Deep learning systems typically suffer from catastrophic forgetting of past knowledge when
acquiring new skills continually. In this paper, we emphasize two dilemmas, representation …

Adversarial domain adaptation has made remarkable advances in learning transferable
representations for knowledge transfer across domains. While adversarial learning …

This study presents the formulation and validation of a three-dimensional Flow Lattice Model
(FLM) with application to the Hygro-Thermo-Chemical (HTC) model for analysis of moisture …

Abstract The de Rham-Hodge theory is a landmark of the 20 th Century's mathematics and
has had a great impact on mathematics, physics, computer science, and engineering. This …

We present a compendium of Hodge decompositions of vector fields on tetrahedral meshes
embedded in the 3D Euclidean space. After describing the foundations of the Hodge …

Recently, topological data analysis has become a trending topic in data science and
engineering. However, the key technique of topological data analysis, ie, persistent …

RNA velocity has the ability to capture the cell dynamic information in the biological
processes; yet, a comprehensive analysis of the cell state transitions and their associated …

3D Morphable Models are a class of generative models commonly used to model faces.
They are typically applied to ill-posed problems such as 3D reconstruction from 2D data …

We build a new probability measure on closed space and plane polygons. The key
construction is a map, given by Hausmann and Knutson, using the Hopf map on quaternions …

We provide a theoretical framework for discrete Hodge-type decomposition theorems of
piecewise constant vector fields on simplicial surfaces with boundary that is structurally …