TY - JOUR

T1 - State concentration exponent as a measure of quickness in Kauffman-type networks

AU - Amari, Shun Ichi

AU - Ando, Hiroyasu

AU - Toyoizumi, Taro

AU - Masuda, Naoki

PY - 2013/2/21

Y1 - 2013/2/21

N2 - We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with an alternative unified framework by using a concept termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate the dynamics of random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed in-degree distributions. As a corollary, only relatively dense majority vote networks can achieve both quickness and robustness. Published by the American Physical Society under the terms of the http://creativecommons.org/licenses/by/3.0/ Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

AB - We study the dynamics of randomly connected networks composed of binary Boolean elements and those composed of binary majority vote elements. We elucidate their differences in both sparsely and densely connected cases. The quickness of large network dynamics is usually quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with an alternative unified framework by using a concept termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate the dynamics of random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed in-degree distributions. As a corollary, only relatively dense majority vote networks can achieve both quickness and robustness. Published by the American Physical Society under the terms of the http://creativecommons.org/licenses/by/3.0/ Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

UR - http://www.scopus.com/inward/record.url?scp=84874508098&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84874508098&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.87.022814

DO - 10.1103/PhysRevE.87.022814

M3 - Article

C2 - 23496575

AN - SCOPUS:84874508098

VL - 87

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

M1 - 022814

ER -