Towards an algebra for cascade effects
Name
1506.06394.pdf
Description
Published version
Size
335.31 KB
Format
Adobe PDF
Checksum (MD5)
a3c5871c50e06a4281eb4963191e5f43
Author(s)
Adam, Elie M
Dahleh, Munther A
Ozdaglar, Asuman E
Date Issued
July 2017
Journal
Logical Methods in Computer Science
Publisher
Saarbrücken : Int. Fed. of Computational Logic
Citation
Adam, Elie M. et al. "Towards an algebra for cascade effects." Logical Methods in Computer Science 13, 3 (July 2017): 1-31 © The Authors
Version
Final published version
Abstract
We introduce a new class of (dynamical) systems that inherently capture cascading effects (viewed as consequential effects) and are naturally amenable to combinations. We develop an axiomatic general theory around those systems, and guide the endeavor towards an understanding of cascading failure. The theory evolves as an interplay of lattices and fixed points, and its results may be instantiated to commonly studied models of cascade effects. We characterize the systems through their fixed points, and equip them with two operators. We uncover properties of the operators, and express global systems through combinations of local systems. We enhance the theory with a notion of failure, and understand the class of shocks inducing a system to failure. We develop a notion of μ-rank to capture the energy of a system, and understand the minimal amount of effort required to fail a system, termed resilience. We deduce a dual notion of fragility and show that the combination of systems sets a limit on the amount of fragility inherited.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution NonCommercial License 4.0
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.23638/LMCS-13(3:1)2017
