Convergence of Phase-Field Free Energy and Boundary Force for Molecular Solvation

We study a phase-field variational model for the solvaiton of charged molecules with an implicit solvent. The solvation free-energy functional of all phase fields consists of the surface energy, solute excluded volume and solute-solvent van der Waals dispersion energy, and electrostatic free energy. The surface energy is defined by the van der Waals--Cahn--Hilliard functional with squared gradient and a double-well potential. The electrostatic part of free energy is defined through the electrostatic potential governed by the Poisson--Boltzmann equation in which the dielectric coefficient is defined through the underlying phase field. We prove the continuity of the electrostatics---its potential, free energy, and dielectric boundary force---with respect to the perturbation of dielectric boundary. We also prove the $\Gamma$-convergence of the phase-field free-energy functionals to their sharp-interface limit, and the equivalence of the convergence of total free energies to that of all individual parts of free energy. We finally prove the convergence of phase-field forces to their sharp-interface limit. Such forces are defined as the negative first variations of the free-energy functional; and arise from stress tensors. In particular, we obtain the force convergence for the van der Waals--Cahn--Hilliard functionals with minimal assumptions.Comment: 40 page

Skeleton based action recognition using translation-scale invariant image mapping and multi-scale deep cnn

This paper presents an image classification based approach for skeleton-based video action recognition problem. Firstly, A dataset independent translation-scale invariant image mapping method is proposed, which transformes the skeleton videos to colour images, named skeleton-images. Secondly, A multi-scale deep convolutional neural network (CNN) architecture is proposed which could be built and fine-tuned on the powerful pre-trained CNNs, e.g., AlexNet, VGGNet, ResNet etal.. Even though the skeleton-images are very different from natural images, the fine-tune strategy still works well. At last, we prove that our method could also work well on 2D skeleton video data. We achieve the state-of-the-art results on the popular benchmard datasets e.g. NTU RGB+D, UTD-MHAD, MSRC-12, and G3D. Especially on the largest and challenge NTU RGB+D, UTD-MHAD, and MSRC-12 dataset, our method outperforms other methods by a large margion, which proves the efficacy of the proposed method