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After the shuffling procedure we can define two distributions, the real distribution found from the actual sequence and the Maximal Entropy Distribution (MED) which we use as the surrogate for the background.
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A maximum entropy distribution signifies the decentralization of the network.
The principle of maximum entropy [26] asserts that the least biased probability distribution satisfying a set of constraints is the maximum entropy distribution, and any other distribution would be assuming information not captured by the constraints.
Maxent outputs the maximum entropy distribution that satisfies a set of environmental constraints.
Based on copulas and univariate maximum entropy margins, multivariate maximum entropy distributions are constructed.
The prior PDF of the image irradiance f E (E i ), for which we use a prior distribution of maximal entropy since little information about the image irradiance is known: the exponential distribution.
For similar reason for encoding protein sequences, in order to cope with changing environments, organisms have to use a mechanism that can generate any distribution, including equal distribution, to reduce the maximal entropy to 0. This kind of mechanism provides flexibility for organisms to change the quantities of certain proteins any time to adapt the environments.
In the maximal entropy principle, assuming stationarity, one looks for the probability distribution which maximizes the statistical entropy given those constraints.
As it is well known from Statistical Mechanics, the exponential distribution (1) can be derived from the Maximal Entropy Principle under some minimal assumptions [20].
From the equation, it is clear that if a signal containing N different points is maximally dispersed (all points being different) then the distribution is a flat horizontal line with a maximal entropy of log2 N.
Those conclusions where obtained using the maximal entropy principle[14].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com