition.

14:00-14:30

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Leader–Follower Synchronization of Multi-Agent Systems Via Hybrid Protocols

Xinzhi Liu

(University of Waterloo)
## Abstract

This talk discusses the leader–follower synchronization problem of complex-valued networked multi-agent systems with time-delay. A hybrid protocol including a continuous-time protocol based on the interaction topology of the follower agents and a pinning delayed impulsive control protocol is proposed. Several delay-dependent leader–follower synchronization criteria are established where various sizes of delays are taken inti account. Particularly, our result shows that leader–follower synchronization of delayed complex-valued multi-agent systems can be achieved even if the proposed hybrid protocol is being subject to relatively large impulse delays. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

14:30-15:00

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Generalized Derivatives of Nonsmooth Difference Equations

Peter Stechlinski

(University of Maine)
## Abstract

Nonsmoothness can arise in difference equations in several ways: because they are a suitable modeling framework for applications that exhibit a mixture of continuous and discrete behavior; because of numerical discretization schemes or analysis techniques applied to nonsmooth continuous-time systems; and because of mathematical techniques that purposefully introduce nonsmoothness to iterative schemes. However, the presence of such nonsmoothness necessitates the development of new tools of analysis since conventional approaches typically require smoothness of the system. After reviewing generalized derivatives theory, we highlight a new sensitivity theory for nonsmooth difference equations that characterizes first-order generalized derivative information of solutions. The theory, which is applicable to both explicit and implicit difference equations, is computationally relevant and it recovers classical theory when participating functions are smooth. We also show how this new theory can be used to analyze the dependence of fixed points and N-cycles on parameters and solve optimal control problems.

15:00-15:30

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Distributed Fake News Detection

Behrouz Touri

(University of California San Diego)
## Abstract

We formulate the problem of fake news detection using distributed fact checkers (agents) with limited and unknown trust. We consider the stream of news/statements as an independently and identically distributed binary source (to model true vs false statements). Upon observing the news, agent $i$ labels it as true or false that reflects the true validity of the statement with some probability $1-\pi_i$. In other words, agent $i$ misclassified each statement with error probability $\pi_i\in (0,1)$, where the parameter $\pi_i$ models the (un)trustworthiness of the $i$th agent. We present an algorithm to learn these parameters resulting in a distributed fact checking algorithm. We provide various aspects of this algorithm and its convergence properties.
This work is a joint work with Ashwin Verma (UCSD) and Prof. Soheil Mohajer (UMN).

Wednesday, 13:30-15:30,

Chernoff Hall 213

Delay Differential Equations and Their Applications

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13:30-14:00

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A quantification of long transient dynamics

Felicia Magpantay

(Queen's University)
## Abstract

The stability of equilibria and asymptotic behaviors of trajectories are often the primary focuses of mathematical modeling.However, many interesting phenomena that we would like to model, such as the ``honeymoon period'' of a disease after the onset of mass vaccination programs, are transient dynamics.
Honeymoon periods can last for decades and can be important public health considerations.
In many fields of science, especially in ecology, there is growing interest in a systematic study of transient dynamics. In this work we attempt to provide a technical definition of ``long transient dynamics'' such as the honeymoon period and explain how these behaviors arise in systems of ordinary differential equations.
We define a transient center, a point in state space that causes long transient behaviors, and derive some of its properties. In the end, we explore some possible extensions of these ideas to systems of delay differential equations.

14:00-14:30

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Lyapunov Function(al)s and Their Applications

Zhisheng Shuai

(University of Central Florida)
## Abstract

This presentation revisits Lyapunov function(al)s and their applications in population dynamics. We highlight recent advancements and ongoing challenges in establishing the global stability of both disease-free and endemic equilibria in infectious disease models. Noteworthy among recent advancements is work on discrete-time epidemiological models, offering promising insights that may steer future directions.

14:30-15:00

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Modeling Treatment Efficacy of Oncolytic Viral Therapy in Cancer

Tanuja Das

(University of Montreal)
## Abstract

Oncolytic viral therapy (OVT) is a promising form of immunotherapy that uses viruses to selectively infect and eliminate cancer cells. These trained viruses replicate within cancer cells, triggering immune responses against cancer. To evaluate the efficacy of OVT, we investigate the dynamics of cancer growth influenced by oncolytic viral activity and the subsequent antibody immune response. Building upon prior research by S. Jahedi, J. Watmuogh, and L. Wang (“Effect of Virus-Specific Immune Response on Outcome of Oncolytic Viral Therapy”), we extend the study by introducing a delay in the immune system’s ability to produce antibodies in response to the virus. As the previous work, we identified two thresholds of virus infection rate: the treatment control threshold ($b_c$) and the treatment optimal threshold ($b_{opt}$) which is delay dependent. Treatment begins to work beyond $b_c$ and achieves full success beyond $b_{opt}$. Further, we assess tumor responses under slow and fast immune systems, exploring various therapy strategies such as single and repeated dosing regimens, varied dosing levels, and timing. Our findings indicate that increasing dosing frequency enhances therapy efficacy, resulting in a higher proportion of infected tumor size relative to the total tumor size.

15:00-15:30

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A new perspective on infection forces with demonstration by a DDE infectious disease model

Tianyu Cheng

(York University)
## Abstract

In this talk, we revisit the notion of infection force from a new angle, which can offer a new perspective to motivate and justify some infection force functions. Our approach can not only explain many existing infection force functions in the literature, but it can also motivate new forms of infection force functions, particularly infection forces depending on disease surveillance of the past. As a demonstration, we propose an SIRS model with delay. We comprehensively investigate the disease dynamics represented by this model, mainly focusing on the local bifurcation caused by the delay and another parameter that reflects the weight of past epidemics in the infection force. We confirm Hopf bifurcations both theoretically and numerically. The results show that, depending on how recent the disease surveillance data are, their assigned weight may have a different impact on disease control measures.

Wednesday, 13:30-15:30,

Chernoff Hall 250 (Aud)

Financial Mathematics

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13:30-14:00

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The second order Esscher for continuous-time models

Tahir Choulli

(University of Alberta)
## Abstract

We introduce the second-order Esscher pricing notion for general continuous-time models. This extends the classical notion of Esscher that is used in finance and actuarial sciences. Depending whether we use directly the assets' prices $S$ or their logarithm, we obtain two principal classes of Esscher pricing densities of-order-two. Besides this novel notion, our contributions has three main parts. In the first part, for every class obtained and using the statistical parametrization of the model, we characterize its second-order Esscher densities via pointwise equations. Furthermore, we discuss the relationship between the two classes and the role of the second order factor specific to our Esscher notion. The second main contribution resides in addressing the pricing problem using the obtained Esscher densities. In fact, we show that the bounds of the Esscher stochastic pricing interval, $){Y}^{\rm{inf}},Y^{\rm{up}}($, are solutions to two constrained reflected linear backward stochastic differential equations (RBSDEs hereafter for short), or equivalently reflected BSDEs with singular non Lipschitz generator. This shows that these constrained reflected BSDEs appear also in other setting beyond the cases of constraints on gain-process or constraints on portfolios. For the Merton jump-diffusion model, we derive this Esscher pricing interval and compare it to Merton's pricing formula. The third main contribution lies in conducting numerical and empirical studies to show and test the role of the second order Esscher in many aspects.
This talk is based on joint work with Alla Elazkany (University of Alberta) and Michele Vanmaele (Ghent University, Belgium).

14:00-14:30

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Estimating the roughness exponent of stochastic volatility from discrete observations of the realized variance

Alexander Schied

(University of Waterloo)
## Abstract

Motivated by the recent success of rough volatility models, we introduce the notion of a roughness exponent to measure the roughness of trajectories. We show that it can be estimated in a model-free manner and we discuss its relations to other roughness measures such as weighted quadratic variation and Besov regularity. Then we we introduce a new estimator that measures the roughness exponent of a continuous trajectory based on discrete observations of its antiderivative. This estimator is then applied to estimating the roughness exponent of the volatility in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. We provide conditions on the underlying trajectory under which our estimator converges in a strictly pathwise sense. Then we verify that these conditions are satisfied by almost every sample path of fractional Brownian motion with sufficiently regular drift. As a consequence, we obtain strong consistency theorems in the context of a large class of rough volatility models. Numerical simulations show that our estimation procedure performs well after passing to a scale-invariant modification of our estimator. This is joint work with Xiyue Han.

14:30-15:00

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Illiquidity, Interest Rates, and Asset Prices

Xiaofei Shi

(University of Toronto)
## Abstract

In this work, we examine the joint effect of illiquidity on the dynamics of asset prices and interest rates. Equilibrium is identified by a system of coupled forward-backward stochastic differential equations, which admit explicit asymptotic solutions in the high-liquidity regime. Illiquidity increases price volatility and the risk premium but decreases the interest rates. (Joint work in progress with Paolo Guasoni and Johannes Muhle-Karbe.)

15:00-15:30

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Geometric Compound Hawkes Process and its Applications in Finance

Anatoliy Swishchuk

(University of Calgary)
## Abstract

We introduce a new model for a stock price, namely, geometric
compound Hawkes process, and show how this model can be applied to
solving many problems in finance, including option pricing (European and
American) and Merton portfolio optimization problems.
This model is a generalization of some well-known models in finance, such
as Cox-Ross-Rubinstein model (1976) (geometric binomial process), Aase
model (1988) (geometric compound Poisson process) and geometric Markov
renewal model (2013), to name a few. Numerical examples are presented as well.

Wednesday, 13:30-15:30,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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13:30-14:00

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Particle-based simulations for compressible flow with slip through local constrictions

Katrin Rohlf

(Toronto Metropolitan University)
## Abstract

Flow through local constrictions has important applications in various areas of biology and engineering. In blood flow applications, for example, knowledge of more detailed flow behaviour through constricted flow geometries can allow for assessment and treatment of conditions such as atherosclerosis, in which stenosed (or constricted) vessels can arise from plaque deposits along the interior of the vessel walls. In general, particle-based methods are computationally expensive, even to date. Efficient methodologies at the mesoscopic scale, rather than fully detailed microscopic options, can provide the trade-off between computational cost and more detailed assessments, compared to solving the macroscopic Navier-Stokes equations.
This talk focuses on recent advances in using a numerically efficient mesoscopic particle-based method for flow applications, called Multi-particle collision dynamics (MPC), that was originally introduced by Malevanets and Kapral in the late 1990s. Theoretical and numerical results will be presented for flow through constricted cylinders using MPC. The particle-based simulations are shown to exhibit built-in compressibility that can, in part, be quantified by a pressure-dependent viscosity in the Navier-Stokes equations. Approximate analytical solutions are provided, that are based on the Karman-Pohlhausen method applied to the compressible Navier-Stokes equations with variable viscosity. The resulting nonlinear ODEs for the pressure gradient are solved numerically with Maple/Matlab, and compared to the particle-based MPC simulation results. The effects of compressibility, slip, pressure-dependent viscosity parameter and geometry changes are assessed, through appropriate velocity/pressure/density curve comparisons between the MPC and the analytical results.

14:00-14:30

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A superconsistent collocation method for high Reynolds number flows

Robert Owens

(Université de Montréal)
## Abstract

We use a novel implicit second-order projection method together with a superconsistent collocation scheme
(Funaro, 1993; Fatone et al., 2005; De l’Isle and Owens, 2021) for the solution of the primitive variable
formulation of the Navier–Stokes equations at very high Reynolds numbers. In particular, we apply a
superconsistent collocation scheme to the convection–diffusion equation arising from one step of the projection
method and this represents the first time that superconsistent collocation methods have been employed for
the solution of a convection–diffusion equation having unsteady convection velocity. In order to evidence the
second-order (in space and time) convergence of our scheme for both the velocity and pressure fields we
choose to solve the two-dimensional unsteady Taylor–Green vortex problem (Taylor and Green, 1937). The
numerical results presented for the solution of the two-dimensional square lid-driven cavity problem are in
excellent agreement over the whole range of Reynolds numbers considered (5000$\leq{\textit{Re}}\leq$1000) with some others in the literature (Ghia et al., 1982; Wang and Liu, 2019; Bruneau and Saad, 2006; Auteri et al., 2002;
Pan and Glowinski, 2000).

14:30-15:00

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Development and analysis in data-driven system identification methods with applications in fluid dynamics

Xinyang Liu

(University of Calgary)
## Abstract

This work will focus on the development and analysis of data-driven system identification methods and applications in fluid dynamics. The objective is aiming to uncover the underlying pattern of the flow based on model-order reduction methods, in addition to the insights of the flow mechanics. The nature of fluid is very intricate mainly because of being nonlinear, immense in spatial-temporal dimensions, sensitive to the boundary conditions and it’s interfered by the noise of irrelevant behaviors during the data measurement. The reduced-order models achieve to identify and reconstruct the principal dynamics indicating the physics of the respective flow. In addition, they filter the noise to prevent from the over-fitting problem. The understanding of the nature of fluid dynamics bridges from the broad existence to the numerous applications in diverse fields, such as performance improvement and energy saving in manufacturing which is a priority area in Canada.

15:00-15:30

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A second-order accurate numerical scheme for the Poisson-Nernst-Planck-Navier-Stokes (PNPNS) system

Yuzhe Qin

(University of British Columbia)
## Abstract

In this talk, we propose and analyze a second order accurate (in both time and space) numerical scheme for the Poisson-Nernst-Planck-Navier-Stokes (PNPNS) system, which describes the ion electrodiffusion in fluids. The marker and cell (MAC) finite difference method is taken as the spatial discretization. In the temporal discretization, the mobility function is updated with a second order accurate extrapolation formula for the sake of unique solvability, and a modified Crank-Nicolson approximation is applied to the singular logarithmic nonlinear term. Nonlinear artificial regularization terms are added in the numerical scheme, so that the positivity-preserving property could be theoretically proved, which comes from the singularity of these artificial terms. Meanwhile, a second order accurate, semi-implicit approximation is applied to the convective term in the PNP evolutionary equation, and the fluid momentum equation is similarly computed. Furthermore, an optimal rate convergence analysis is provided in this paper, in which the higher order asymptotic expansion for the numerical solution, the rough error estimate and refined error estimate techniques have to be included to accomplish such an analysis. This work combines the following theoretical properties for a second order accurate numerical scheme for the PNPNS system:
(i) second order accuracy in both time and space,
(ii) unique solvability and positivity,
(iii) energy stability, and (iv) optimal rate convergence. A few numerical results are presented to validate the theoretical analysis.

Wednesday, 13:30-15:30,

Stirling Hall 401

25th Canadian Symposium on Fluid Dynamics

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13:30-14:00

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Mathematical modelling of dissolution of particles subject to forced and free convection

Kevin Moroney

(University of Limerick)
## Abstract

Solid particle dissolution is an important physicochemical process occurring in many everyday scenarios, including consumption of pharmaceutical and food products, application of granular fertilizers and preparation of chemical solutions for cleaning or in a laboratory setting. One important application is the dissolution of drug particles in the body to make active pharmaceutical ingredients available for absorption for a therapeutic purpose. In this context, in vitro dissolution testing is an important procedure to gain an understanding of the rate and extent of drug release in different physiologically relevant solvents and under different hydrodynamic conditions. One tool for this purpose is the United States Pharmacopeia (USP) apparatus 4 [1], a flow-through cell in which dissolution of particulate systems in a controlled flow environment is evaluated under a range of conditions. In this study, we consider the canonical problem of dissolution of a solid initially spherical particle in a solvent. The dissolution rate and shape evolution of the particle may be influenced by mass transfer mechanisms including molecular diffusion of the dissolved drug, forced convection induced by the pumped solvent and free convection resulting from density gradients arising from drug concentration differences around the particle. Recently published work describing dissolution dominated by forced [2] and free convection [3] will be presented. The dissolution models are derived from fundamental conservation laws accounting for the role of the different mass transfer mechanisms and used to study the shape evolution of the particle over time. For the purposes of modelling dissolution of large populations of polydisperse drug particles in systems such as the apparatus 4, simpler approaches involving mass-balance arguments are typically necessary. The ability of some specific mass transfer correlations used in these models, which are based on steady flow past a sphere, to capture the overall complex dissolution behaviour in different regimes is assessed.
[1] United States Pharmacopeial Convention. The United States Pharmacopeia 2011 : USP 34 ; the National Formulary : NF 29. United States Pharmacopeial Convention, 2010.
[2] Assunção, M., M. Vynnycky, and K. M. Moroney. "On the dissolution of a solid spherical particle." Physics of Fluids 35.5 (2023).
[3] Assunção, M., M. Vynnycky, and K. M. Moroney. "Free-convective dissolution of a solid spherical particle." Physics of Fluids 36.4 (2024).

14:00-14:30

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Squeeze cementing at microscale: Effect of capillary forces and pore blockage

Mahdi Izadi

(University of British Columbia)
## Abstract

Gas leakage is a common problem in hydrocarbon wells, occurring through fractures, fissures, and microannuli forming along cement-casing and cement-formation interfaces. The geometrical features of micro-annuli exhibit high variability due to irregularities in the operational parameters. To prevent gas leakage, a process called squeeze cementing is used, which involves pumping a thin cement slurry into the microannulus under pressure. In our previous work, we developed a numerical framework to investigate the idealized problem of radial invasion of viscoplastic fluids, representing cement slurry, into Hele-Shaw cell geometries filled with Newtonian fluid. The Hele-Shaw of this work has randomized gap thickness and represents microannulus. We further proposed a multi-perforation invasion scenario. This model allows us to model the cement invasion into a section of the wellbore and to explore the effect of different operational parameters.
This work extends our previous model by introducing two critical physical phenomena at the small scale: capillary forces and pore blockage. This work is joint with I. A. Frigaard from the University of British Columbia.

14:30-15:00

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Primary cementing of oil and gas wells: translating knowledge through predictive software

Mariana Carrasco-Teja

(UBC)
## Abstract

Primary cementing is the process of placing a cement sheath in the annulus between the casing and the formation in an open hole of an oil or gas well. Our group at UBC has been at the forefront of developing models for primary cementing over the past 20 years. Our current goal is to bring our models from research codes and laboratory experiments, directly into the hands of Canadian stakeholders, in the form of useable predictive software.
In this talk we will describe our primary cementing models, and our predictive software development project. We model the process as the displacement of viscoplastic fluids in an inclined, non-concentric, narrow annulus. Our 2D model uses a Hele-Shaw approach to describe the displacement, and the Herschel-Bulkley model to describe the fluids. We will overview the evolution of our 2D model, including as a purely laminar, immiscible displacement, the addition of transitional and turbulent regimes, and adding dispersion to the interface to better match our 3D simulations and laboratory experiments results.

15:00-15:30

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Effect of consistency and flow indices of a shear-thinning fluid on hydrodynamics of a coaxial mixer

Ali Rahimzadeh

(Toronto Metropolitan University)
## Abstract

Gas dispersion in non-Newtonian fluids is widely applicable in numerous chemical and biochemical processes. However, the investigation into the effect of the power-law model constants describing the rheological behavior of shear-thinning fluids has not yet been undertaken. The utilization of computational fluid dynamics (CFD) techniques is considered a promising approach for exploring the impact of fluid rheological behavior on gas dispersion within complex fluids. In this study, a numerical model was developed to simulate the hydrodynamics of gas dispersion in non-Newtonian fluids using a coaxial mixer. Subsequently, a series of experiments was conducted to assess the mass transfer efficacy of a coaxial mixer to validate the numerical model. Various methods, including dynamic gassing-in and electrical resistance tomography (ERT), were employed to quantify mass transfer and gas hold-up profiles. The influence of fluid rheological properties, gas flow number, and rotating mode on power consumption, mass transfer coefficient, bubble size profile, and hydrodynamics was examined experimentally and numerically. A response surface model (RSM) was employed to explore the individual effects of power-law model constants on mass transfer in an aerated coaxial mixer. The RSM model utilized five levels for the consistency index (k), five levels for the flow index (n), and three levels for the gas flow number. This study revealed that the co-rotating coaxial mixer was well-suited for dispersing gas within a fluid with high consistency. In contrast, the counter-rotating mixer proved effective in enhancing gas dispersion within a fluid with a lower flow index. This phenomenon occurred because the central and anchor impellers, rotating in opposing directions, intensified the shear rate in areas distant from the central impeller, thereby reducing the stagnant fluid zones within the coaxial mixer.

Wednesday, 13:30-15:30,

Stirling Hall 414

Transforming Optimization Problems: Geometric, Statistical, and Physical Perspectives

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13:30-14:00

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Pareto Meets Laplace: Geometric, Statistical, and Physical Approaches to Optimization via Integral Transforms

Greg van Anders

(Queen's University)
## Abstract

A spectacular array of 20th century technologies were developed by scientists and engineers who relied on integral transform techniques. Standard practice in control theory, signal processing, and many other fields leverages the paradoxical fact that many problems are far more tractable when they are mapped out of their original context a dual representation via integral transforms. Integral transforms rule many domains, however there are other domains, such as optimization where they are not standard practice. In this talk, we describe a set of integral transform techniques that can be applied to problems that are conventionally studied through the lens of optimization. We show that integral transforms of open geometric, statistical, and physical lines of attack on optimization. We review some recent applications of this framework to problems in designing materials at the nanoscale and point to applications for systems at human scales and above.

14:00-14:30

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Turning up the Heat on Gradient-Based Optimization

Hazhir Aliahmadi

(Queen's University)
## Abstract

Gradient-based methods are a cornerstone of mathematical optimization. However, strictly following the gradient to a local optimum is problematic for non-convex optimization, which has led to a zoo-full of methods that augment gradients to avoid pitfalls. In this talk we argue that information theory provides a unique way to augment gradient descent that makes minimally-biased assumptions about the structure of the solution space of optimization problems. We will show that information-theoretic augmented gradient descent is mathematically equivalent to physical systems at finite temperature. We will describe implementations of this approach that show established techniques from molecular dynamics provide powerful tools for optimization problems that bear little resemblance to molecular systems.

14:30-15:00

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The Steklov-Helmholtz spectrum in the plane

Kshitij Patil

(Simon Fraser University)
## Abstract

For a given wave number $\mu\in\mathbb{R}$ and bounded domain $\Omega \subset \mathbb{R}^2$ with boundary $M$, the Steklov-Helmholtz eigenvalue problem is to find eigenfunctions $u$ and eigenvalues $\sigma\in\mathbb{R}$ such that,
\[
\begin{cases}
-\Delta u -\mu^2 u = 0 \text{ in } \Omega,\\
\partial_\nu u = \sigma u \text{ on } M,
\end{cases}
\]
where $\nu$ is the outward unit normal to $M$. We suggest a robust and exponentially converging numerical method to approximate the Steklov-Helmholtz eigenvalues for analytic domains in the plane. The robustness is with respect to the choice of the wave number $\mu_D$ (exceptional) which could correspond to a Dirichlet-Laplace eigenvalue. In this case, as $\mu^2$ approaches a Dirichlet-Laplace eigenvalue of multiplicity $\ell$ from the left, the first $\ell$ $\sigma$s approach $-\infty$. Our method involves converting the PDE into a BIE and the use of a single layer potential ansatz for $u$ involving the fundamental solution and some unknown density $\phi$. We are led to a generalized eigenvalue problem where the matrices correspond to the discretized layer potentials. In case of exceptional wave numbers $\mu_D$ we look at the SVD of the discretized single layer matrix. Using the single layer, we reconstruct the eigenfunctions $u$ from the eigendensities $\phi$. We establish a scaling property for the eigenvalues and propose a conjecture for the number of negative eigenvalues. Using the layer potentials we are also able to solve a variety of boundary and eigenvalue problems for the Laplace and Helmholtz equations. We also extend the method to include domains of genus 1. Currently, we are working on a shape optimization problem and relaxing the the regularity requirements on the boundary $M$.

Wednesday, 13:30-15:30,

Stirling Hall A

Pattern formation for novel reaction-diffusion systems in the fully nonlinear regime

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13:30-14:00

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Symmetry-Breaking Patterns with Equal Diffusivities and Diffusion-Induced Synchrony for Compartmental Reaction-Diffusion Systems:

Michael Ward

(University of British Columbia)
## Abstract

We provide an overview of some results for pattern formation and
diffusion-induced synchrony for a 2D PDE-ODE bulk-cell model, where
one or more bulk diffusing species are coupled to nonlinear
intracellular reactions that are confined within a disjoint collection
of small circular compartments. The bulk species are coupled to the
spatially segregated intracellular reactions through Robin conditions
across the cell boundaries. For this compartmental-reaction diffusion
system, we show that symmetry-breaking bifurcations leading to stable
asymmetric steady-state patterns, as regulated by a membrane binding
rate ratio, occur even when two bulk species have equal bulk
diffusivities. This result is in distinct contrast to the usual, and
often biologically unrealistic, large differential diffusivity ratio
requirement for Turing pattern formation from a spatially uniform
state. Secondly, for the case of one-bulk diffusing species in R^2, we
derive a new memory-dependent ODE integro-differential system that
characterizes how intracellular oscillations in the collection of
cells are synchronized through the PDE bulk-diffusion field. By using a
fast numerical approach relying on the ``sum-of-exponentials'' method
to derive a time-marching scheme for this nonlocal system, diffusion
induced synchrony is examined for various spatial arrangements of
cells.This theoretical modeling framework, relevant when spatially
localized nonlinear oscillators are coupled through a PDE diffusion
field, is distinct from the traditional Kuramoto paradigm for studying
oscillator synchronization on networks or graphs. Numerical
challenges, some still only partially resolved, for numerically
implementing our analytical theory are discussed.

14:00-14:30

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The analysis and simulation of memory-dependent oscillations for a cell-bulk model

Merlin Pelz

(University of British Columbia)
## Abstract

The Kuramoto model has been used for the last decades to gain insight into the behaviour of coupled discrete oscillators, as it is simple enough to be analyzed and exhibits a breadth of possible behaviours, such as synchronization, oscillation quenching, and chaos. However, the question arises how one can derive precise coupling terms between spatially localized oscillators that interact through a time-dependent diffusion field. We focus on a compartmental-reaction diffusion system with nonlinear intracellular kinetics of two species inside each small and well-separated cell with reactive boundary conditions. For the case of one-bulk diffusing species in $\mathbb{R}^2$, we derive a new memory-dependent integro-ODE system that characterizes how intracellular oscillations in the collection of cells are coupled through the PDE bulk-diffusion field. By using a fast numerical approach relying on the ``sum-of-exponentials'' method to derive a time-marching scheme for this nonlocal system, diffusion induced synchrony (in-phase, anti-phase, mixed-mode etc.) is examined for various spatial arrangements of cells. This theoretical modelling framework, relevant when spatially localized nonlinear oscillators are coupled through a PDE diffusion field, is distinct from the traditional Kuramoto paradigm for studying oscillator synchronization on networks or graphs. It opens up new avenues for characterizing synchronization phenomena associated with various discrete oscillatory systems in the sciences, such as quorum-sensing behaviour.

14:30-15:00

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Existence, Stability and Slow Dynamics of Spikes in a 1D Minimal Keller–Segel Model with Logistic Growth

Fanze Kong

(University of British Columbia)
## Abstract

We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller-Segel model of chemotaxis that includes the effect of logistic growth of the cellular population. Our analysis of localized patterns for this two-component reaction-diffusion (RD) model is based, not on the usual limit of a large chemotactic drift coefficient, but instead on the singular limit of an asymptotically small diffusivity of the chemoattractant concentration field.
In the limit, steady-state and quasi-equilibrium 1D multi-spike patterns are constructed asymptotically. To determine the linear stability of steady-state $N$-spike patterns, we analyze the spectral properties associated with both the “large” $O(1)$ and the “small” $o(1)$ eigenvalues associated with the linearization of the Keller-Segel model. By analyzing a nonlocal eigenvalue problem characterizing the large eigenvalues, it is shown that $N$-spike equilibria can be destabilized by a zero-eigenvalue crossing leading to a competition instability if the cellular diffusion rate exceeds a threshold, or from a Hopf bifurcation if a relaxation time constant is too large. In addition, a matrix eigenvalue problem that governs the stability properties of an $N$-spike steady-state with respect to the small eigenvalues is derived. From an analysis of this matrix problem, an explicit range of cellular diffusion rate where the $N$-spike steady-state is stable to the small eigenvalues is identified. Finally, for quasi-equilibrium spike patterns that are stable on an $O(1)$ time-scale, we derive a differential algebraic system (DAE) governing the slow dynamics of a collection of localized spikes. Unexpectedly, our analysis of the KS model with logistic growth in the small chemical diffusion rate regime is rather closely related to the analysis of spike patterns for the Gierer-Meinhardt RD system.

15:00-15:30

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Spikes and Small Targets with Lévy Flights

Daniel Gomez

(University of Pennsylvania)
## Abstract

The fractional order s of a Lévy flight controls the algebraic decay of its corresponding jump length distribution. When $s\gt 1/2$ , $s=1/2$, or $s\lt 1/2$ the corresponding one-dimensional Lévy flights is qualitatively similar to Brownian motion in $N=1$, $N=2$, and $N\geq3$ dimensions. In this talk we describe how this correspondence manifests in the asymptotic analysis of two fractional problems: the characterization of spike equilibrium solutions to singularly perturbed reaction-diffusion systems, and the analysis of the first-hitting-time (FHT) for a Lévy flight to a small target. Our asymptotic results provide insights into how the fractional order affects the linear stability of spike solutions, as well as how target sparsity determines the optimal fractional order minimizing the first-hitting-time.

Wednesday, 13:30-15:30,

Stirling Hall B

AI for Enhancing Public Health and Healthcare in Canada

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13:30-14:00

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Leveraging Artificial Intelligence for Diseases Outbreak Support

Jude Kong

(York University)
## Abstract

Real-time delivery of credible information is critical throughout disease outbreaks to predict changes in the outbreak as early as possible and guide public health measures. However, too little data, collected too slowly, can affect the accuracy of these predictions and the efficacy of mitigation efforts. Advances in artificial intelligence (AI) can fill gaps in data and improve disease outbreak response at every stage. AI-powered tools have enabled monitoring the spread of diseases at local, state, and national levels; predicting upcoming peaks and their intensities; identifying hot spots; guiding the purchase and allocation of healthcare resources; informing decisions and policies, both for closing down facilities and for reopening them; and optimizing vaccination rollout strategies. In this talk, I will discuss harnessing AI to fill gaps in data and improve disease outbreak response at every stage. In particular, I will present some of the AI-based frameworks that we designed and deployed during COVID-19 to support the efforts of decision-makers, the medical community, and the public in managing every stage of the COVID-19 crisis. These frameworks utilize innovative AI models to integrate both conventional (e.g., historical data) and unconventional data (e.g., Google Trends, Google Trends Rate, social media, satellite data, and economic activity data).

14:00-14:30

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Multivariate joint modeling for clustered data with application to periodontal disease

Sean Xinyang Feng

(University of Toronto)
## Abstract

Multivariate joint modeling that integrates multiple longitudinal data and a terminal event for clustered data has increased interest in medical research. In the study of periodontal disease, probing pocket depth and recession serve as tooth-level biomarkers that are associated with the risk of tooth loss. Considering the natural clustering of the teeth within individuals, we propose a clustered multivariate joint model to assess the effect of multiple tooth-level longitudinal biomarkers on the risk of tooth loss. We estimate our joint model using a Bayesian estimation approach. We showed that our method outperforms the alternative joint model that ignores the cluster effects. We further use our proposed joint model to make dynamic prediction on the probability of tooth loss within a specified time horizon, given a set of baseline and longitudinal predictors, and assess the performance of dynamic prediction for clustered data.

14:30-15:00

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Enabling and Enhancing Data Utilization with Generative AI in Public Health and Drug Discovery

Helen Chen

(University of Waterloo)
## Abstract

Artificial intelligence (AI) is increasingly being integrated into every phase of drug development and patient care. The ongoing innovations in AI-driven methodologies are largely contingent on the availability of extensive, high-quality data sets. However, data access is often hindered by rigorous regulatory and privacy constraints, especially concerning real-world data routinely collected in healthcare. This challenge is especially pronounced in the realms of healthcare and drug discovery, where it significantly impedes progress. Data sets are frequently assembled independently, with minimal overlap, leading to data scarcity. This scarcity complicates data curation for researchers attempting to address pivotal research questions that span multiple data sets. Synthetic data, especially those produced using generative AI techniques, offer potential solutions to these privacy concerns and help mitigate the data deficiency.
In her presentation, Dr. Chen will discuss her research in generative AI, focusing on two specific applications: 1) the use of synthetic data as a privacy-enhancing tool for the Public Health Agency of Canada, and 2) synthetic data for drug discovery. She will share insights from her experience in generating, evaluating, and distributing large volumes of synthetic data sets. Additionally, Dr. Chen will introduce a groundbreaking diffusion GNN model, Syngand, designed for the end-to-end generation of ligand and pharmacokinetic data.

15:00-15:30

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Leveraging AI for Enhanced Disease Diagnosis: From Viral Infections to Cancer Cachexia

Suzan Farhang-Sardroodi

(Department of Pharmacology and Toxicology, University of Toronto)
## Abstract

The rapid and precise differentiation between influenza and COVID-19 is significant, given their similar early symptoms but significantly different effects on public health. At this mini-symposium, I will present how artificial intelligence can tackle this challenge through a supervised machine learning (ML) model that effectively distinguishes between these infections. Validated by strong performance indicators (ROC AUC ? 91%), this model uses synthetic data of viral infections to identify unique disease markers. Feature selection has pinpointed essential factors such as viral load and productively infected cells, which are vital for predicting disease progression and guiding specific interventions. Additionally, I will briefly discuss our ongoing research into developing an ML framework that explains the intricacies among various cellular entities. This study seeks to decode the mechanisms of cancer cachexia and immune dysregulation by focusing on the immune balances influencing tumour and muscle outcomes. Generally, these endeavours highlight the profound impact of AI in advancing disease diagnosis and deepening our understanding of complex biological systems, which aligns with Canada’s objectives to enhance healthcare outcomes via cutting-edge technologies.

Wednesday, 13:30-15:30,

Stirling Hall C

New challenges and new faces in mathematical ecology

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Note: First talk is 30 mins, each additional talk is 20 mins. The remaining 30 mins will be used for discussion.

13:30-14:00

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Hybrid mechanistic machine-learning models: Towards causal discovery of ecological covariates

Pouria Ramazi

(Brock University)
## Abstract

Mathematical biology has advanced to a level where it can mechanistically model many complex ecological processes. Nevertheless, some time-varying variables are often assumed to be fixed as they may depend on several ecological covariates, the governing dynamics of which are not exactly known. This simplification can be overcome by using hybrid mechanistic machine-learning models, where the dynamics of already well-studied variables are modelled using mechanistic models, such as differential equations, and the potentially complex and yet not fully developed dynamics of the remaining variables are modelled using machine learning algorithms. This approach has proven successful in predicting ecological phenomena; however, the machine learning part remains a black box, limiting the gained insight. We propose using causal Bayesian networks for the machine learning part. This way, while often maintaining or improving the prediction accuracy of previous models, causal relationships between the variables can be partly identified and used for developing mechanistic sub-models to replace the machine-learning part. While this approach can be readily applied to ecological processes, several challenges still need to be addressed to realize its full potential.

14:00-14:30

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Predictive modelling of cyanobacterial blooms in Alberta lakes

Russell Milne

(University of Alberta)
## Abstract

Blooms of cyanobacteria (CB) can disrupt lake ecosystems by killing large numbers of lake organisms, including members of key fish species. Climate change is projected to exacerbate this problem by increasing water temperatures to be closer to those that facilitate maximum CB growth. This raises the question of how temperature increases, and the more severe CB blooms that result from them, will affect the viability and health of other lake species. To address this, we construct a stoichiometric model that includes common components of an Alberta lake food web (CB, algae, daphnia, yellow perch, walleye), and features the effects of oxygen depletion caused by CB blooms and uptake of microcystin secreted by CB. We fit this model using field data from CB observations in Alberta lakes, and simulate it under different warming scenarios to predict the magnitude and effects of CB blooms in the future.

14:30-15:00

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Modeling the Impact of Seasonality on Mosquito Population Dynamics: Insights for Vector Control Strategies

Joseph Baafi

(Memorial University)
## Abstract

Mosquitoes are important vectors for the transmission of some major infectious diseases of humans, i.e., malaria, dengue, west Nile virus and Zika virus. The burden of these diseases is different for different regions, being highest in tropical and subtropical areas, which have high annual rainfall, warm temperatures, and less pronounced seasonality. The life cycle of mosquitoes consists of four distinct stages: eggs, larvae, pupae, and adults. These life stages have different mortality rates and only adults can reproduce. Seasonal weather may affect the population dynamics of mosquitoes, and the relative abundance of different mosquito stages, since the maturation rate to the next stage depends on temperature, and because egg survival depends on rainfall. We developed a stage-structured model that considers laboratory experiments describing how temperature and rainfall affects the reproduction, maturation and survival of different Anopheles mosquito stages, the species that transmits the parasite that causes malaria. We consider seasonal temperature and rainfall patterns and describe the stage-structured population dynamics of the Anopheles mosquito in Ain Mahbel, Algeria, Cape Town, South Africa, Nairobi, Kenya and Kumasi, Ghana. We find that regional differences in seasonal weather patterns affect mosquito population dynamics. Control strategies often target one specific life stage, for example, applying larvicides to kill mosquito larvae, or spraying insecticides to kill adult mosquitoes. Our findings suggest that differences in seasonal weather patterns affect mosquito stage structure, and best approaches to vector control may vary between regions.

15:00-15:30

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Predator-Prey Interactions in Arctic Canada: Discrete-Time Model of Lemmings, Foxes and Snowy Owls on Bylot Island

Sanuri Himansa

(University of British Columbia, Okanagan)
## Abstract

Bylot Island, in the Canadian Arctic, is home to a predator-prey system that includes snowy owls, arctic foxes, and lemmings. The latter are prey for both the snowy owls and foxes. Snowy owls reside periodically on the island, their presence or absence depending on the availability of the prey only. Unlike many other predator-prey systems, the composition of the food web (whether it includes one or two predators) depends on the internal dynamics of the system.
We begin with an ordinary differential equation model, that we reduce to a simple one-species discrete map. The simplicity of this map allows us to prove several key aspects of solution behaviour, and fully characterise the cyclic and pseudo-cyclic dynamics in the owl-fox-lemming system. Furthermore, we observe a bistability-like behaviour between two- and three-cycle solutions. The persistence of arctic predator-prey systems is under threat due to climate change, and our work contributes to efforts to understand the dynamics of these important species.

Wednesday, 16:15-17:00,

Biosciences 1101 (Aud)

Plenary: Annalisa Quaini

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16:15-17:00

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Nonlinear Spatial Filtering for Large Eddy Simulation

Annalisa Quaini

(University of Houston)
## Abstract

The direct numerical simulation (DNS) of a fluid flow resolves all the flow structures with a properly refined mesh. When the convection dominates the dynamics, as in numerous applications, very fine meshes are required, making DNS computationally unaffordable for practical purposes. A possible way to reduce the computational cost without sacrificing accuracy is to solve for the flow average using a mesh coarser than that required by DNS and introduce a model for the effects not captured by the flow average alone. Among such alternatives to DNS, Large Eddy Simulation (LES) is one of the most widely used for practical applications in science and engineering. We will discuss an LES appraoch that applies a differential nonlinear low-pass filter to the (non-physical) solution computed with the fluid dynamics model and a coarse mesh. Since the nonlinear filter is added sequentially to the fluid dynamics model, the implementation of this LES model does not require any major modification of a legacy solver. Through applications to the incompressible Navier-Stokes equations, weakly compressible Euler equations, and the quasi-geostrophic equations, we will demostrate the efficacy and efficiency of our LES approach.

Wednesday, 17:30-18:30,

Biosciences 1101 (Aud)

Plenary: Ram Murty

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17:30-18:30

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The Math Behind the Chat(GPT)

M. Ram Murty

(Queen's University)
## Abstract

We present an informal outline of how ChatGPT works and describe the underlying mathematical concepts behind it. For instance, graph theory, vector calculus, linear algebra, Markov models, and probabilistic inference are all used in a fundamental way. The talk will not be too technical and is suitable for a general audience.

Thursday, 8:30-9:15,

Biosciences 1101 (Aud)

Plenary: Marta Lewicka

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8:30-9:15

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The Monge-Ampere system and the isometric immersion system: convex integration in arbitrary dimension and codimension

Marta Lewicka

(University of Pittsburgh)
## Abstract

The Monge-Ampere equation $\det\nabla^2 v =f$ posed on a $d=2$ dimensional domain $\omega$ and in which we are seeking a scalar (i.e. dimension $k=1$) field $v$, has a natural weak formulation that appears as the constraint condition in the $\Gamma$-limit of the dimensionally reduced non-Euclidean elastic energies. This formulation reads:
\[\frac{1}{2}(\nabla v\otimes \nabla v) + \text{sym}\nabla w= - (\text{curl} \, \text{curl})^{-1}f \]
and it allows, via the Nash-Kuiper scheme of convex integration, for constructing multiple solutions that are dense in $C^0(\omega)$, at the regularity $C^{1,\alpha}$ for any $\alpha \lt 1/3$, no matter the sign of the right hand side function $f$.
Does a similar result hold in higher dimensions $d \gt 2$ and codimensions $k \gt 1$? Indeed, it does, but one has to replace the Monge-Ampere equation by the Monge-Ampere system that we hereby propose, by altering $\text{curl} \, \text{curl}$ to the corresponding operator which arises from the prescribed Riemann curvature problem, similarly to how the prescribed Gaussian curvature problem leads to the Monge-Ampere equation in $2d$.
Our main general result is a proof of flexibility of the Monge-Ampere system at $C^{1,\alpha}$ for $\alpha \lt 1/(1+d(d+1)/k)$ for arbitrary $d$ and $k$, and at $C^{1,1}$ when $k\geq d(d+1)$. We will also discuss other improvements and parallel results and techniques valid both for the Monge-Ampere system and for the isometric immersion system.

Thursday, 10:00-12:00,

Chernoff Hall 117

Contributed Session IV

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10:00-10:15

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Can smartphone apps reveal fishing pressure?

Azar Taheri Tayebi

(Brock University)
## Abstract

Anglers, through their actions and choices, can significantly impact the dynamics of fish populations. Understanding angler behaviors can play an important role in minimizing negative impacts such as disruption of fish habitats and depletion of fish populations. Collecting angler behavior by traditional surveys can be very costly. An alternative innovative method is using citizen-reported data from online platforms.
Correlations were found between these citizen-reported data and the data from traditional surveys.
It is, however, unclear whether angler behaviors measured from the two sources are directly related, implying that they are neither independent nor become independent conditioned on any other ``intermediate" variables such as environmental variables. We used Bayesian networks to investigate this question for angler pressure and catch rate from aerial surveys and the MyCatch smartphone application.
To assess the uncertainty in our findings, we used Bayesian Model Averaging to estimate the probability of existence of the direct relationships.
The study provides insight into the potential use of citizen-reported data to understand angler behavior on a large scale.

10:15-10:30

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Deep learning-based wireless control systems for underwater robotic communication

Shahbad Alam

(Memorial University of Newfoundland)
## Abstract

One of the challenges for underwater robotic swarms is ensuring effective coordination among themselves by transmitting information. The conventional inertial navigation technique may accurately estimate robots' position and orientation. However, this approach does not provide precise information about the surrounding environment, which requires solving $y(t) = \int_{-\infty}^{\infty} x(t) h(t-\tau)d\tau + \epsilon(t)$ for $h(t)$ and $x(t)$ from partial measurements of $y(t)$. To solve this challenging mathematical problem, this research has proposed to combine orthogonal frequency division multiplexing with the long-short term memory neural network-based deep learning technique. Thus, an efficient wireless control system for acoustic underwater swarms has been developed. This talk will discuss the mathematical foundation behind the proposed acoustic communication methodology and present numerical simulation results for underwater robots. A case study of deep learning-based acoustic communication between underwater robots was considered. The effects of the environmental noise and that of the neural network architecture were analyzed. Results indicate that the deep learning-based solutions for underwater robots are more efficient than traditional wireless communication methods.

10:30-10:45

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Mathematical Modelling of Complete and Truncated Denitrification and Dissimilatory Nitrate Reduction to Ammonium (DNRA) in Agricultural Soils

Tamara Kostyuk

(York University)
## Abstract

We analyse mathematical models of denitrifying and DNRA bacteria utilizing nitrate oxide $(NO_x)$ and COD (acetate) as substrates. First, we consider a model implementing the Liebig's minimum principle for bacterial growth so that bacterial growth is limited by the most scarce substrate. We find this system's equilibria and analyse its possible outcomes. Then we modify this model by including two Monod terms in the bacterial growth formulation, one for each substrate, to make the model more realistic and allow each substrate's concentration influence the bacteria population's growth. We analyse this model's steady states and stability. We compare the two models and show how the changes in the model's structure affect the equilibria feasibility and stability boundaries. We show how the system outcomes depends on the initial conditions (C/N ratio and concentrations) as well as the bacterial species' characteristics. Lastly, we explore truncated reactions with the addition of a 3rd species.

10:45-11:00

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Modelling sex-specific whole-body responses to feeding and fasting

Stéphanie Abo

(University of Waterloo)
## Abstract

Men exhibit a preference for carbohydrate metabolism, whereas women tend to favor lipid metabolism. Significant sex-based differences in energy oxidation are evident across various metabolic states, including fasting and feeding. While some of these differences can be attributed to variations in body composition—such as increased fat mass in women and higher muscle mass in men—there are also inherent disparities in metabolic fluxes. For instance, women exhibit increased rates of lipolysis independent of body composition. However, there remain gaps in our understanding of how sex influences the metabolism of specific organs and how these differences manifest at the systemic level. To address some of these gaps, we developed a sex-specific, whole-body, multi-scale model of metabolism during feeding and fasting. Our model represents healthy young adults (male and female) and integrates cellular metabolism in organs with whole-body responses following various mixed meals, particularly high-carbohydrate and high-fat meals. We explored sex-related variations in metabolic responses during both the absorptive and postabsorptive phases following meals. Our model predicted that sex-related metabolic differences observed at the systemic level are driven by variations in nutrient storage and oxidation patterns in the liver, skeletal muscle, and adipose tissue. We also identified a candidate mechanism, possibly more prevalent in the female liver, where lipids are redirected toward carbohydrate metabolism to support hepatic glucose production.

11:00-11:15

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Simulation and analysis of double charge layers in an electrolyte for a Lithium-ion battery

Laura Keane

(York University)
## Abstract

Rechargeable batteries such as Lithium-ion batteries (LIBs) are becoming widespread in our society as a means of powering devices. Mathematical modelling can be a valuable tool for gaining insight into observed behaviors and in aiding battery testing as we increase our dependence on these LIBs.
Double charge layers are narrow boundary regions between the two main components of a battery: the electrode and the electrolyte. The behavior in these regions can differ from that observed in the bulk due to the reactions occurring and the transfer of ions at the interfaces. We use mathematical modelling techniques such as numerical simulation and asymptotic analysis to gain a deeper understanding of what is happening in these layers.
Historically, there has been considerably more investigation and modelling regarding liquid electrolytes and their double charge layers in comparison with the less established solid electrolyte. We consider a model for a solid electrolyte under zero charge flux equilibrium and isothermal conditions. We use an auxiliary variable to transform from a finite domain to an infinite domain to avoid numerical artifacts of near singularities and to facilitate robust numerical simulations. We use asymptotic techniques to characterize the true width of the boundary layer of the electrolyte. We find that the asymptotic matching between the different regions is non-standard, and we therefore implement a pseudo matching technique to complete our asymptotic solution.

11:15-11:30

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Towards a new combination therapy with vectored immunoprophylaxis for HIV: modeling

Qi Deng

(York University)
## Abstract

Latently infected cells are considered as a major barrier to curing Human Immunodeficiency Virus (HIV) infection. Reactivation of latently infected cells followed by killing the actively infected cells may be a potential strategy "shock and kill") to purge the latent reservoir. Based on vectored immunoprophylaxis (VIP) experiment that can elicit bNAbs, in this paper a mathematical model is formulated to explore the efficacy of "shock and kill" strategy with VIP. We derive the basic reproduction number $R_{0}$ of the model and show that $R_{0}$ completely determines the dynamics of the model: if $R_{0}$ is less than 1, the disease-free equilibrium is globally asymptotically stable; if $R_{0}$ is larger than 1, the system is uniformly persistent. Numerical simulations suggest that the "shock and kill" strategy with VIP can effectively control HIV infection while this strategy cannot eradicate the reservoir without VIP although it can alleviate the HIV infection. To model the administration of drugs and vaccine more realistically, pharmacokinetics and pulse vaccination are incorporated into the model of ordinary differential equations. The resultants are described by impulsive differential equations. The thresholds are obtained for the frequency and strength of the vaccination to eliminate the viruses. Furthermore, the most appropriate times are numerically investigated for starting a short-term latency-reversing agents (LRAs) treatment relative to ART considering the toxicity of LRAs. The results show that LRAs treatment at the beginning of ART might be a better option. These results have important implications for the design of HIV cure-related clinical trials.

11:30-11:45

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Finite-time Linear Quadratic Control of Partial Differential-Algebraic Equations

Ala' Alalabi

(University of Waterloo)
## Abstract

Controller synthesis methods for PDAEs are needed in order stabilize their dynamics and/or to achieve desired performance. One valuable technique in controller design is linear quadratic (LQ) control. Significant progress has been made to design LQ controllers for DAEs, addressing both index-1 and higher index-systems. However, research on LQ control for PDAEs is still in its early stages.
We consider finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs). The discussion is restricted to those that are radial with index-0; this corresponds to a nilpotency degree of 1. We establish the existence of a unique minimizing optimal control. A projection is used to derive a system of differential Riccati-like equation coupled with an algebraic equation, yielding the solution of the optimization problem in a feedback form. This generalizes the well-known result for PDEs to this class of PDAEs. These equations and hence the optimal control can be calculated without construction of the projected PDAE. Finally, we provide numerical simulations to illustrate application of the theoretical results.

11:45-12:00

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Periodic dynamics of a mosquito population suppression model based on Wolbachia-infected males

Yufeng Wang

(York University)
## Abstract

In this talk, we explore and study a mosquito population suppression model, consisting of two sub-models switching each other, based on Wolbachia-infected mosquitoes. Under the assumptions that the releases of Wolbachia-infected males are impulsive and periodic and the waiting period between two consecutive releases is not less than the sexually active lifespan of Wolbachia-infected males, we give a fairly complete description of the periodic dynamics of the model including the nonexistence of periodic solutions and the existence of a unique periodic solution and exact two periodic solutions. We also analyze the asymptotic stability of each periodic solution and each constant equilibrium in detail. Finally, some numerical examples are provided to illustrate our theoretical results.

Thursday, 10:00-12:00,

Chernoff Hall 211

Recent Progress on the Intersections of Nonlinear Dynamics, Control, Learning, and Optimization

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10:00-10:30

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Estimator design using Jordan-based long short term memory networks

Kirsten Morris

(University of Waterloo)
## Abstract

Estimation of a dynamical system refers to estimating the state of the system given an imperfect model, noisy measurements and, possibly, some information about the initial state. While Kalman filtering is optimal for estimation of linear systems with Gaussian noise, calculation of optimal estimators for high-order nonlinear systems of ordinary differential equations is challenging. A common method is to linearize the system at each step and use a Kalman filter for the linearization; this is known as an Extended Kalman Filter (EKF). However, this approach is not optimal and is not always even stable. Several researchers have proposed alternative methods by using feed-forward and recurrent neural networks. We focus on establishing a pathway to optimal methods for state estimation of high-order systems by using recurrent connections motivated by Jordan recurrent neural networks(JRNs). We train a long short term network based on Jordan structure for state estimation of systems with Gaussian noise on the model and measurements. We compare it to the corresponding Elman structure based long-short term memory network(ELSTM) and the Kalman filter(KF) for linear systems and EKF for nonlinear systems for several examples of discretized systems of ordinary differential equations. The results suggest that the use of long-short term memory networks can improve estimation error and also computation time as compared to an EKF for nonlinear systems. We also notice that Jordan based long-short-term memory networks(JLSTMs) train faster than ELSTMs to reach a similar performance. This is work with Avneet Kaur, University of Waterloo.

10:30-11:00

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Pole Placement and Feedback Stabilization for Linear Ensemble Systems

Xudong Chen

(Washington University in St. Louis)
## Abstract

We consider discrete ensembles of linear, scalar control systems with single-inputs. Assuming that all the individual systems are unstable, we investigate whether there exist linear feedback control laws that can asymptotically stabilize the ensemble system. We provide necessary/sufficient conditions for feasibility of pole placement in the left half plane and for feedback stabilizability of the ensemble systems.

11:00-11:30

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Turnpike phenomena in pest management models

Roberto Guglielmi

(University of Waterloo)
## Abstract

We investigate the occurrence of turnpike phenomena in optimal control problems describing optimal pest management strategies by means of the Sterile Insect Technique (SIT).
With this aim, we develop new sufficient conditions for the turnpike behavior based on the connection between the hyperbolicity of the optimality system derived from Pontryagin's Maximum Principle and the turnpike property of finite horizon optimal control problems.

11:30-12:00

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Physics-Informed Characterization and Control of Stability for Nonlinear Systems

Yiming Meng

(University of Illinois Urbana-Champaign)
## Abstract

Stability analysis of nonlinear dynamical systems is crucial in many fields, where understanding the domain of attraction for an asymptotically stable equilibrium point helps determine if systems can stabilize after experiencing faults. Since Lyapunov's landmark paper more than a hundred years ago, Lyapunov functions have been key in nonlinear stability analysis, and extensive research has been conducted on constructing Lyapunov functions through computational methods.
In this research series, we systematically investigate the use of physics-informed neural networks to compute Lyapunov functions, encoding the Lyapunov conditions into the Zubov partial differential equation (PDE) for training neural networks. We demonstrate that using the Zubov equation can closely approximate regions of attraction to their true domains. We also examine approximation errors and the convergence to Zubov’s unique viscosity solution, then provide verifiable conditions for neural Lyapunov functions using satisfiability modulo theories (SMT) solvers for formal verification. The results demonstrate that this computational tool surpasses traditional sums-of-squares (SOS) methods that employ semidefinite programming (SDP).
Furthermore, we expand the tool's functionalities to support the formulation and solving of optimal control problems for control-affine systems using physics-informed neural network policy iteration (PINN-PI). We outline the methodology that enables the learning and verification of PINN for optimal stabilization tasks. Demonstrating with classical control examples, we show that the learned optimal controller significantly improves performance and provides verifiable regions of attraction, especially in high-dimensional nonlinear systems.
Lastly, we address the scenario of unknown systems by proposing a lifting approach that maps observable data into an infinite-dimensional function space, thus generating a flow governed by the proposed `Zubov-Koopman' operators. By learning such an operator over a fixed time interval, we can indirectly approximate the solution to Zubov’s equation through iterative applications of the learned operator on the identity function. Our physics-informed algorithm, underpinned by a comprehensive investigation of the regularities of Zubov-Koopman operators and their associated quantities, demonstrates strong convergence to the true operator, reduces the amount of required data, and yields desirable estimation results.

Thursday, 10:00-12:00,

Chernoff Hall 213

Learning and control for robotics systems

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10:00-10:30

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Adaptformer: Sequence Models as Adaptive Iterative Planners

Yash Vardhan Pant

(University of Waterloo)
## Abstract

Despite recent advances in learning-based behavioral planning for autonomous systems, decision-making in multi-task missions remains a challenging problem. For instance, a mission might require a robot to explore an unknown environment, locate the goals, and navigate to them, even if there are obstacles along the way. Such behavioral planning problems are difficult to solve due to: a) sparse rewards, meaning a reward signal is available only once all the tasks in a mission have been satisfied, and b) the agent having to perform tasks at run-time that are not covered in the training data (demonstrations), e.g., demonstrations only from an environment where all doors were unlocked.
Consequently, state-of-the-art decision-making methods in such settings are limited to missions where the required tasks are well-represented in the training demonstrations and can be solved within a short (temporal) planning horizon.
To overcome these limitations, we propose AdaptFormer, a stochastic and adaptive planner that utilizes sequence models for sample-efficient exploration and exploitation. This framework relies on learning an energy-based heuristic, which needs to be minimized over a sequence of high-level decisions. To generate successful action sequences for long-horizon missions, AdaptFormer aims to achieve shorter sub-goals, which are proposed through an intrinsic (learned) sub-goal curriculum.
Through these two key components, our method allows for generalization to out-of-distribution tasks and environments, i.e., missions that were not a part of the training data. Empirical results in multiple simulation environments demonstrate the effectiveness of our method. Notably, it not only outperforms the state-of-the-art method by up to $25\%$ in multi-goal maze reachability tasks, but it also successfully adapts to multi-task missions that the state-of-the-art method could not complete while leveraging only demonstrations (for training) on single-goal-reaching tasks.

10:30-11:00

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Beyond Prediction: What’s Next in Model Predictive Control for Resilient Aerial Autonomy?

Melissa Greeff

(Queens University)
## Abstract

The speed and agility of aerial robots make them ideally suited to efficient search-and-rescue missions, aid in disaster-relief scenarios, allow for efficient deliveries, and facilitate mobility-on-demand services. However, achieving resilient long-term aerial autonomy in less structured, changing environments and in safety-critical interactions is still an open challenge. This talk focuses on our latest research in learning-based model predictive control for resilient aerial autonomy. We argue that what is learned and how the model is used are both application and system-dependent. We demonstrate this through three applications: 1) vision-based GPS-denied flight, 2) cooperative landing of aerial vehicles on surface vessels, and 3) resource-constrained agile flight. In each application, we learn a different relevant model capturing limitations of the system, environment changes, or dynamic disturbances. We highlight how each model can be exploited to make predictions that enable more resilient autonomy.

11:00-11:30

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Exploring Bipedal Walking: Insights from Human Motion

Yue Hu

(University of Waterloo)
## Abstract

Bipedal walking in humanoid robots can be a complex challenge, while humans have mastered walking for a variety of challenging conditions. However, the differences in mechanical designs between humans and robots are significant. In this presentation, we will begin by examining the subtleties of human walking, focusing especially on its compliance characteristics, and discuss how these can be applied to humanoid robotics. We will then explore how the core principles of human motion could be translated to humanoid robots through the use of optimal control strategies, employing both simplified and comprehensive body models.

11:30-12:00

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Optimization-based feedback control of learned robot tasks

Gennaro Notomista

(University of Waterloo)
## Abstract

This talk presents an optimization-based formulation for the execution of learned robot tasks. The considered robot tasks are encoded by value functions approximated using the reinforcement learning paradigm. These value functions are then used to define constraints of a convex optimization program by using control Lyapunov functions. The interdependence relation between different robot tasks is enforced during the learning process and leveraged to prove convergence of the task execution. The proposed approach is showcased on a team of mobile robots executing coordinated tasks.

Thursday, 10:00-12:00,

Chernoff Hall 250 (Aud)

Financial Mathematics

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10:00-10:30

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Hilbert Space-Valued LQ Mean Field Games: An Infinite-Dimensional Analysis

Dena Firoozi

(HEC Montreal)
## Abstract

In this talk we present a comprehensive study of Hilbert space-valued Linear-Quadrati (LQ) mean field games (MFGs), generalizing the classic LQG mean field game theory to scenarios where the state equations are driven by infinite-dimensional stochastic equations. In this framework, state and control processes take values in separable Hilbert spaces. Moreover, the state equations involve infinite dimensional noises, namely Q-Wiener processes. All agents are coupled through the average state of the population appearing in their linear dynamics and quadratic cost functional. In addition, the diffusion coefficient of each agent involves the state, control, and the average state processes. We first discuss the well-posedness of a system of coupled infinite-dimensional stochastic evolution equations, which forms the foundation of MFGs in Hilbert spaces. Next, we present the Nash Certainty Equivalence principle and obtain a unique Nash equilibrium for the limiting Hilbert space-valued MFG. Finally, we establish the $\epsilon$-Nash property for the finite-player game in Hilbert space.

10:30-11:00

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Modelling spot and option-on-futures prices of the EU carbon allowance

Rogemar Mamon

(The University of Western Ontario)
## Abstract

This research work investigates the behaviour of the spot price of carbon emission allowance in the European Union Emissions Trading Scheme (EU ETS). Motivated by the volatility clustering phenomenon, we embed a regime-switching mechanism into four stochastic models governed by a hidden Markov chain, which enables time-dependent parametrisation. We examine the pricing of European-style futures call options under the proposed modelling setups. The models are assessed by comparing the pricing errors using Bloomberg's call option data on EUA futures. The proposed regime-switching geometric Brownian motion is deemed as the best-fitting model amongst the alternatives developed in this study. This is a joint work with Y Chen (Scotiabank), F Spagnolo (Brunel London U and U of Messina) and N Spagnolo (Brunel London U and Australian National U).

11:00-11:30

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Mathematical Modelling of the Accumulation Phase

Adam Metzler

(Wilfrid Laurier University)
## Abstract

We develop a framework for modelling wealth accumulation during the accumulation phase of the retirement planning process. We illustrate how the framework can be used to compare and contrast a wide variety of savings and investment plans, and how it can be used to critically evaluate conventional wisdom and popular rules of thumb. Much of the existing mathematical literature on the accumulation phase focuses on the identification of optimal savings/investment policies. By contrast, the focus here is the development of tools that can generate insights into the complex relationship between risk and return at long time horizons, and communicate those insights to non-expert audiences.

11:30-12:00

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Dichotomy for Levy-type dividends and capital problems

Alexandre Roch

(UQAM)
## Abstract

I will present solutions to optimal dividends and capital injection problems in which the cash flows of the firm is driven by a Levy process. I consider both the general (singular) case and the case in which dividends are constrained to be absolutely continuous with an upper bound as a function of the current firm process. In both situations, the capital injection process is general and shown to be only optimal when capital is injected at 0. Using viscosity techniques, I show that there exists a threshold above which the firm pays dividends at the maximal rate. In the Brownian case, I present a dichotomy result in which it is either optimal to inject capital at 0, or not at all. This is determined by the boundary condition of the HJB variational inequality. In the general Levy case, the boundary condition depends on whether the Levy process has unbounded variation or not. In all cases, there exists a lower threshold at which it is no longer optimal to inject capital.

Thursday, 10:00-12:00,

Stirling Hall 301D (Aud)

25th Canadian Symposium on Fluid Dynamics

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10:00-10:30

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Periodic motions of a harmonic oscillator in a Newtonian fluid

Giusy Mazzone

(Queen's University)
## Abstract

We consider the periodic motions of a harmonic oscillator (consisting of a mass-spring system) and a fluid occupying an infinite three-dimensional channel. The fluid flow is governed by the Navier-Stokes equations subject to a prescribed time-periodic flow rate. External time-periodic body forces (with the same period as the flow rate) may also be applied on the fluid and on the mass. Physical intuition could suggest that, under a prescribed time-periodic flow rate and time-periodic forces, the fluid would exert on the oscillator a time-periodic force having frequency matching the natural frequency of the oscillator. In this scenario, the phenomenon of resonance would occur (since the oscillator is undamped), and the generic motion of the oscillator would be characterized by oscillations with increasing amplitude. In mathematical terms, this means that no periodic motion would exist. We show that this intuition is not correct and, in fact, the fluid dissipation provides sufficient damping to guarantee the existence of periodic motions for the fluid-oscillator system, no matter what the period of the flow rate is, if the flow rate is "small". In addition, the fluid flow tends to the "generalized time-periodic Poiseuille flow" at channel inlets/outlets.

10:30-11:00

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Simulating compressible flows including energy flows

Colin Denniston

(The University of Western Ontario)
## Abstract

I will discuss a method we recently derived and implemented to simulate compressible flows including energy. The method is based on the lattice Boltzmann method including higher moments in the discretization of the velocity distribution. A Chapman-Enskog expansion maps the resulting model to the Navier-Stokes equations for fully compressible flow with energy flow. In addition to simple fluids, the method can be adapted to model liquid-gas and viscoelastic systems.

11:00-11:30

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Analytical Insights into the Rheology of mRNA-Loaded Lipid Nanodumbbells

Mona Kanso

(MIT)
## Abstract

In one important chemical engineering unit operation of messenger ribonucleic acid
(mRNA) vaccine manufacture, the precious mRNA payload is encapsulated in lipid
nanoparticles. Recent elegant cryogenic-transmission electron microscopy [Biophys J 120,
2766 (2021)] reveals these lipid nanoparticles take the form of dumbbell suspensions.
When encapsulating their mRNA payloads, these dumbbells can be both lopsided and
interpenetrating, with the smaller of the two beads carrying the payload. In this work, we
arrive at analytical expressions for these suspensions of lopsided lipid nanoparticle
dumbbells encapsulating mRNA payloads. For this, we exploit rigid dumbbell theory [Appl
Sci Res, 30, 268 (1975)], which relies on the orientation distributions of the lopsided
dumbbells to predict the suspension rheology, and specifically to predict how this departs
from Newtonian behavior. Our results include analytical expressions for the relaxation
time, rotational diffusivity, zero-shear viscosity, shear stress relaxation function, steady-shear viscosity and both the viscous part and minus the elastic part of the complex
viscosity.

Thursday, 10:00-12:00,

Stirling Hall 401

25th Canadian Symposium on Fluid Dynamics

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10:00-10:30

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Dynamics of buoyant miscible flows and instabilities in a confined medium

Soheil Akbari

(University of British Columbia)
## Abstract

The success of the cement plug placement in plug and abandonment (P&A) of oil and gas wells is governed by the interface between the cement and the in-place (usually Newtonian) fluid. In this study, we investigate buoyant miscible flows of a high-dense viscoplastic fluid placed on top of a low-dense Newtonian fluid in a vertical pipe where the fluids are separated by a gate valve before initiating the flow. We use mainly experiments, accompanied by complementary numerical simulations and semi-analytical methods, to analyze the influences of the flow and fluid parameters on the flow dynamics. The fluids are miscible, and the timescale of our experiments is adequately short so that the fluids do not mix remarkably. Upon opening the gate valve, the interface can become unstable over the initial setting time, allowing the fluids’ propagation and displacement flow. By varying the flow and fluid parameters such as rheology and density of the dense viscoplastic fluid, we observe some flow regimes. We also develop a lubrication approximation model using the Herschel-Bulkley constitutive equation in which we can classify the flow regimes versus an elegant combination of the dimensionless flow parameters. The results are in general helpful for improving the quality of the cement plug placement in P&A operations. This work is joint with S. Charabin and I. Frigaard from the University of British Columbia.

10:30-11:00

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Rayleigh-Bérnard Convection with a Robin Boundary Condition

Jason Olsthoorn

(Queen's University)
## Abstract

Rayleigh-Bénard convection is commonly modelled with a fixed surface temperature. However, the surface temperature of many geophysical systems, such as lakes, are coupled to the atmosphere. This atmosphere acts as a cooling plate but with finite conductivity. We account for this finite conductivity through the Biot number $\beta$ and show how this parameter affects the net heat transport through the system. Using an appropriately defined dynamical Rayleigh number $\hbox{Ra}_e$, we recover many of the results from the standard Rayleigh-Bénard model.
Further, we extend this model to include the nonlinear equation of state of freshwater. By including these effects, we clarify the different convective regimes in real systems.

11:00-11:30

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Numerical continuation of localized states in sheared annular electroconvection

Gregory Lewis

(Ontario Tech University)
## Abstract

We use numerical continuation methods to investigate the flows that occur in a mathematical model of the sheared annular electroconvection experiment. In particular, we study the flow of a liquid crystal film suspended between two annular electrodes, and subjected to an electric potential difference and a radial shear. Due to the Smectic A nature of the liquid crystal, the fluid can be considered two-dimensional, and its motion can be effectively modelled using the 2-D incompressible Navier-Stokes equations coupled with an equation for charge continuity. This system is a close analogue of some laboratory-scale geophysical flow experiments (e.g. the differentially-heated rotating annulus) and to simplified models of the rotating equatorial regions of planetary atmospheres and planetary interiors.
In this system, flows that resemble a rotating wave with one or more isolated vortices can be observed. Using numerical continuation based on time-integration, we investigate the bifurcation structure that connects these flows with other forms of rotating waves. In particular, a Newton-Krylov method, which exploits the rotating nature of the flows, is implemented for the continuation of these states, and linear stability analysis of a flow map is used to identify the flow transitions that result due to changes in the model parameters.
This is joint work with Stephen Morris and M.C. Pugh of University of Toronto.

11:30-12:00

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Two-dimensional Numerical Simulations of Mixing under Ice Keels

Nicolas Grisouard

(University of Toronto)
## Abstract

Changes in sea ice conditions directly impact the way the wind transfers energy to the Arctic Ocean. The thinning and increasing mobility of sea ice is expected to change the size and speed of ridges on the underside of ice floes, called ice keels, which cause turbulence and impact upper-ocean stratification. However, the effects of changing ice keel characteristics on below-ice mixing are difficult to determine from sparse observations and have not been directly investigated in numerical or laboratory experiments. Here, for the first time, we examine how the size and speed of an ice keel affect the mixing of various upper-ocean stratifications using 16 two-dimensional numerical simulations of a keel moving through a two-layer flow. We find that the irreversible ocean mixing and the characteristic depth over which mixing occurs each vary significantly across a realistic parameter space of keel sizes, keel speeds, and ocean stratifications. Furthermore, we find that mixing does not increase monotonically with ice keel depth and speed, but instead depends on the emergence and propagation of vortices and turbulence. These results suggest that changes to ice keel speed and depth may have a significant impact on below-ice mixing across the Arctic Ocean, and highlight the need for more realistic numerical simulations and observational estimates of ice keel characteristics.

Thursday, 10:00-12:00,

Stirling Hall 414

Transforming Optimization Problems: Geometric, Statistical, and Physical Perspectives

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10:00-10:30

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Optimal Conditions for Risk: Frameworks for Assessing Climate Risk in Human Systems with Environmental Coupling

Irina Babayan

(Queen's University)
## Abstract

The 2023 wildfire season gave Canadians a graphic display of ways climate change can have ruinous effects on our lives and livelihood. Despite the visibility of such extreme events, people will be affected by climate change in ways that don't dominate the news cycle. A particular area of concern is in human systems that combine interaction with the environment and optimization. Optimization underlies the operation of many social and economic systems, but as, e.g., the 2008 financial crisis showed, optimization results are strongly assumption-contingent. In this talk, we will present a degradation--loss framework for quantifying the effects of environmental degradation on optimized human systems. We will give example applications of this framework to questions related to land-use planning, and suggest ways the framework could be applied to optimization more broadly.

10:30-11:00

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Putting Matter where it Matters: High-Performance, Physics-Based Approaches to Problems in Additive Manufacturing

Aidan Sheedy

(Queen's University)
## Abstract

Additive manufacturing offers the ability to (literally) reshape our manufactured- and built environment. However, key issues, including questions about robustness, that impede the use of additive manufacturing at scale are difficult to address with conventional optimization paradigms. In this talk, we present a high-performance code that extends topology optimization, the leading paradigm for additive manufacturing design, via a novel Pareto-Laplace filter. This filter has the key property that it couples the physical behaviour of actual, physical products to analogues of physical processes that occur in the space of possible design solutions. We show that the solution space "physics" gives insight into key questions about robust design in additive manufacturing.

11:00-11:30

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When Change is the Only Certainty: Physical Approaches to Optimization Problems that are not Exactly Poseable

Pheerawich Chitnelawong

(Queen's University)
## Abstract

Optimization techniques are invaluable in a range of disciplines where precisely-posed problems capture key elements of the real-world systems in question. However, there are also real-world systems where optimal performance is desirable, but where it is not possible to precisely pose the underlying problems. One example of this is complex products where development, procurement, production, and/or deployment timescales are long compared to the timescale of design parameters prompted by, e.g., technological change. Such fundamental mismatches in the rate at which human processes evolve pose significant challenges for conventional optimization paradigms. Here, we use information theory to show that frameworks for describing the physics of information provide useful insight into inexactly-poseable optimization problems. We illustrate the application of this framework with examples from problems in naval architecture.

Thursday, 10:00-12:00,

Stirling Hall A

Infectious disease modelling for small jurisdictions

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10:00-10:30

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Age-adjusted, Activity-Based Contact Probability Model for Infectious Diseases

Lisa Kanary

(Public Health Agency of Canada)
## Abstract

Restrictions on gatherings play a crucial role in mitigating the spread of contagious illnesses. Limitations on activities were potentially implemented without clearly establishing the effectiveness of these restrictions in controlling the spread of the disease during the pandemic. A mathematical model was developed to calculate the likelihood of coming into contact with an infected person based on the prevalence rate, the activities engaged in and an age adjustment factor to account for differences between the age demographics of infected versus activity participants. Results of a sensitivity analysis indicated that the age adjustment factor was important to include when the difference in prevalence between age groups was sufficiently large, and prevalence and activity group sizes were moderate. An RShiny application, which would allow travellers to assess their likelihood of contact when visiting another location, was created to show how the model could be adopted for individuals evaluating their own behaviours in future outbreaks and pandemics.

10:30-11:00

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Modelling pathogen introductions into jurisdictions

Julien Arino

(University of Manitoba)
## Abstract

To understand the dynamics of diseases in small jurisdictions, it is important to understand the processes through which a jurisdiction of any size imports a pathogen. Indeed, developing a better sense of the conditions that lead to the initial local spread and potential establishment of a novel pathogen is a prerequisite to devising techniques to curb its spread. I will present some work considering the introduction process, mainly using stochastic models.

11:00-11:30

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Urban, suburban, rural, and isolated: the mathematics of borders and the effectiveness of travel restrictions and border controls.

James Watmough

(University of New Brunswick)
## Abstract

Roughly speaking, non pharmaceutical interventions for a contagious disease aim to slow disease spread by putting barriers to transmission between individuals or groups. Familiar interventions range from hand-washing and mask-wearing to reduce transmission between individuals, to school and workplace restrictions or closures to reduce numbers of contacts within the community, and, at the larger scale, to travel restrictions and border closures to break connections between communities and jurisdictions. Hence, understanding the effectiveness of travel restrictions and border closures requires a mathematical representation of a community in the context of disease transmission and control. Many small communities are isolated, but the degree of isolation varies widely. This can be represented mathematically with variations on compartmental multi-group, or multi-patch SIR models. Travel restrictions decrease coupling between patches. At the other extreme, many small communities are nestled in larger metropolises. Although these communities may not seem isolated from the larger metropolis, they face similar challenges to their isolated cousins. They are often underrepresented and neglected, and they may have stronger within-community connections than between community connections, leading to rapid disease spread. This can again be modelled using multi-patch SIR models with stronger coupling, or the community can be viewed as a subgraph in a larger network model. Of course, many communities fall in between two extremes of isolated and metropolitan. Most communities in New Brunswick, for example, are small rural communities, but they almost seem to blend into one another with roads and houses scattered everywhere. In this presentation I will use both the compartmental and network models to examine disease spread within and between communities and the implications for disease control.

11:30-12:00

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Strategic Timing and Resource Allocation for Optimal Isolation and Travel Restrictions in Infectious Disease Control

George Adu-Boahen

(Memorial University)
## Abstract

In response to epidemic outbreaks, health authorities implement control strategies such as travel restrictions, lockdowns, and quarantine guidelines to isolate infected individuals and curb disease spread. These strategies require the allocation of limited resources, which have impactful consequences on both social and economic activities. Given the constraints on resources, they are further influenced by disease characteristics such as infection, recovery, and incidence rates, all of which impact the best cause of action to undertake.
Here, we analyze the necessary conditions for optimal control and derive explicit solutions for minimizing the size of an outbreak. We suggest optimal strategies for a model focusing solely on isolation, one exclusively on travel restrictions, and another that combines both approaches.
The strategies proposed here have several notable elements that distinguish them from previous research. Interestingly, isolation is a more effective tool than travel restrictions, where the latter often has a negligible role in influencing epidemic trends.
Moreover, a critical factor in determining the best course of action is whether the resources are sufficient to contain the disease during the outbreak. A higher $u_{max}$, indicative of more rigorous control, can lead to a marked reduction in outbreak magnitude, demanding fewer total resources, and the reverse is also true.
Thus, decision-makers should consider the local infection rates, the trajectory of the epidemic, and the patterns of movement in and out of the region when addressing resource constraints and enacting disease control measures.

Thursday, 10:00-12:00,

Stirling Hall B

Computational Neuroscience

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10:00-10:30

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First return times for a Rayleigh process model of fluctuating brain rhythms

Andre Longtin

(University of Ottawa)
## Abstract

We consider the amplitude of a two-dimensional Ornstein-Uhlenbeck process which is governed by the Rayleigh stochastic differential equation. to cross a threshold from below or above and return to this threshold. The time spent either above or below a given threshold is known as a first-return time (FRT), and is of special interest in neuroscience to characterize brain rhythm amplitude excursions known as bursts. It also appears in the context of critical avalanche and other branching processes. The probability density of FRTs based on standard Fokker-Planck theory is non-normalizable, in contrast to the density of first passage times. We use a recently proposed technique to analytically compute the density of FRTs. It involves an expansion of the Fokker-Planck eigenfunctions along with a correction to the normalization. Our FRT densities are in good agreement with those computed from numerical realizations of the Rayleigh process over a wide range of parameters, both for trajectories above and below threshold. The theoretical expressions need to be evaluated with care in the former case due to the proximity of the roots of the Tricomi confluent hypergeometric function. The results provide analytical insight into threshold crossing statistics in neural network oscillations based e.g. on the Wilson-Cowan equations below the Hopf bifurcation. It is striking that the whole problem is governed by a single meta-parameter, namely, the ratio of noise strength to linear stability coefficient.

10:30-11:00

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Assistant Professor

Lyle Muller

(Western University)
## Abstract

Neurons in cortex are connected in intricate patterns, with local- and long-range connections and distance-dependent time delays for transmitting signals. In recent work, we have found that spontaneous and stimulus-driven waves of neural activity travel over these networks, sparsely modulating the spiking activity of the local network as they pass. The waves represent changes in the moment-by-moment activity state of these networks, which in turn directly shapes neuronal responses to incoming visual input and causes measurable effects in visual perception.
Understanding how the networks of cortex generate these sophisticated dynamics, however, remains an open problem. This is due, in part, to the fact that connecting the specific structure of networks to the resulting nonlinear dynamics is a difficult problem in general. Experiments also suggest one mechanism for these waves could be the distance-dependent time delays due to transmitting spikes along the axons connecting neurons across these networks. Analyzing the underlying network mechanism for these waves thus represents an additional mathematical challenge, as we need to consider systems with many time delays.
In this talk, I will present recent results from my group connecting the structure of individual networks to the resulting dynamics in systems of nonlinear Kuramoto oscillators. We introduce a complex-valued approach that allows linking the precise structure of connections in the network to the spatiotemporal patterns that will occur in individual simulations. This approach allows understanding these activity patterns through an analytical form related to the eigenspectrum of the graph adjacency matrix. This, in turn, leads to analytical predictions for the precise traveling wave patterns that will emerge in these systems. Finally, I will present our latest efforts to understand computation with spatiotemporal dynamics in neural systems using these nonlinear network models.

11:00-11:30

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Rapid changes in synchronizability in conductance-based neuronal networks with conductance-based coupling

Wilten Nicola

(University of Calgary)
## Abstract

Real neurons connect to each other non-randomly. These connectivity graphs can potentially impact the ability of networks to synchronize, along with the dynamics of neurons and the dynamics of their connections. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin–Huxley model or the Morris–Lecar model impacts synchronizability remains unknown. One powerful tool to resolve the synchronizability of these networks is the master stability function (MSF). Here, we apply and extend the MSF approach to networks of Morris–Lecar neurons with conductance-based coupling to determine under which parameters and for which graphs the synchronous solutions are stable. We consider connectivity graphs with a constant non-zero row sum, where the MSF approach can be readily extended to conductance-based synapses rather than the more well-studied diffusive connectivity case, which primarily applies to gap junction connectivity. In this formulation, the synchronous solution is a single, self-coupled, or “autaptic” neuron. We find that the primary determining parameter for the stability of the synchronous solution is, unsurprisingly, the reversal potential, as it largely dictates the excitatory/inhibitory potential of a synaptic connection. However, the change between “excitatory” and “inhibitory” synapses is rapid, with only a few millivolts separating stability and instability of the synchronous state for most graphs. We also find that for specific coupling strengths (as measured by the global synaptic conductance), islands of synchronizability in the MSF can emerge for inhibitory connectivity. We verified the stability of these islands by direct simulation of pairs of neurons coupled with eigenvalues in the matching spectrum.

Thursday, 10:00-12:00,

Stirling Hall C

New challenges and new faces in mathematical ecology

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10:00-10:30

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Steady states and evolution of dispersal in river networks

Olga Vasilyeva

(Memorial University of Newfoundland, Grenfell Campus)
## Abstract

Steady states of nonlinear reaction-diffusion-advection (RDA) models can be viewed as solutions of a system of two first order ODEs (subject to appropriate boundary conditions). Geometrically, they are represented by orbits in the phase plane, generated by the corresponding flow operator. In this talk, I will discuss applications of the phase plane technique in a logistic RDA model in a river network setting. Here, a steady state is represented by a configuration of orbits in the corresponding phase plane satisfying geometric constraints induced by junction and boundary conditions. While in a single river case the basic shape of the steady state is determined by the boundary conditions, in the case of a river network, it is significantly affected by the geometry of the network (lengths of the segments and their cross-section areas). In a joint work with F. Lutscher and D. Smith, we exploit this phenomenon in the context of evolution of dispersal in a Y-shaped network. Namely, we consider the possibility of invasion of a steady state of a resident species by a species with different diffusivity. It turns out that the outcome of this interaction depends on the geometry of the network as well.

10:30-11:00

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Evolutionary dynamics at the leading edge of biological invasions

Silas Poloni

(University of Victoria)
## Abstract

Novel evidence shows that space itself is a driver for rapid evolution during biological invasions. Individuals that are able to colonize new regions faster are favored, since population densities, and thus interspecific competition, tend to be small therein. These individuals’ offsprings are equally capable of spreading, and the best ones at it are further selected for at the novel leading edge. The process repeats itself through multiple generations, and leads to spatial sorting, in which phenotypes get arranged through space, from worst spreaders at the core to the best ones at the leading edge. Noteworthy, experiments for such phenomena are few, due to the large spatio-temporal scales usually involved, with famous examples being cane toads (Rhinella marina) and the common myna (Acridotheres tristis). This way, mathematical models have been developed to provide quantitative estimates of how fast populations can spread, using the classical notion of asymptotic spreading speeds, and, through trait distributions, how selection takes place at the leading edge. In this talk, we’ll go over the main concepts involved in building reaction-diffusion models for such evolutionary processes, and their main outcomes. We will also present a novel framework of analysis that can help us understand such phenomena in a simplified manner that may be applied for other classes of models.

11:00-11:30

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Evolution of Seed Masting (Or Not?)

Mahdi Salehzadeh

(Simon Fraser University)
## Abstract

Masting represents a fascinating phenomenon in the plant kingdom characterized by intermittent and synchronized reproductive efforts, such as the production of seeds. This evolutionary strategy has evolved repeatedly and is widespread in nature. While masting has been studied empirically and there exist numerous verbal theories hypothesizing what eco-evolutionary conditions should favour this phenomenon, there remains a notable absence of theoretical literature formalizing and testing these hypotheses. Here we take steps to address this gap– using formal invasion analyses. We show that the benefit and cost of seed masting are determined by the balance of two main causal mechanisms: intraspecific interactions, such as competition, and interspecific interactions, such as parasitism. While we examine only one of many possible hypothesized mechanisms favouring the evolution of masting, our results demonstrate a need for additional modelling in this area.

11:30-12:00

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The evolution of emergence times in a consumer-resource system

Abel Sarah

(University of Ottawa)
## Abstract

The ability of a consumer to access its resource depends on the relative timing (phenology) of the respective life cycles. The Match-Mismatch Hypothesis states that the optimal strategy for the consumer is to be in complete synchrony with its resource, while population dynamics models indicate that a slightly offset consumer gains higher densities in the long run. Neither approach explicitly considers the evolutionary dynamics that arise when emergence time is a heritable trait. We build a hybrid dynamical model for a consumer and its resource, each structured by the individual’s emergence time as a heritable (with mutation) trait. The active season (consumption, offspring production) is modeled by continuous differential equations, while the passive season (survival until the following year) is modeled by a discrete map. We simulate the model to explore how the mean and variance of the emergence time distribution, as well as the total population density, evolve. Depending on initial conditions, we find different outcomes such as an evolutionary arms race to increasingly early emergence times, or convergence to steady states. Our work sheds new light onto an old debate and allows us to include external factors (such as temperature) to study how climate change may affect emergence times and consumer-resource synchrony.