We study some properties of singular positive solutions to the conformally invariant equations. We prove an asymptotic blow rate estimate for positive solutions near the singular set with some conditions about the Minkowski dimension of the set.

We consider the general $f$-divergence formulation of bidirectional generative modeling, which includes VAE and BiGAN as special cases. We present a new optimization method for this formulation, where the gradient is computed using an adversarially learned discriminator.

With the two-stage fourth-order temporal evolution of the gas distribution function and Weighted Essential Non-Oscillatory (WENO) reconstruction, a high-order finite difference gas-kinetic scheme is proposed.

In random matrix theory, one of the central topics is the limiting behavior of eigenvalues and eigenvectors of random matrices under fixed-rank perturbations. A famous model, raised by Johnstone, is the so-called spiked covariance matrix model.

The polygenic risk score (PRS) derived from the genome-wide association studies (GWASs) predicts the individualized genomic predisposition to complex traits/diseases.

In this paper, the multiscale unified gas-kinetic wave-particle (UGKWP) method has been implemented on three-dimensional unstructured mesh with the capability of large-scale parallel computing.

Cryo-EM detects protein conformations froze in solution, and thus provides a promising way to characterize these conformational changes. In order to detect the conformational change, we developed a new algorithm to obtain multiple conformations and their populations from Cryo-EM datasets.

In this seminar I will talk about a provably stable architecture for Neural Ordinary Differential Equations (ODEs) which achieves non-trivial adversarial robustness under white-box adversarial attacks even when the network is trained naturally.