Reactive explorers to unravel network topology

Ihusan Adam, Duccio Fanelli, Timoteo Carletti, Giacomo Innocenti

Research output: Contribution to journalArticle

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Abstract

A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Dif- ferent equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.
Original languageEnglish
JournalEuropean Physical Journal B
Volume92
Issue number99
DOIs
Publication statusPublished - 8 May 2019

Fingerprint

Relocation
Network Topology
topology
Topology
Modulation
Sampling
relocation
entry
Localized Source
Experiments
Mean-field Approximation
sampling
scalars
modulation
Control Parameter
Connectivity
Ensemble
estimates
approximation
Numerical Experiment

Keywords

  • Statistical and Nonlinear Physic
  • network reconstruction
  • Dynamical systems

Cite this

Adam, Ihusan ; Fanelli, Duccio ; Carletti, Timoteo ; Innocenti, Giacomo. / Reactive explorers to unravel network topology. In: European Physical Journal B. 2019 ; Vol. 92, No. 99.
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Reactive explorers to unravel network topology. / Adam, Ihusan; Fanelli, Duccio; Carletti, Timoteo; Innocenti, Giacomo.

In: European Physical Journal B, Vol. 92, No. 99, 08.05.2019.

Research output: Contribution to journalArticle

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AU - Innocenti, Giacomo

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AB - A procedure is developed and tested to recover the distribution of connectivity of an a priori unknown network, by sampling the dynamics of an ensemble made of reactive walkers. The relative weight between reaction and relocation is gauged by a scalar control parameter, which can be adjusted at will. Dif- ferent equilibria are attained by the system, following the externally imposed modulation, and reflecting the interplay between reaction and diffusion terms. The information gathered on the observation node is used to predict the stationary density as displayed by the system, via a direct implementation of the celebrated Heterogeneous Mean Field (HMF) approximation. This knowledge translates into a linear problem which can be solved to return the entries of the sought distribution. A variant of the model is then considered which consists in assuming a localized source where the reactive constituents are injected, at a rate that can be adjusted as a stepwise function of time. The linear problem obtained when operating in this setting allows one to recover a fair estimate of the underlying system size. Numerical experiments are carried so as to challenge the predictive ability of the theory.

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