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EnglishWe introduce a method of characterizing the complexity of the minima of a given function, of N variables, by means of the entropy, S(N), of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to the (relative) measure of its basin of attraction. The behavior of S(N), for large N, gives a well defined entropy density sigma for the minima, with respect to the chosen minima-generating law. sigma characterizes the complexity of the minima in a rather natural way in the framework of information theory, i.e., the number of bits one uses to transmit one (typical) minimum configuration is similar or equal to N sigma/ln2.
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| Titolo: | Complexity of the Minimum Energy Configurations |
| Autori: | |
| Data di pubblicazione: | 1995 |
| Rivista: | |
| Abstract: | We introduce a method of characterizing the complexity of the minima of a given function, of N variables, by means of the entropy, S(N), of a measure selected as follows: One chooses an algorithm which computes the minima, and assigns to a single minimum a probability equal to the (relative) measure of its basin of attraction. The behavior of S(N), for large N, gives a well defined entropy density sigma for the minima, with respect to the chosen minima-generating law. sigma characterizes the complexity of the minima in a rather natural way in the framework of information theory, i.e., the number of bits one uses to transmit one (typical) minimum configuration is similar or equal to N sigma/ln2. |
| Handle: | http://hdl.handle.net/11581/241970 |
| Appare nelle tipologie: | Articolo |
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