Graph spectral characterization of the XY model on complex networks

Paul Expert, Sarah De Nigris, Taro Takaguchi, Renaud Lambiotte

Résultats de recherche: Contribution à un journal/une revueArticle

Résumé

There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

langueAnglais
Numéro d'article012312
journalPhysical Review E
Volume96
Numéro1
Les DOIs
étatPublié - 11 juil. 2017

Empreinte digitale

XY Model
Complex Networks
Graph in graph theory
Time series
Spin Models
Signature
Decompose
Class
signatures
decomposition
Signal Analysis
Spectral Decomposition
Power Spectrum
Nonlinear Dynamics
Activation
Transform
Model-based
Topology
Interaction
Evidence

Citer ceci

@article{b1fc32aafd5843cfa127717805f3038d,
title = "Graph spectral characterization of the XY model on complex networks",
abstract = "There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.",
author = "Paul Expert and {De Nigris}, Sarah and Taro Takaguchi and Renaud Lambiotte",
year = "2017",
month = "7",
day = "11",
doi = "10.1103/PhysRevE.96.012312",
language = "English",
volume = "96",
journal = "Physical Review E",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

Graph spectral characterization of the XY model on complex networks. / Expert, Paul; De Nigris, Sarah; Takaguchi, Taro; Lambiotte, Renaud.

Dans: Physical Review E, Vol 96, Numéro 1, 012312, 11.07.2017.

Résultats de recherche: Contribution à un journal/une revueArticle

TY - JOUR

T1 - Graph spectral characterization of the XY model on complex networks

AU - Expert,Paul

AU - De Nigris,Sarah

AU - Takaguchi,Taro

AU - Lambiotte,Renaud

PY - 2017/7/11

Y1 - 2017/7/11

N2 - There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

AB - There is recent evidence that the XY spin model on complex networks can display three different macroscopic states in response to the topology of the network underpinning the interactions of the spins. In this work we present a way to characterize the macroscopic states of the XY spin model based on the spectral decomposition of time series using topological information about the underlying networks. We use three different classes of networks to generate time series of the spins for the three possible macroscopic states. We then use the temporal Graph Signal Transform technique to decompose the time series of the spins on the eigenbasis of the Laplacian. From this decomposition, we produce spatial power spectra, which summarize the activation of structural modes by the nonlinear dynamics, and thus coherent patterns of activity of the spins. These signatures of the macroscopic states are independent of the underlying network class and can thus be used as robust signatures for the macroscopic states. This work opens avenues to analyze and characterize dynamics on complex networks using temporal Graph Signal Analysis.

UR - http://www.scopus.com/inward/record.url?scp=85026435468&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.012312

DO - 10.1103/PhysRevE.96.012312

M3 - Article

VL - 96

JO - Physical Review E

T2 - Physical Review E

JF - Physical Review E

SN - 1539-3755

IS - 1

M1 - 012312

ER -