The department congratulates Joseph Ingenito, Tierney Baldwin, and Michael Luo on giving their honors presentations, as follows:
Joseph Ingenito (4/21/21) – “Hysteresis in the Kuramoto Model With Inertia”
Abstract: The Kuramoto Model (KM) is a dynamical system of coupled oscillator networks that exhibits collective synchronization. Previous work has analyzed the transition from incoherence to coherence on random networks in the first order KM. However, extending this analysis to the second order KM still remains unsolved.
In this work we study the emergence of special spatial patterns called q-twisted states of the second order KM on random networks. In particular we present numerical evidence of multistability wherein both q-twisted states and incoherent states are both stable. Finally, to explain this phenomenon we present preliminary analysis connecting the dynamics to that of a damped driven pendulum.
Dr. Matthew Mizuhara served as the advisor for this project.
Tierney Baldwin (4/27/21) – “Sifting through Siphonophore Swimming: Studying Nectophore Offset Synchronizations”
Abstract: Siphonophores are among the longest organisms living in our oceans, growing up to 130 ft long. Their size makes it difficult to study them in a laboratory setting, but their fragility and the depth they live at (approximately 700-1000m below the surface) makes it hard to study them in the wild. At the head of the siphonophore are nectosomes, members of the colony whose structure is specialized to be the swimming component of the siphonophore. The nectosome propels the siphonophore forward through water; and consists of two nectophores, which are the bells that contract and expand to expel water. The nectosome can be thought of as two jellyfish bells glued together. Little is currently known about the swimming behaviors of siphonophores.
I designed a 2D model of the giant siphonophore and varied the Reynolds number (i.e. the size of the siphonophore) and the offset synchronization (i.e. whether the right and left nectophores contracted/expanded in sync or asynchronously, and if asynchronous, the length of time that one side would be delayed by). In the end, I found that variation offset synchronization has little effect on the swimming speed of the siphonophore but may have a greater effect on the cost of transport.
Dr. Nicholas Battista was the advisor for this research.
Michael Luo (4/28/21) – “Using Nonlinear Mixed Effects to Optimize a Model of Immunotherapy-Treated Murine Melanoma”
Abstract: An outstanding challenge in the clinical care of cancer is moving from a one-size-fits-all approach that relies on population-level statistics towards personalized therapeutic design. In this work, we use nonlinear mixed effects (NLME) models to personalize treatment in an ordinary differential equation model of cancer immunotherapy. We then compared the treatment response predicted by this model to that of an alternative fitting methodology.
Unexpectedly, we found that personalized optimal treatment protocols are sensitive to the fitting methodology utilized, which raises concerns about the ability of mathematical models to make reliable predictions about personalized treatment response. Despite obvious differences in predictive outcomes between the two methods, with a bit more data to inform our model, we can still use our models to make suggestions about optimal treatment protocol.
Dr. Jana Gevertz was the advisor for this research.