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Conditional number of synchronization-time matrix

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I was reading through this 2011 publication in journal Chaos titled "A phase-synchronization and random-matrix based approach to multichannel time-series analysis with application to epilepsy". Here is the link to the paper: www.ncbi.nlm.nih.gov/pmc/articles/PMC3172996/ I would like to make some observations on the section of "choice of diagonal elements" in this paper:

My tree planting pledge

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I donated to plant 32 trees for my birthday. This is through "Plant for the Planet" foundation supported by United Nations in their Trillion tree campaign. http://www.plant-for-the-planet.org/#!/2159/113 If everyone joins in to donate to this cause then this target is achievable. Please consider to donate.