MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • Engineering Systems Division
  • Engineering Systems Division (ESD) Working Paper Series
  • View Item
  • DSpace@MIT Home
  • Engineering Systems Division
  • Engineering Systems Division (ESD) Working Paper Series
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

A New Model Of Cascades On Random Networks With A Threshold Rule Fundamentals

Author(s)
Whitney, Daniel E.
Thumbnail
Downloadesd-wp-2009-08.pdf (537.6Kb)
Metadata
Show full item record
Abstract
Percolation or cascades on random networks are typically analyzed using generating functions. This approach requires that the network be assumed infinite and weakly connected. These assumptions are not obeyed by real or simulated networks on which this theory is often used. In this paper we offer a theory that assumes a finite network with arbitrary average nodal degree and apply it to the case where cascades follow a threshold rule, that is, that a node will change state (“flip”) only if a fraction, exceeding a given threshold, of its neighbors has changed state previously. The model is a dynamic Markov model whose state transition matrix, recalculated after each step, records the probability that a node of degree k has i flipped neighbors after j steps in the cascade’s evolution. The model reproduces a number of previously unreported behaviors observed in simulations. These include the ability to create cascades in a domain previously predicted to forbid cascades as well as a “near death” behavior in which cascades initially appear about to die but later explode. Cascades in the “no cascades” region require a sufficiently large seed of initially flipped nodes or else the cascade will die out. The model and simulations are compared with a foundational paper by Watts which used the generating function theory.
Date issued
2009-10
URI
http://hdl.handle.net/1721.1/102842
Publisher
Massachusetts Institute of Technology. Engineering Systems Division
Series/Report no.
ESD Working Papers;ESD-WP-2009-08

Collections
  • Engineering Systems Division (ESD) Working Paper Series

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.