Potts ferromagnets on coexpressed gene networks: identifying maximally stable partitions.
Clustering gene expression data by exploiting phase transitions in granular ferromagnets requires transforming the data to a granular substrate. We present a method using the recently introduced homogeneity order parameter Lambda [H. Agrawal, Phys. Rev. Lett. 89, 268702 (2002)]] for optimizing the parameter controlling the "granularity" and thus the stability of partitions. The model substrates obtained for gene expression data have a highly granular structure. We explore properties of phase transition in high q ferromagnetic Potts models on these substrates and show that the maximum of the width of superparamagnetic domain, corresponding to maximally stable partitions, coincides with the minimum of Lambda.
Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel. feagrawa@wicc.weizmann.ac.il
Himanshu
H
Agrawal
Eytan
E
Domany
D003110:Colonic Neoplasms / Q000235:genetics; D015870:Gene Expression; D006801:Humans; D008957:Models, Genetic; D005810:Multigene Family