%0 Journal Article %1 Tamm2014Islands %A Tamm, M. . V. %A Shkarin, A. . B. %A Avetisov, V. . A. %A Valba, O. . V. %A Nechaev, S. . K. %D 2014 %J Physical Review Letters %K hamiltonian\_models, motifs biological-networks er-networks %N 9 %R 10.1103/PhysRevLett.113.095701 %T Islands of Stability in Motif Distributions of Random Networks %U http://dx.doi.org/10.1103/PhysRevLett.113.095701 %V 113 %X We consider random non-directed networks subject to dynamics conserving vertex degrees and study analytically and numerically equilibrium three-vertex motif distributions in the presence of an external field, \$h\$, coupled to one of the motifs. For small \$h\$ the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger \$h\$ a transition into some trapped motif state occurs in Erd\Hos-Rényi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a non-zero cubic term. A localization transition should always occur if the entropy function is non-convex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks.

@article{Tamm2014Islands, abstract = {We consider random non-directed networks subject to dynamics conserving vertex degrees and study analytically and numerically equilibrium three-vertex motif distributions in the presence of an external field, \$h\$, coupled to one of the motifs. For small \$h\$ the numerics is well described by the "chemical kinetics" for the concentrations of motifs based on the law of mass action. For larger \$h\$ a transition into some trapped motif state occurs in Erd\H{o}s-R\'enyi networks. We explain the existence of the transition by employing the notion of the entropy of the motif distribution and describe it in terms of a phenomenological Landau-type theory with a non-zero cubic term. A localization transition should always occur if the entropy function is non-convex. We conjecture that this phenomenon is the origin of the motifs' pattern formation in real evolutionary networks.}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Tamm, M. . V. and Shkarin, A. . B. and Avetisov, V. . A. and Valba, O. . V. and Nechaev, S. . K.}, biburl = {https://www.bibsonomy.org/bibtex/23b100acdb84f5b469b2646d6712a1937/nonancourt}, citeulike-article-id = {12457587}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevLett.113.095701}, citeulike-linkout-1 = {http://arxiv.org/abs/1307.0113}, citeulike-linkout-2 = {http://arxiv.org/pdf/1307.0113}, day = 26, doi = {10.1103/PhysRevLett.113.095701}, eprint = {1307.0113}, interhash = {1e7744ca3b3c28d93b080195cb497cdb}, intrahash = {3b100acdb84f5b469b2646d6712a1937}, issn = {1079-7114}, journal = {Physical Review Letters}, keywords = {hamiltonian\_models, motifs biological-networks er-networks}, month = aug, number = 9, posted-at = {2014-08-26 17:20:16}, priority = {2}, timestamp = {2019-08-01T16:10:11.000+0200}, title = {{Islands of Stability in Motif Distributions of Random Networks}}, url = {http://dx.doi.org/10.1103/PhysRevLett.113.095701}, volume = 113, year = 2014 }