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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)
Using a combination of artificial intelligence methods (e.g. machine learning, natural language processing) and legal analysis to characterize social and environmental justice issues in the transportation industry (Advisor: Amanda Stathopoulos).
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)
Nonlinear analysis and math modeling with application in astrophysics and social systems (Advisor: Daniel M. Abrams).
Dynamics of cell differentiation in the gastrulating mouse embryo (Advisor: Madhav Mani)
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).
My research is centered on machine unlearning with a focus on certifying data removal with various mathematical privacy definitions, and defining a balance of privacy interests for different parties - particularly the party requesting data removal, and the party who possesses the machine model. (Advisor: Diego Klabjan)
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)
(Advisor: Neelesh Patankar)
Nonlinear optimization of physics-based simulations (Advisor: Daniel Lecoanet)
(Advisor: David Chopp)
Modeling and analysis of single cell RNA sequencing data (Advisor: Rosemary Braun).
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).
Using modeling approaches to investigate the neural basis of learning and memory, specifically by exploring the mechanisms and properties of the olfactory system (Advisor: Hermann Riecke).
Decomposing biomedical data into components and groups for analysis. More specificly, using Bayesian statistics in order to compute the Tucker decomposition of tensors (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).
Mathematical modeling of fruit fly navigation and behaviour (Advisor: William Kath, Marco Gallio).
I develop mathematical models to understand pain crisis events in Sickle Cell Disease. The modelling approach draws from Stochastic Processes, Dynamical Systems and Machine Learning. (Advisor: 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)
(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
Samuel Halahurich
Jingkai Huang
Yiqing Penelope Jiang
Yiheng Li
Yuxuan Liang
Nhat Nam Nguyen
Ray Prasad
Alexis Robles
Rohan Rajendra
Jasmine Sirvent
Hao Wang
Yu Wang
Zichun Wei
Kimberly Williams
Zhixuan Xia
