Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network

Abstract Unravelling underlying complex structures from limited resolution measurements is a known problem arising in many scientific disciplines. We study a stochastic dynamical model with a multiplicative noise. It consists of a stochastic differential equation living on a graph, similar to approa...

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Autores principales:	Inbar Seroussi, Nir Sochen
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Moment Lyapunov Exponent Limited Measurement Resolution Lattice Topology Vertex Function Transient Graph Medicine R Science Q
Acceso en línea:	https://doaj.org/article/362737978fec4c1a93282d3fb5e1d5c4
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spelling	oai:doaj.org-article:362737978fec4c1a93282d3fb5e1d5c42021-12-02T11:40:37ZSpectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network10.1038/s41598-018-32650-52045-2322https://doaj.org/article/362737978fec4c1a93282d3fb5e1d5c42018-09-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-32650-5https://doaj.org/toc/2045-2322Abstract Unravelling underlying complex structures from limited resolution measurements is a known problem arising in many scientific disciplines. We study a stochastic dynamical model with a multiplicative noise. It consists of a stochastic differential equation living on a graph, similar to approaches used in population dynamics or directed polymers in random media. We develop a new tool for approximation of correlation functions based on spectral analysis that does not require translation invariance. This enables us to go beyond lattices and analyse general networks. We show, analytically, that this general model has different phases depending on the topology of the network. One of the main parameters which describe the network topology is the spectral dimension $$\tilde{{\boldsymbol{d}}}$$ d˜ . We show that the correlation functions depend on the spectral dimension and that only for $$\tilde{{\boldsymbol{d}}}$$ d˜ > 2 a dynamical phase transition occurs. We show by simulation how the system behaves for different network topologies, by defining and calculating the Lyapunov exponents on the graph. We present an application of this model in the context of Magnetic Resonance (MR) measurements of porous structure such as brain tissue. This model can also be interpreted as a KPZ equation on a graph.Inbar SeroussiNir SochenNature PortfolioarticleMoment Lyapunov ExponentLimited Measurement ResolutionLattice TopologyVertex FunctionTransient GraphMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-10 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Moment Lyapunov Exponent Limited Measurement Resolution Lattice Topology Vertex Function Transient Graph Medicine R Science Q
spellingShingle	Moment Lyapunov Exponent Limited Measurement Resolution Lattice Topology Vertex Function Transient Graph Medicine R Science Q Inbar Seroussi Nir Sochen Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
description	Abstract Unravelling underlying complex structures from limited resolution measurements is a known problem arising in many scientific disciplines. We study a stochastic dynamical model with a multiplicative noise. It consists of a stochastic differential equation living on a graph, similar to approaches used in population dynamics or directed polymers in random media. We develop a new tool for approximation of correlation functions based on spectral analysis that does not require translation invariance. This enables us to go beyond lattices and analyse general networks. We show, analytically, that this general model has different phases depending on the topology of the network. One of the main parameters which describe the network topology is the spectral dimension $$\tilde{{\boldsymbol{d}}}$$ d˜ . We show that the correlation functions depend on the spectral dimension and that only for $$\tilde{{\boldsymbol{d}}}$$ d˜ > 2 a dynamical phase transition occurs. We show by simulation how the system behaves for different network topologies, by defining and calculating the Lyapunov exponents on the graph. We present an application of this model in the context of Magnetic Resonance (MR) measurements of porous structure such as brain tissue. This model can also be interpreted as a KPZ equation on a graph.
format	article
author	Inbar Seroussi Nir Sochen
author_facet	Inbar Seroussi Nir Sochen
author_sort	Inbar Seroussi
title	Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
title_short	Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
title_full	Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
title_fullStr	Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
title_full_unstemmed	Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network
title_sort	spectral analysis of a non-equilibrium stochastic dynamics on a general network
publisher	Nature Portfolio
publishDate	2018
url	https://doaj.org/article/362737978fec4c1a93282d3fb5e1d5c4
work_keys_str_mv	AT inbarseroussi spectralanalysisofanonequilibriumstochasticdynamicsonageneralnetwork AT nirsochen spectralanalysisofanonequilibriumstochasticdynamicsonageneralnetwork
_version_	1718395573289091072

Spectral Analysis of a Non-Equilibrium Stochastic Dynamics on a General Network

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