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Identifying transition rates of ionic channels of star-graph branch type

We consider how to determine all transition rates of an ionic channel when it can be conformationally described by a star-graph branch Markov chain with continuous time. It is found that all transition rates are uniquely determined by the distributions of their lifetime and death-time at the end state of each branch. An algorithm to exactly calculate all transition rates is developed. Numerical examples are included to demonstrate the application of our approach to data.