33 citations · 111 across the 14 of their papers we have counts for
14 papers
Reconstructing Noisy Gene Regulation Dynamics Using Extrinsic-Noise-Driven Neural Stochastic Differential Equations
Jiancheng Zhang, Xiangting Li, Xiaolu Guo +6
Proper regulation of cell signaling and gene expression is crucial for maintaining cellular function, development, and adaptation to environmental changes. Reaction dynamics in cel…
An efficient Wasserstein-distance approach for reconstructing jump-diffusion processes using parameterized neural networks
Mingtao Xia, Xiangting Li, Qijing Shen +1
We analyze the Wasserstein distance (-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a t…
Kinetic theories of state- and generation-dependent cell populations
Mingtao Xia, Tom Chou
We formulate a general, high-dimensional kinetic theory describing the internal state (such as gene expression or protein levels) of cells in a stochastically evolving population.…
Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations
Mingtao Xia, Xiangting Li, Qijing Shen +1
We provide an analysis of the squared Wasserstein-2 () distance between two probability distributions associated with two stochastic differential equations (SDEs). Based on th…
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations
Mingtao Xia, Xiangting Li, Qijing Shen +1
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provid…
Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions
Mingtao Xia, Xiangting Li, Tom Chou
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recover…
Adaptive Hermite Spectral Methods in Unbounded Domains
Tom Chou, Sihong Shao, Mingtao Xia
Recently, new adaptive techniques were developed that greatly improved the efficiency of solving PDEs using spectral methods. These adaptive spectral techniques are especially suit…
Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
Mingtao Xia, Lucas Böttcher, Tom Chou
Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. A…
Controlling epidemics through optimal allocation of test kits and vaccine doses across networks
Mingtao Xia, Lucas Böttcher, Tom Chou
Efficient testing and vaccination protocols are critical aspects of epidemic management. To study the optimal allocation of limited testing and vaccination resources in a heterogen…
Kinetic theory for structured populations: application to stochastic sizer-timer models of cell proliferation
Mingtao Xia, Tom Chou
We derive the full kinetic equations describing the evolution of the probability density distribution for a structured population such as cells distributed according to their ages…
A frequency-dependent -adaptive technique for spectral methods
Mingtao Xia, Sihong Shao, Tom Chou
When using spectral methods, a question arises as how to determine the expansion order, especially for time-dependent problems in which emerging oscillations may require adjusting…
Efficient Scaling and Moving Techniques for Spectral Methods in Unbounded Domains
Mingtao Xia, Sihong Shao, Tom Chou
When using Laguerre and Hermite spectral methods to numerically solve PDEs in unbounded domains, the number of collocation points assigned inside the region of interest is often in…
Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them
Lucas Böttcher, Mingtao Xia, Tom Chou
Different ways of calculating mortality ratios during epidemics have yielded very different results, particularly during the current COVID-19 pandemic. We formulate both a survival…
PDE models of adder mechanisms in cellular proliferation
Mingtao Xia, Chris D. Greenman, Tom Chou
Cell division is a process that involves many biochemical steps and complex biophysical mechanisms. To simplify the understanding of what triggers cell division, three basic models…