Three-Dimensionally Embedded Graph Convolutional Network (3DGCN) for Molecule Interpretation

We present a three-dimensional graph convolutional network (3DGCN), which predicts molecular properties and biochemical activities, based on 3D molecular graph. In the 3DGCN, graph convolution is unified with learning operations on the vector to handle the spatial information from molecular topology. The 3DGCN model exhibits significantly higher performance on various tasks compared with other deep-learning models, and has the ability of generalizing a given conformer to targeted features regardless of its rotations in the 3D space. More significantly, our model also can distinguish the 3D rotations of a molecule and predict the target value, depending upon the rotation degree, in the protein-ligand docking problem, when trained with orientation-dependent datasets. The rotation distinguishability of 3DGCN, along with rotation equivariance, provides a key milestone in the implementation of three-dimensionality to the field of deep-learning chemistry that solves challenging biochemical problems.Comment: 39 pages, 14 figures, 5 table

Information inequalities and Generalized Graph Entropies

In this article, we discuss the problem of establishing relations between information measures assessed for network structures. Two types of entropy based measures namely, the Shannon entropy and its generalization, the R\'{e}nyi entropy have been considered for this study. Our main results involve establishing formal relationship, in the form of implicit inequalities, between these two kinds of measures when defined for graphs. Further, we also state and prove inequalities connecting the classical partition-based graph entropies and the functional-based entropy measures. In addition, several explicit inequalities are derived for special classes of graphs.Comment: A preliminary version. To be submitted to a journa

CNDO/2 Study of C2H2 + H2O System

Different configurations of the C2H2 + H2O system obtained by various translations and rotations of H2O around the C2H2 molecule were studied. The two molecules were found to form not only hydrogen bond but also a charge transfer complex

Information Theory in Describing the Electronic Structures of Atoms

An information approach to the description of atoms by introducing »differential« entropy characteristics of chemical elements has been developed. These quantities clearly reflect the horizontal and vertical structure of the periodic table, and the main features of atomic electron structures, such as delay in filling d- and f-subshells, the action of Hund\u27s first rule, the anomalies in the electronic structure of some atoms, the appearance of the first electron having a given value of some quantum number, etc. The necessity of change in the position of lanthanides and actinides in the periodic table is discussed

Representations and descriptors unifying the study of molecular and bulk systems

Establishing a unified framework for describing the structures of molecular and periodic systems is a long-standing challenge in physics, chemistry, and material science. With the rise of machine learning methods in these fields, there is a growing need for such a method. This perspective aims to discuss the development and use of three promising approaches-topological, atom-density, and symmetry-based-for the prediction and rationalization of physical, chemical, and mechanical properties of atomistic systems across different scales and compositions

Integrated information increases with fitness in the evolution of animats

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.Comment: 27 pages, 8 figures, one supplementary figure. Three supplementary video files available on request. Version commensurate with published text in PLoS Comput. Bio