Pretraining molecular representation models without labels is fundamental to various applications. Conventional methods mainly process 2D graphs and focus solely on tasks, making their pretrained incapable of characterizing 3D geometry thus defective for downstream tasks. In this work, we tackle pretraining in a complete novel sense. particular, first propose adopt an equivariant energy-based m...

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

A graphic language—the graphic κ calculus—modeling protein interactions at the domain level is introduced. Complexation, activation and mixed forms of interaction are expressed as graph rewriting rules. A compilation in a low-level graph rewriting calculus, called mobile κ, is given and shown to be correct up to some suitable notion of observational equivalence. This intermediate language is of...

The generation of molecular graphs by computer programs has undergone some changes. The development is reported with focus on various mathematical methods that are created and employed in this process. No attempt has been made to explicitely state and prove the theorems but this overview contains hints to the relevant literature. In particular, a new generator MOLGEN 4.0 is described that aims ...

The development of a recently proposed method for calculating molecular properties is outlined. The approach is based on the idea of constructing optimized compound samples for structure-property or structure-activity correlations by means of the so-cailed comparability graphs (CG) of isomeric compounds. A dynamic comparability principle is devised, proceeding from a series of standard molecula...