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Graphs are central to the chemical sciences, providing a natural language to describe molecules, proteins, reactions, and industrial processes. They capture interactions and structures that underpin materials, biology, and medicine. This…

The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…

Discrete Mathematics · Computer Science 2020-12-08 Marzieh Eidi , Amirhossein Farzam , Wilmer Leal , Areejit Samal , Jürgen Jost

Leveraging hypergraph structures to model advanced processes has gained much attention over the last few years in many areas, ranging from protein-interaction in computational biology to image retrieval using machine learning. Hypergraph…

Human-Computer Interaction · Computer Science 2021-12-07 Maximilian T. Fischer , Alexander Frings , Daniel A. Keim , Daniel Seebacher

Mapping the chemical reaction pathways and their corresponding activation barriers is a significant challenge in molecular simulation. Given the inherent complexities of 3D atomic geometries, even generating an initial guess of these paths…

Computational Physics · Physics 2025-01-24 Akihide Hayashi , So Takamoto , Ju Li , Yuta Tsuboi , Daisuke Okanohara

Deciphering the control principles of metabolism and its interaction with other cellular functions is central to biomedicine and biotechnology. Yet, understanding the efficient control of metabolic fluxes remains elusive for large-scale…

Molecular Networks · Quantitative Biology 2015-09-04 Georg Basler , Zoran Nikoloski , Abdelhalim Larhlimi , Albert-László Barabási , Yang-Yu Liu

We address a fundamental problem in chemistry known as chemical reaction product prediction. Our main insight is that the input reactant and reagent molecules can be jointly represented as a graph, and the process of generating product…

Neural and Evolutionary Computing · Computer Science 2018-12-27 Kien Do , Truyen Tran , Svetha Venkatesh

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…

Machine Learning · Computer Science 2019-05-31 Jenny Liu , Aviral Kumar , Jimmy Ba , Jamie Kiros , Kevin Swersky

In this work, we propose a general inversion framework to non-uniquely invert a very large class of ordinary differential equations (ODEs) into chemical reaction networks. A thorough treatment of the relevant chemical reaction network…

Molecular Networks · Quantitative Biology 2023-01-25 Su Hyeong Lee

We discuss chemical reaction networks and metabolic pathways based on stoichiometric network analysis, and introduce deformed toric ideal constraints by the algebraic geometrical approach. This paper concerns steady state flux of chemical…

Molecular Networks · Quantitative Biology 2013-04-24 Masamichi Sato , Kenji Fukumizu

A theory is developed which uses "networks" (directed acyclic graphs with some extra structure) as a formalism for expressions in multilinear algebra. It is shown that this formalism is valid for arbitrary PROPs (short for 'PROducts and…

Rings and Algebras · Mathematics 2012-04-12 Lars Hellström

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This…

Machine Learning · Statistics 2017-03-16 Jose Lugo-Martinez , Predrag Radivojac

The analysis of complex reaction networks is of great importance in several chemical and biochemical fields (interstellar chemistry, prebiotic chemistry, reaction mechanism, etc). In this article, we propose to simultaneously refine and…

Molecular Networks · Quantitative Biology 2008-03-11 Raphaël Plasson , Hugues Bersini , Axel Brandenburg

For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and automatedly. These…

Chemical Physics · Physics 2019-05-24 Gregor N. Simm , Alain C. Vaucher , Markus Reiher

We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…

Dynamical Systems · Mathematics 2017-11-22 Bernhard Brehm , Bernold Fiedler

We describe modeling approaches to a "network" of connected enzyme-catalyzed reactions, with added (bio)chemical processes that introduce biochemical filtering steps into the functioning of such a biocatalytic cascade. Theoretical…

Molecular Networks · Quantitative Biology 2016-12-13 Vladimir Privman

Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…

Classical Analysis and ODEs · Mathematics 2014-04-28 Inom Mirzaev , David Matthew Bortz

Generative deep learning has become pivotal in molecular design for drug discovery, materials science, and chemical engineering. A widely used paradigm is to pretrain neural networks on string representations of molecules and fine-tune them…

Machine Learning · Computer Science 2025-03-21 Jonathan Pirnay , Jan G. Rittig , Alexander B. Wolf , Martin Grohe , Jakob Burger , Alexander Mitsos , Dominik G. Grimm

Molecular "fingerprints" encoding structural information are the workhorse of cheminformatics and machine learning in drug discovery applications. However, fingerprint representations necessarily emphasize particular aspects of the…

Machine Learning · Statistics 2016-08-26 Steven Kearnes , Kevin McCloskey , Marc Berndl , Vijay Pande , Patrick Riley

A lot of progress has been made in recent times for simulating accurately the ground state energy of small molecules and their potential energy surface, using quantum-classical hybrid computing architecture. While these single point energy…

Quantum Physics · Physics 2022-10-18 Nirmal M R , Shampa Sarkar , Manoj Nambiar , Sriram Goverapet Srinivasan

We present an extension of our Molecular Transformer architecture combined with a hyper-graph exploration strategy for automatic retrosynthesis route planning without human intervention. The single-step retrosynthetic model sets a new state…