4.0 Article

Geometry and symmetry in biochemical reaction systems

Related references

Note: Only part of the references are listed.
Article Mathematics

Spectral theory of Laplace operators on oriented hypergraphs

Raffaella Mulas et al.

Summary: This paper demonstrates several new spectral properties of the normalized Laplacian for oriented hypergraphs, such as discussions on eigenvalue 1, duplicate vertices, and introduction of new quantities for bounding eigenvalues. Additionally, the Cheeger constant is generalized, classical Cheeger bounds are extended for certain classes of hypergraphs, and it is shown that a geometric quantity can lower-bound the largest eigenvalue, along with generalizing the notion of coloring number for proving a Hoffman-like bound. Finally, the spectrum of the unnormalized Laplacian for Cartesian products of hypergraphs is explored.

DISCRETE MATHEMATICS (2021)

Article Mathematics

Sharp Bounds for the Largest Eigenvalue

R. Mulas

Summary: The classical sharp bounds for the largest eigenvalue of the normalized Laplace operator have been generalized to the case of chemical hypergraphs, where N/(N - 1) <= lambda(N) <= 2.

MATHEMATICAL NOTES (2021)

Article Physics, Multidisciplinary

Exploiting symmetry in network analysis

Ruben J. Sanchez-Garcia

COMMUNICATIONS PHYSICS (2020)

Article Physics, Fluids & Plasmas

Coupled dynamics on hypergraphs: Master stability of steady states and synchronization

Raffaella Mulas et al.

PHYSICAL REVIEW E (2020)

Article Mathematics

Hypergraph Laplace operators for chemical reaction networks

Juergen Jost et al.

ADVANCES IN MATHEMATICS (2019)

Article Mathematics, Applied

Symmetry induced group consensus

Isaac Klickstein et al.

CHAOS (2019)

Article Mathematics, Applied

Spectra of cycle and path families of oriented hypergraphs

Luke Duttweiler et al.

LINEAR ALGEBRA AND ITS APPLICATIONS (2019)

Article Mathematics, Applied

A characterization of oriented hypergraphic Laplacian and adjacency matrix coefficients

Gina Chen et al.

LINEAR ALGEBRA AND ITS APPLICATIONS (2018)

Article Biochemistry & Molecular Biology

The STRING database in 2017: quality-controlled protein-protein association networks, made broadly accessible

Damian Szklarczyk et al.

NUCLEIC ACIDS RESEARCH (2017)

Article Mathematics, Applied

A characterization of oriented hypergraphic balance via signed weak walks

Vinciane Chen et al.

LINEAR ALGEBRA AND ITS APPLICATIONS (2015)

Article Mathematics

Spectral properties of oriented hypergraphs

Nathan Reff

Electronic Journal of Linear Algebra (2015)

Review Biotechnology & Applied Microbiology

Signaling hypergraphs

Anna Ritz et al.

TRENDS IN BIOTECHNOLOGY (2014)

Article Multidisciplinary Sciences

Cluster synchronization and isolated desynchronization in complex networks with symmetries

Louis M. Pecora et al.

NATURE COMMUNICATIONS (2014)

Article Mathematics

Spectra of combinatorial Laplace operators on simplicial complexes

Danijela Horak et al.

ADVANCES IN MATHEMATICS (2013)

Article Mathematics, Applied

An oriented hypergraphic approach to algebraic graph theory

Nathan Reff et al.

LINEAR ALGEBRA AND ITS APPLICATIONS (2012)

Article Mathematics, Applied

Graph spectra as a systematic tool in computational biology

Anirban Banerjee et al.

DISCRETE APPLIED MATHEMATICS (2009)

Article Physics, Fluids & Plasmas

Spectral characteristics of network redundancy

Ben D. MacArthur et al.

PHYSICAL REVIEW E (2009)

Article Biochemical Research Methods

Hypergraphs and Cellular Networks

Steffen Klamt et al.

PLOS COMPUTATIONAL BIOLOGY (2009)

Article Mathematics, Applied

Symmetry in complex networks

Ben D. MacArthur et al.

DISCRETE APPLIED MATHEMATICS (2008)

Review Cell Biology

Graph theory and networks in Biology

O. Mason et al.

IET SYSTEMS BIOLOGY (2007)

Article Physics, Mathematical

Complex networks: From graph theory to biology

Annick Lesne

LETTERS IN MATHEMATICAL PHYSICS (2006)

Article Physics, Multidisciplinary

Subgraph centrality and clustering in complex hyper-networks

E Estrada et al.

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS (2006)

Review Mathematics, Applied

The structure and function of complex networks

MEJ Newman

SIAM REVIEW (2003)

Article Biochemistry & Molecular Biology

Real-time PCR-based method for the estimation of genome sizes

J Wilhelm et al.

NUCLEIC ACIDS RESEARCH (2003)

Article Biochemistry & Molecular Biology

BIND: the Biomolecular Interaction Network Database

GD Bader et al.

NUCLEIC ACIDS RESEARCH (2003)

Article Multidisciplinary Sciences

Network motifs: Simple building blocks of complex networks

R Milo et al.

SCIENCE (2002)

Article Biochemistry & Molecular Biology

The KEGG databases at GenomeNet

M Kanehisa et al.

NUCLEIC ACIDS RESEARCH (2002)

Article Biochemistry & Molecular Biology

BIND - The Biomolecular Interaction Network Database

GD Bader et al.

NUCLEIC ACIDS RESEARCH (2001)