Research

Here are some interesting projects that I have done.

Fiber Product Homotopy Method for Multiparameter Eigenvalue Problems

We develop the fiber product homotopy method for solving multiparameter eigenvalue problems (MEPs). Our method tracks several copies of the eigenvalue; they should all converge to the same value if our method performs correctly.
We show that the fiber product homotopy method theoretically finds all eigenpairs of an MEP with probability one. It is especially well-suited for dimension-deficient singular MEPs, a weakness of all other existing methods.
We show that the fiber product MEP that we solve in the fiber product homotopy method, although mathematically equivalent to a standard MEP, is typically a much better-conditioned problem.

We define a hierarchical mixture model to describe the development of cells, and give a clear definition of trajectory and pseudotime. The uncertainty of model parameters can also be quantified. Variational Inference can be applied to estimate the model parameters
We compared different metrics such as trajectory graph similarity, cluster assignment accuracy, and pseudotime correlation, with other well-known methods on both simulated and real datasets.
We apply our model to perform trajectory analysis on massive mouse brain developing datasets by integrating different data sources and adjusting for cell-cycle effects.

I constructed convolutional neural networks in TensorFlow to recognize 3755 offline isolated handwritten Chinese characters, tried different shapes of convolutional kernels to extract features, and concluded the best combination of horizontal and vertical feature-selecting kernels, which had obtained 97% accuracy.
I constructed a web app by Django and then put the model into use on the web.