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haviors or strategies. When both players are present. each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to Zero. We obtain general, analytical results for n-st

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—• 76 Figure 5 no breast cancer 9900 These frequencies, namely those that really foster insight, deserve a special name. We decided to call them Markov frequencies because of the natural analogy with Markov chains. In fact: 1) Our tree consists of two chains which are joined at the root. 2) Each n

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ase the problem can be reduced to computing absorption probabilities in Marken, chains, where each state represent the number of mutants. Hence the Markov chain Ls linear in the number of vertices of the graphs, and since absorption probabilities in Markov chains can be computed in polynomial time (by

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given time [35]. Then we can use the fixation probabilities, or their large N asymptotic values [5, 155], and describe the system effectively as a Markov process on n homogeneous strategy states. This description, however, can lead to very different conditions for arbitrary selection and for weak sele

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omplicated pro- cesses. Before computers, no languages were good for that. Piaget tried algebra and Freud tried dia- grams; other psychologists used Markov chains and matrices, but none came to much. Behaviorists, quite properly, had ceased to speak at all. Linguists flocked to formal syntax, and made

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obability matrix, M;p, called a Markov matrix named for one of the two great Russian mathematicians, both students of Pafnuti Lvovich Chebyshev, the Markov brothers. The entries of each row in the MM; are transformed into transition 108 HOUSE_OVERSIGHT_013608 probabilities, so that the sum of the deci

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d in discrete conductance events with a small set of characteristic open and closed times. The distributions of each of could be fitted with its own, Markov process derived, exponential. With technical advances and improved temporal resolution, more characteristic times and their associated a = 2 exponent