RESEARCH

Ecological Dynamics in Soil Microbial Community under Environmental Change

• Constructed the ODE model for the metabolite and population dynamics in microbiome systems.
• Asymptotically solved the dynamics of the ODE model.
• Constructed the numerical method to fit the model to the time series dataset from the experiments.
• Applied machine learning methods to process the genomic sequencing dataset and perform dimension reduction.

Mathematical Models for 3D Force Inference Method in Multicellular Systems

• Constructed mathematical models of 3D geometry and mechanical balance in cellular aggregates.
• Analytically solved the inverse problem of mechanical balance in 3D multicellular systems.
• Proved a new physics theory on mechanical zero modes in 3D multicellular systems.
• Built a numerical program (in MATLAB) to infer mechanical states from 3D images of cellular aggregates.
• Implemented image analysis on 3D microscopic dataset (via ImageJ).

Eco-evolutionary Dynamics Driven by Horizontal-Gene-Transfer in Mcriobial Community

• Constructed stochastic models for genetic dynamics in eco-evolutionary system.
• Analytically solved the mean-feild solution of the model using random matrix theory.
• Performed numerical simulations (in Python) on the horizontal gene transfer phenomena.

Mathematical Models and Learning Process on Morphological Cellular Automata

• Constructed mathematical models combining graph dynamics and Cellular Automata.
• Simulated organ development by applying artificial neural networks in the Cellular Automata model.
• Applied Monte-Carlo optimization method (in Python) for the learning process to achieve size control.