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PhD Students
Parameter identifiability and estimation for rate-based models of synaptic plasticity (Advisor: James Fitzgerald).
Using an overset grid scheme to study the dynamics of particles confined to fluid interfaces. (Advisors: David Chopp and Michael Miksis)
Developing experimental design methods to address identifiability issues in sparse model selection (SINDy) as applied to synthetic biological systems (Advisor: Niall Mangan).
Modeling firing responses of Drosophila thermosensory neurons based on gene expression profiles (Advisors: William Kath and Marco Gallio)
Mathematical modeling of active particles confined within droplets in the Stokes flow regime (Advisor: Petia Vlahovska).
Design of computer simulations with probability and applied analysis (Advisor: Chang-Han Rhee).
Community structure of single cell RNA sequencing data. (Advisor: Rosemary Braun)
Evan Gibbs
Nonlinear analysis and math modeling with application in astrophysics and social systems (Advisor: Daniel M. Abrams).
Numerical methods for simulating astrophysical and geophysical systems (Advisor: Daniel Lecoanet)
Microbiome organization and adaptation. (Advisor: Madhav Mani)
Using dynamical systems, mathematical modeling, and data analysis to understand how individual decisions and interactions give rise to collective social patterns, with applications to scientific collaboration, conversation dynamics, and occupational mobility. (Advisor: Daniel Abrams)
I work on machine learning applications in health care and autonomous parking. I recently completed a project on implementation and application of Monte Carlo Tree Search (MCTS) to feature acquisition with focus on medical diagnosis application. I am currently working on development and implementation of federated MCTS with application to autonomous parking (Advisor: Diego Klabjan).
Mathematical modelling of tissue deformation appearing in the esophageal diseases using continuum mechanics theories, dynamical systems theory and numerical simulations. (Advisor: Neelesh Patankar).
Techniques for interpretability and measuring model similarity in deep learning (Advisor: Luís Amaral)
Statistical modelling of biological systems from sequence data, focusing on machine learning and maximum entropy models. (Advisor: Rosemary Braun)
Designing and analyzing gradient algorithms with applications to reinforcement learning, machine unlearning, and low-rank training. (Advisor: Diego Klabjan)
Mathematical modeling and analysis of dynamical systems that couple mechanics, neurology, and biochemistry to study the function (and dysfunction) of organ systems, primarily the esophagus and the left ventricle (Advisor: Neelesh A. Patankar).
Mathematical modeling, asymptotic analysis, and numerical simulation of nutrient-limited biofilm growth on agar with moving interfaces (Advisor: David Chopp).
Designing computer vision models and algorithms to detect, locate, and specify degraded tissue states in medical imaging of the urethra. Mapping gene expression and modeling physical behavior to understand underlying mechanics in different esophageal disease phenotypes (Advisor: Neelesh Patankar).
Algorithms for machine learning (Advisor: Diego Klabjan).
Mathematical modeling of firefly (P. malaccae) synchronization built on a framework of nonlinear dynamics and coupled oscillators. Developing computer vision algorithms for tracking the identities and flashing patterns of individual fireflies in a swarm (Advisor: Daniel Abrams).
Investigating the dynamics of nonlinear systems with an emphasis on population dynamics (Advisors: Alvin Bayliss and Vladimir Volpert).
Numerical modeling using high performance computing of astrophysical systems like black holes and space plasma (Advisor: Sasha Tchekhovskoy).
Modeling social media interactions with rewiring networks and data-driven geometric discovery of dynamical systems phase portraits (Advisors: Cristián Huepe and Daniel Abrams).
Mathematical modeling of wastewater networks for uncertainty quantification. (Advisors: Niall Mangan, Aaron Packman)
I work on high-dimensional statistical learning and generative modeling, focusing on how complex and multimodal data from multiple sources can be represented through a shared low-dimensional latent space. (Advisor: Naichen Shi)
Lauren Yan
(1) Study the dynamics of the 1,2-PD utilization pathway (a metabolism pathway of Salmonella in human gut) and connect the mathematical analysis back to the evolutionary pressure/demand. (2) Fit Lotka-Volterra model with incomplete data (relative abundance rather than absolute abundance). Identify the non-identifiability between the models. (Advisor: Niall Mangan)
Numerical simulation and asymptotic analysis of nonlinear electrodynamics across a biomembrane. (Advisors: Petia Vlahovska and Michael Miksis)
Mathematical modeling of electrostatics of ellipsoidal and spherical particles. (Advisors: Michael Miksis and Petia Vlahovska)
MS Students
Jingzhu Dai
Yidan Feng
Zhaoyang Guan
Jingkai Huang
Yiqing Penelope Jiang
Yiheng Li
Yuxuan Liang
Nhat Nam Nguyen
Evan Parish
Ray Prasad
Rohan Rajendra
Daniel Rekoske
Jasmine Sirvent
Daniel Soto
Hao Wang
Ruixu Wang
Zichun Wei
Kimberly Williams
Zhixuan Xia
