Potts ferromagnets on coexpressed gene networks: identifying maximally stable partitions |
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Authors: | Agrawal Himanshu Domany Eytan |
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Affiliation: | Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel. feagrawa@wicc.weizmann.ac.il |
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Abstract: | 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. |
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