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Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…

Discrete Mathematics · Computer Science 2016-04-22 Christoph Flamm , Daniel Merkle , Peter F. Stadler , Uffe Thorsen

The purpose of this review is to introduce the reader to graph kernels and the corresponding literature, with an emphasis on those with direct application to chemoinformatics. Graph kernels are functions that allow for the inference of…

Machine Learning · Statistics 2022-08-29 James Young

Accurately modeling chemical reactions in molecular dynamics simulations requires detailed pre- and post-reaction templates, often created through labor-intensive manual workflows. This work introduces a Python-based algorithm that…

Computational Engineering, Finance, and Science · Computer Science 2025-07-24 Julian Konrad , Robert Meißner

The chemical concrete machine is a graph rewriting system which uses only local moves (rewrites), seen as chemical reactions involving molecules which are graphs made up by 4 trivalent nodes. It is Turing complete, therefore it might be…

Formal Languages and Automata Theory · Computer Science 2013-09-27 Marius Buliga

Based on graphic lambda calculus, we propose a program for a new model of asynchronous distributed computing, inspired from Hewitt Actor Model, as well as several investigation paths, concerning how one may graft lambda calculus and knot…

Distributed, Parallel, and Cluster Computing · Computer Science 2013-12-17 Marius Buliga , Louis H. Kauffman

Biology is perhaps the most complex of the sciences, given the incredible variety of chemical species that are interconnected in spatial and temporal pathways that are daunting to understand. Their interconnections lead to emergent…

Biological Physics · Physics 2023-09-11 Henry V. Jakubowski , Henry Agnew , Bartholomew E. Jardine , Herbert M. Sauro

We present a systematic investigation using graph neural networks (GNNs) to model organic chemical reactions. To do so, we prepared a dataset collection of four ubiquitous reactions from the organic chemistry literature. We evaluate seven…

Machine Learning · Computer Science 2020-07-10 Serim Ryou , Michael R. Maser , Alexander Y. Cui , Travis J. DeLano , Yisong Yue , Sarah E. Reisman

One approach to studying the system-wide organization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental…

Molecular Networks · Quantitative Biology 2010-08-17 Petter Holme , Mikael Huss

A nut graph is a graph on at least 2 vertices whose adjacency matrix has nullity 1 and for which non-trivial kernel vectors do not contain a zero. Chemical graphs are connected, with maximum degree at most three. We present a new algorithm…

Combinatorics · Mathematics 2017-09-14 Kris Coolsaet , Patrick W. Fowler , Jan Goedgebeur

Atomistic simulations are essential tools in chemistry and materials science, accelerating the discovery of novel catalysts, energy storage materials, and pharmaceuticals. However, running these simulations remains challenging due to the…

Chemical Physics · Physics 2025-06-11 Thang D. Pham , Aditya Tanikanti , Murat Keçeli

The graph isomorphism problem asks whether two graphs are identical up to vertex relabeling. While the exact problem admits quasi-polynomial-time classical algorithms, many applications in molecular comparison, noisy network analysis, and…

Quantum Physics · Physics 2026-03-31 Prateek P. Kulkarni

One of the main goals of Artificial Life is to research the conditions for the emergence of life, not necessarily as it is, but as it could be. Artificial Chemistries are one of the most important tools for this purpose because they provide…

Adaptation and Self-Organizing Systems · Physics 2021-12-08 Germán Kruszewski , Tomas Mikolov

Background. In the last decades, several life science resources have structured data using the same framework and made these accessible using the same query language to facilitate interoperability. Knowledge graphs have seen increased…

In this paper, the transfer matrix technique using the $k$-matching vector is developed to compute the number of $k$-matchings in an arbitrary graph which can be constructed by successive amalgamations over sets of cardinality two. This…

Combinatorics · Mathematics 2025-12-10 Simon Grad , Sandi Klavžar

We introduce MetaChem, a language for representing and implementing Artificial Chemistries. We motivate the need for modularisation and standardisation in representation of artificial chemistries. We describe a mathematical formalism for…

Emerging Technologies · Computer Science 2020-06-16 Penelope Faulkner Rainford , Angelika Sebald , Susan Stepney

The graph isomorphism (GI) problem is the computational problem of finding a permutation of vertices of a given graph $G_1$ that transforms $G_1$ to another given graph $G_2$ and preserves the adjacency. In this work, we propose a quantum…

Quantum Physics · Physics 2019-01-23 Xi Li , Hanwu Chen

Modeling molecules as undirected graphs and chemical reactions as graph rewriting operations is a natural and convenient approach tom odeling chemistry. Graph grammar rules are most naturally employed to model elementary reactions like…

Discrete Mathematics · Computer Science 2012-08-17 Jakob L. Andersen , Christoph Flamm , Daniel Merkle , Peter F. Stadler

A method which casts the chemical source term computation into an artificial neural network (ANN)-inspired form is presented. This approach is well-suited for use on emerging supercomputing platforms that rely on graphical processing units…

Chemical Physics · Physics 2021-05-11 Shivam Barwey , Venkat Raman

The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this invariant for connected chemical graphs of given order and size and characterize the…

Large language models (LLMs) are beginning to reshape how chemists plan and run reactions in organic synthesis. Trained on millions of reported transformations, these text-based models can propose synthetic routes, forecast reaction…

Artificial Intelligence · Computer Science 2025-08-08 Kartar Kumar Lohana Tharwani , Rajesh Kumar , Sumita , Numan Ahmed , Yong Tang