Critical network cascades with re-excitable nodes: Why treelike approximations usually work, when they break down, and how to correct them

Physical Review. E
Sarthak ChandraMichelle Girvan

Abstract

Network science is a rapidly expanding field, with a large and growing body of work on network-based dynamical processes. Most theoretical results in this area rely on the so-called locally treelike approximation. This is, however, usually an "uncontrolled" approximation, in the sense that the magnitudes of the error are typically unknown, although numerical results show that this error is often surprisingly small. In this paper we place this approximation on more rigorous footing by calculating the magnitude of deviations away from tree-based theories in the context of discrete-time critical network cascades with re-excitable nodes. We discuss the conditions under which tree-like approximations give good results for calculating network criticality, and also explain the reasons for deviation from this approximation, in terms of the density of certain kinds of network motifs. Using this understanding, we derive results for network criticality that apply to general networks that explicitly do not satisfy the locally treelike approximation. In particular, we focus on the biparallel motif, the smallest motif relevant to the failure of a tree-based theory in this context, and we derive the corrections due to such motifs on the condi...Continue Reading

References

Aug 10, 2000·Nature·R AlbertA L Barabasi
Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·C Moore, M E Newman
Jan 3, 2001·Physical Review Letters·D S CallawayD J Watts
Mar 22, 2001·Nature·S H Strogatz
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R Pastor-Satorras, A Vespignani
Sep 26, 2001·Proceedings. Biological Sciences·R V Solé, J M Montoya
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R M May, A L Lloyd
Nov 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Marián Boguñá, Romualdo Pastor-Satorras
Jan 7, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Adilson E Motter, Ying-Cheng Lai
Aug 2, 2007·Journal of Mathematical Biology·Erik Volz
Mar 21, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vladimir R V Assis, Mauro Copelli
Oct 2, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Joel C Miller
Dec 17, 2009·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Woodrow L ShewDietmar Plenz
Mar 24, 2010·Journal of Mathematical Biology·Joel C Miller
Sep 28, 2010·Physical Review Letters·Roni ParshaniShlomo Havlin
Jan 7, 2011·The Journal of Neuroscience : the Official Journal of the Society for Neuroscience·Woodrow L ShewDietmar Plenz
Mar 17, 2011·Physical Review Letters·Daniel B LarremoreJuan G Restrepo
Apr 27, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Sergey MelnikJames P Gleeson
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·José Luis Iribarren, Esteban Moro
Sep 26, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Daniel B LarremoreJuan G Restrepo
Feb 4, 2014·PloS One·Jeff AlstottDietmar Plenz
Apr 15, 2016·Physical Review. E·Filippo Radicchi, Claudio Castellano

❮ Previous
Next ❯

Citations

Apr 15, 2021·Journal of the Royal Society, Interface·Brandon AlexanderMichelle Girvan

❮ Previous
Next ❯

Related Concepts

Trending Feeds

COVID-19

Coronaviruses encompass a large family of viruses that cause the common cold as well as more serious diseases, such as the ongoing outbreak of coronavirus disease 2019 (COVID-19; formally known as 2019-nCoV). Coronaviruses can spread from animals to humans; symptoms include fever, cough, shortness of breath, and breathing difficulties; in more severe cases, infection can lead to death. This feed covers recent research on COVID-19.

Blastomycosis

Blastomycosis fungal infections spread through inhaling Blastomyces dermatitidis spores. Discover the latest research on blastomycosis fungal infections here.

Nuclear Pore Complex in ALS/FTD

Alterations in nucleocytoplasmic transport, controlled by the nuclear pore complex, may be involved in the pathomechanism underlying multiple neurodegenerative diseases including Amyotrophic Lateral Sclerosis and Frontotemporal Dementia. Here is the latest research on the nuclear pore complex in ALS and FTD.

Applications of Molecular Barcoding

The concept of molecular barcoding is that each original DNA or RNA molecule is attached to a unique sequence barcode. Sequence reads having different barcodes represent different original molecules, while sequence reads having the same barcode are results of PCR duplication from one original molecule. Discover the latest research on molecular barcoding here.

Chronic Fatigue Syndrome

Chronic fatigue syndrome is a disease characterized by unexplained disabling fatigue; the pathology of which is incompletely understood. Discover the latest research on chronic fatigue syndrome here.

Evolution of Pluripotency

Pluripotency refers to the ability of a cell to develop into three primary germ cell layers of the embryo. This feed focuses on the mechanisms that underlie the evolution of pluripotency. Here is the latest research.

Position Effect Variegation

Position Effect Variagation occurs when a gene is inactivated due to its positioning near heterochromatic regions within a chromosome. Discover the latest research on Position Effect Variagation here.

STING Receptor Agonists

Stimulator of IFN genes (STING) are a group of transmembrane proteins that are involved in the induction of type I interferon that is important in the innate immune response. The stimulation of STING has been an active area of research in the treatment of cancer and infectious diseases. Here is the latest research on STING receptor agonists.

Microbicide

Microbicides are products that can be applied to vaginal or rectal mucosal surfaces with the goal of preventing, or at least significantly reducing, the transmission of sexually transmitted infections. Here is the latest research on microbicides.