Applied Math
Organizers: ryzhik [at] stanford.edu (Lenya Ryzhik) & lexing [at] stanford.edu (Lexing Ying)
For more information and access to abstracts, click here.
Past Events
In growing populations, the fate of mutations depends on their competitive ability against the ancestor and their ability to colonize new territory. I will discuss a theory that integrates both aspects fitness via a coupling between two classic reaction-diffusion equations: the KPZ equation,…
We consider the advection-diffusion equation on T^2 with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove enhanced dissipation on the timescale |logν|, where ν is the diffusivity parameter. This is the optimal decay rate as ν→0 for…
This presentation focuses on the connection between GNNs (Graph Neural Networks) and mathematical optimization. We have recently found that, by defining an LP (Linear Programming) on a specific graph, GNNs can determine the feasibility of the LP problem and solve it with any desired…
Quantum phase estimation (QPE) is of essential importance in the field of quantum computing, serving as a foundational component of many quantum algorithms. This presentation will delve into the latest advancements that have been made to enhance the efficiency and practicality of QPE. We…
Approximate message passing (AMP) is a family of iterative algorithms that are known to optimally solve many high-dimensional statistics optimization problems. In this talk, I will explain how to simulate a broad class of AMP algorithms in polynomial time using “local statistics hierarchy”…
We have deduced a weakly nonlinear, weakly dispersive Boussinesq system for water waves on a 1D branching channel, namely on a graph. The reduced model requires a compatibility condition at the graph’s node, where the main reach bifurcates into two reaches. Our new nonlinear compatibility…
The world teems with examples of invasion, in which one steady state spatially invades another. Invasion can even display a universal character: fine details recur in seemingly unrelated systems. Reaction-diffusion equations provide a mathematical framework for these phenomena. In this talk, I…
Abstract:
While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-…
For several classes of models (continuous space polymer models in
positive and zero temperature, HJB equations in dynamic environments),
we show that the shape function (also known as the effective
Lagrangian in the homogenization context) is differentiable and give a
formula for…
We present a framework of predictive modeling of unknown system from measurement data. The method is designed to discover/approximate the unknown evolution operator, i.e., flow map, behind the data. Deep neural network (DNN) is employed to construct such an approximation. Once an accurate DNN…