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Found 8 papers, 2 papers with code
Kinetic theories of state- and generation-dependent cell populations
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
We provide an analysis of the squared Wasserstein-2 ($W_2$) distance between two probability distributions associated with two stochastic differential equations (SDEs).
A Spectral Approach for Learning Spatiotemporal Neural Differential Equations
Rapidly developing machine learning methods has stimulated research interest in computationally reconstructing differential equations (DEs) from observational data which may provide additional insight into underlying causative mechanisms.
Overcompensation of transient and permanent death rate increases in age-structured models with cannibalistic interactions
There has been renewed interest in understanding the mathematical structure of ecological population models that lead to overcompensation, the process by which a population recovers to a higher level after suffering a permanent increase in predation or harvesting.
Spectrally Adapted Physics-Informed Neural Networks for Solving Unbounded Domain Problems
We propose a solution to such problems by combining two classes of numerical methods: (i) adaptive spectral methods and (ii) physics-informed neural networks (PINNs).
Controlling epidemics through optimal allocation of test kits and vaccine doses across networks
Efficient testing and vaccination protocols are critical aspects of epidemic management.
PDE models of adder mechanisms in cellular proliferation
Existence and uniqueness of weak solutions to our 2+1-dimensional PDE model are proved, leading to the convergence of the discretized numerical solutions and allowing us to numerically compute the dynamics of cell population densities.
How heterogeneous thymic output and homeostatic proliferation shape naive T cell receptor clone abundance distributions
Using a mean-field approximation to the solution of a regulated birth-death-immigration model and a modification arising from sampling, we systematically quantify how TCR-dependent heterogeneities in immigration and proliferation rates affect the shape of clone abundance distributions (the number of different clones that are represented by a specific number of cells, or "clone counts").
