MSc Thesis Defense

Speaker: Mahajabin Mohsin (Western)

"Restricted Horizontal Transmission Reverses the Effect of Host Mixing on Virulence Evolution"

Time: 09:30

Room: MC 204

Understanding how host mixing influences virulence evolution is important for predicting disease emergence and spread. Previous theoretical studies have shown that increased host mixing favors higher pathogen virulence, whereas vertical transmission tends to select for more prudent host exploitation. In this thesis, we investigate whether this prediction remains valid using a model with different pathogen transmission scales. Specifically, we assume that horizontal transmission occurs at a local scale within patches, while vertical transmission occurs at a global scale across the population. Our model predicts that the relationship between host mixing and virulence can be reversed when horizontal transmission is locally restricted. We propose that this reversal occurs because lower virulence allows pathogens to exploit local host populations for longer periods. Overall, our key assumptions emphasize that virulence evolution with host mixing depends not only on the pathogens' transmission mode, but also on the spatial structure of the host population.

MSc Thesis Defense

Speaker: Juhee Kim (Western)

"Recovering Permutation Groups from an Error-Prone Sampler"

Time: 13:00

Room: MC 107

This thesis studies the recovery of an unknown permutation group $G \leq S_n$ from independent observations of an error-prone sampling process that samples uniformly from $G$ with probability $1-p$, and samples uniformly from $S_n$ with probability $p$. This model is motivated by the numerical computation of monodromy groups using homotopy continuation, where path-tracking errors may result in faulty monodromy permutation computations. We study the effects of these errors under the simplifying assumption that the distribution induced by path-tracking errors is the uniform distribution on $S_n$. We first establish the fragility of the standard approach for computing $G$ and, applying results from probabilistic group theory, present our own algorithms which can reliably recover $G$ even when the error rate $p$ is high.

MSc Thesis Defense

Speaker: Aditya Rao (Western)

"Control and computation in nonlinear oscillator networks"

Time: 13:30

Room: ZOOM

Nonlinear oscillator networks are of widespread interest in physics, chemistry, biology, engineering, and machine learning. Here, we study the dynamics of nonlinear oscillator networks in two settings. First, we develop a mathematically exact method for controlling the Kuramoto-Sakaguchi model of coupled oscillator networks, capable of steering such networks to a rich variety of dynamical states, such as synchrony, desynchrony, chimera states, and phase-locked attractors of any configuration. Then, we formulate a recurrent neural network for machine learning, related to the Kuramoto-Sakaguchi model, and analyze its input-driven dynamics in terms of a spectral decomposition as the network performs an image sequence prediction task. These results contribute to the theory of nonlinear oscillator networks and to their potential for mathematically grounded applications.