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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. 相似文献
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Cluster Analysis of Gene Expression Data 总被引:1,自引:0,他引:1
Eytan Domany 《Journal of statistical physics》2003,110(3-6):1117-1139
The expression levels of many thousands of genes can be measured simultaneously by DNA microarrays (chips). This novel experimental tool has revolutionized research in molecular biology and generated considerable excitement. A typical experiment uses a few tens of such chips, each dedicated to a single sample—such as tissue extracted from a particular tumor. The results of such an experiment contain several hundred thousand numbers, that come in the form of a table, of several thousand rows (one for each gene) and 50–100 columns (one for each sample). We developed a clustering methodology to mine such data. In this review I provide a very basic introduction to the subject, aimed at a physics audience with no prior knowledge of either gene expression or clustering methods. I explain what genes are, what is gene expression and how it is measured by DNA chips. Next I explain what is meant by clustering and how we analyze the massive amounts of data from such experiments, and present results obtained from analysis of data from colon cancer, brain tumors and breast cancer. 相似文献
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Unbiased samples of ground states were generated for the short-range Ising spin glass with J(ij) = +/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations." 相似文献
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Eytan Barouch 《Studies in Applied Mathematics》1977,56(2):169-185
A resonance of a magnetic impurity with a quantum spin-chain is studied. A Fresnel diffraction pattern is found. 相似文献
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Eytan G. Kopeika N. S. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1978,6(3):261-265
The rise time of a gas-filled photodiode at blue-green wavelengths is found to be less than that at red wavelengths. As photoionization of excited atoms in such devices increases response to light of decreasing wavelength over that provided by the photocathode, spectral differences in rise time are also attributed to the same mechanism. It is suggested that these phenomena decrease parasitic inductance of the tube. This implies that rise times in glow discharge detectors of EM radiation can be improved through miniaturization of inter-electrode spacing. 相似文献
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Transitions from symmetry-adapted to symmetry-broken solutions of variational problems are classified according to the nature of the discontinuity involved. Two systems in which a second-order transition occurs are studied. 相似文献