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Introduction: molecular geometry, the three-dimensional arrangement of atoms within a molecule, is fundamental to understanding chemical reactivity, physical properties, and biological activity. The prevailing models used to describe…
A major limitation and a continuing source of confusion in the interpretation of molecular line observations has been the large degree of chemical complexity that is observed in star-forming molecular cores. The past decade has seen…
Molecule design is a fundamental problem in molecular science and has critical applications in a variety of areas, such as drug discovery, material science, etc. However, due to the large searching space, it is impossible for human experts…
According to density functional theory, any chemical property can be inferred from the electron density, making it the most informative attribute of an atomic structure. In this work, we demonstrate the use of established physical methods…
In this paper, we describe {\sc quantitative graph theory} and argue it is a new graph-theoretical branch in network science, however, with significant different features compared to classical graph theory. The main goal of quantitative…
Tensor network methods are taking a central role in modern quantum physics and beyond. They can provide an efficient approximation to certain classes of quantum states, and the associated graphical language makes it easy to describe and…
Subgraph isomorphism counting is known as #P-complete and requires exponential time to find the accurate solution. Utilizing representation learning has been shown as a promising direction to represent substructures and approximate the…
In order to define the process of restrosynthesis of a new organic molecule, it is often necessary to be able to draw inspiration from that of a molecule similar to the target one of which we know such a process. To compute such a…
In this perspective article, we present a multidisciplinary approach for characterizing protein structure networks. We first place our approach in its historical context and describe the manner in which it synthesizes concepts from quantum…
Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…
In recent years, artificial intelligence has played an important role on accelerating the whole process of drug discovery. Various of molecular representation schemes of different modals (e.g. textual sequence or graph) are developed. By…
We view molecular optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be…
We consider some problems concerning the maximum number of (strong) dominating sets in a regular graph, and their weighted analogues. Our primary tool is Shearer's entropy lemma. These techniques extend to a reasonably broad class of graph…
We present an elaborate framework for formally modelling pathways in chemical reaction networks on a mechanistic level. Networks are modelled mathematically as directed multi-hypergraphs, with vertices corresponding to molecules and…
The modern thermodynamics of discrete systems is based on graph theory, which provides both algebraic methods to define observables and a geometric intuition of their meaning and role. However, because chemical reactions are usually…
Modern computational chemistry has reached a stage at which massive exploration into chemical reaction space with unprecedented resolution with respect to the number of potentially relevant molecular structures has become possible. Various…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
Recent advances in artificial intelligence have propelled the development of innovative computational materials modeling and design techniques. Generative deep learning models have been used for molecular representation, discovery, and…
Accurately determining and classifying the structure of complex networks is the focus of much current research. One class of network of particular interest are metabolic pathways, which have previously been studied from a graph theoretical…
Chemical toxicity prediction using machine learning is important in drug development to reduce repeated animal and human testing, thus saving cost and time. It is highly recommended that the predictions of computational toxicology models…