4 papers
Degenerate constants in degree inequalities for Sobolev circle maps: on some problems posed by Brezis
Xu'an Dou, Zeyu Jin
We sharpen the constants in two degree inequalities for circle-valued Sobolev maps in degenerate regimes, as or . The two proofs use the same power trick tog…
Numerical analysis for leaky-integrate-fire networks under Euler-Maruyama
Xu'an Dou, Frank Chen, Kevin K Lin +1
Leaky integrate-and-fire (LIF) networks are standard reduced models for spike-based neural dynamics and a natural substrate for neuromorphic computation. We study time-driven Euler…
Resolving the Blow-Up: A Time-Dilated Numerical Framework for Multiple Firing Events in Mean-Field Neuronal Networks
Xu'an Dou, Louis Tao, Zhe Xue +1
In large-scale excitatory neuronal networks, rapid synchronization manifests as {multiple firing events (MFEs)}, mathematically characterized by a finite-time blow-up of the neuron…
On partial diffusion and mixing without hypoellipticity
Xu'an Dou, Delphine Salort, Didier Smets
A simple Markov process is considered involving a diffusion in one direction and a transport in a transverse direction. Quantitative mixing rate estimates are obtained with limited…