Active phase discovery in heterogeneous catalysis via topology-guided sampling and machine learning.

Understanding active phases across interfaces, interphases, and even within the bulk under varying external conditions and environmental species is critical for advancing heterogeneous catalysis. Describing these phases through computational models faces the challenges in the generation and calculation of a vast array of atomic configurations. Here, we present a framework for the automatic and efficient exploration of active phases.

A general method for computing the Homfly polynomial of DNA double crossover 3-regular links.

In the last 20 years or so, chemists and molecular biologists have synthesized some novel DNA polyhedra. Polyhedral links were introduced to model DNA polyhedra and study topological properties of DNA polyhedra. As a very powerful invariant of oriented links, the Homfly polynomial of some of such polyhedral links with small number of crossings has been obtained.

Ear decomposition of 3-regular polyhedral links with applications.

In this paper, we introduce a notion of ear decomposition of 3-regular polyhedral links based on the ear decomposition of the 3-regular polyhedral graphs. As a result, we obtain an upper bound for the braid index of 3-regular polyhedral links. Our results may be used to characterize and analyze the structure and complexity of protein polyhedra and entanglement in biopolymers.

The braid index of complicated DNA polyhedral links.

The goal of this paper is to determine the braid index of two types of complicated DNA polyhedral links introduced by chemists and biologists in recent years. We shall study it in a more broad context and actually consider so-called Jaeger's links (more general Traldi's links) which contain, as special cases, both four types of simple polyhedral links whose braid indexes have been determined and the above two types of complicated DNA polyhedral links. Denote by b(L) and c(L) the braid index and crossing number of an oriented link L, respectively.