In recent years, we have witnessed a widespread application of machine learning
techniques in the field of materials science, owing to the increased availability of research …

Although deep learning approaches have had tremendous success in image, video and
audio processing, computer vision, and speech recognition, their applications to three …

A suitable feature representation that can both preserve the data intrinsic information and
reduce data complexity and dimensionality is key to the performance of machine learning …

This work introduces a number of algebraic topology approaches, including multi-
component persistent homology, multi-level persistent homology, and electrostatic …

Proteins are the most important biomolecules for living organisms. The understanding of
protein structure, function, dynamics, and transport is one of the most challenging tasks in …

Topological data analysis (TDA) is an emerging mathematical concept for characterizing
shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful …

Advanced mathematics, such as multiscale weighted colored subgraph and element specific
persistent homology, and machine learning including deep neural networks were integrated …

This handbook provides an up-to-date compendium of fundamental computer science
topics, techniques, and applications. Along with updating and revising many of the existing …

Lipid bilayers play a fundamental role in many biological processes, and a considerable
effort has been invested in understanding their behavior and the mechanism of topological …

We present the performances of our mathematical deep learning (MathDL) models for D3R
Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free …