Consider the linear transport equation in 1D under an external confining potential
For
This paper introduces a novel generative encoder (GE) framework for generative imaging and image processing tasks like image reconstruction, compression, denoising, inpainting, deblurring, and super-resolution. GE unifies the generative capacity of GANs and the stability of AEs in an optimization framework instead of stacking GANs and AEs into a single network or combining their loss functions as in existing literature. GE provides a novel approach to visualizing relationships between latent spaces and the data space. The GE framework is made up of a pre-training phase and a solving phase. In the former, a GAN with generator
and the image
Consider the linear transport equation in 1D under an external confining potential
For
We study the convergence rate of a continuous-time simulated annealing process
We consider optimal control of fractional in time (subdiffusive, i.e., for
We establish existence of finite energy weak solutions to the kinetic Fokker-Planck equation and the linear Landau equation near Maxwellian, in the presence of specular reflection boundary condition for general domains. Moreover, by using a method of reflection and the
In two dimensions, we consider the problem of inversion of the attenuated