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Titlebook: Discrete Probability Models and Methods; Probability on Graph Pierre Brémaud Textbook 2017 Springer International Publishing Switzerland 20

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Occipito-Cervical Fixation TechniquesRecall the method of the inverse in order to generate a discrete random variable . with distribution .. A crude algorithm based on this method would perform successively the tests ., ., ., until the answer is positive. Although very simple in principle, the inverse method has the following drawbacks when the size . of the state space . is large.
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Recurrence of Markov Chains,In a homogeneous Markov chain, some states are visited infinitely often while others are never visited after a finite random time. These states are naturally called recurrent and transient respectively. Among the recurrent states some have the property that the mean time between successive visits to this state is finite.
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Markov Fields on Graphs,Markov fields are also called Gibbs fields in honour of the founder of Statistical Mechanics (Gibbs, 1902). Although they were historically of special interest to physicists, they have recently found applications in other areas, in particular in image processing.
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Coding Trees,Entropy is an example of a physical concept that has found a new life in the engineering and computing sciences. This chapter concentrates on the aspects involving tree structures, namely source coding and the generation of discrete random variables from random numbers.
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