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Maximal entropy random walk (MERW) is a popular type of biased random walk on a graph, in which transition probabilities are chosen accordingly to the principle of maximum entropy, which says that the probability distribution which best represents the current state of knowledge is the one with largest entropy.
The principle of maximum caliber (MaxCal) or maximum path entropy principle, suggested by E. T. Jaynes, [1] can be considered as a generalization of the principle of maximum entropy. It postulates that the most unbiased probability distribution of paths is the one that maximizes their Shannon entropy. This entropy of paths is sometimes called ...
Any random graph model (at a fixed set of parameter values) results in a probability distribution on graphs, and those that are maximum entropy within the considered class of distributions have the special property of being maximally unbiased null models for network inference [2] (e.g. biological network inference).
An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock ...
4.2×10 −1: Probability of being dealt only one pair in poker 5.0×10 −1: Chance of getting a 'head' in a coin toss. Physically less than 0.5; approximately 4.9983×10 −1 for US nickel accounting for 1.67×10 −4 (1-in-6000 chance) of coin landing on its edge. [21] Probability of being dealt no pair in poker 10 0: 1×10 0: Certain
Maximum entropy; Soft configuration ... and ask for the probability P that there is a path from the top ... 1 − 2p 3 − 2p 4 − 2p 5 − 7p 6 + 18p 7 + 11p 8 − ...
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Claude Shannon. The Shannon number, named after the American mathematician Claude Shannon, is a conservative lower bound of the game-tree complexity of chess of 10 120, based on an average of about 10 3 possibilities for a pair of moves consisting of a move for White followed by a move for Black, and a typical game lasting about 40 such pairs of moves.