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This Concept Map, created with IHMC CmapTools, has information related to: b9. K-S Entropy, A rate (an average rate) is any quantity divided by the time during which it applies. Hence, any computed entropy divided by the associated time gives a average entropy rate - an average entropy per unit time. ???? Thirdly, K-S entropy is a limiting value. For discrete systems or observations, two limits are involved. The entropy rate as time lengthens to infinity, and bin size (width of classes) shrinks to zero., Entropy, or information, varies depending on the distribution of probabilities. Entropy does not depend on actual values of the variable; it is just a statistic that characterizes an ensemble of probabilities. ???? Relations between information and probability also apply to entropy and probability., Relations between information and probability also apply to entropy and probability. ???? Whether the context is one of information or entropy, probabilities are the foundation or essence of it all; they are required basic data., The probabilities used in solving the equation (sequence probabilities) are the likelihood that the system will follow each of the various possible routes that finish at the chosen time. The summation then is over all the routes represented in the data (Nt). ???? Over three consecutive measurements with two possible states there are eight possible routes. For each of the eight sequence probabilities we calculate and the add up the resulting eight values. That sum is the information entropy for time 3., Shannon’s entropy (information entropy) cannot by itself identify chaos. Its value is always positive and finite, and can vary a lot, depending on the control parameter, number and size of compartments and other factors. ???? First, K-S entropy requires sequence probabilities (the probabilities that the system will follow various routes over time). K-S entropy deals with information or uncertainty associated with a time sequence of measurements or observations., Secondly, K-S entropy represents a rate. The distinctive or indicative feature about a dynamical regime is not entropy by itself but rather the entropy rate. ???? A rate (an average rate) is any quantity divided by the time during which it applies. Hence, any computed entropy divided by the associated time gives a average entropy rate - an average entropy per unit time., Sequence probabilities in chaos analysis usually are based on lagged values of a single variable. That means pseudo phase space. As with attractor reconstruction, the two aspects that we can vary are the lag itself and the number of phase space dimensions. ???? Secondly, K-S entropy represents a rate. The distinctive or indicative feature about a dynamical regime is not entropy by itself but rather the entropy rate., b9.Kolmogorov-Sinai Entropy The equations for information entropy form the basis of another type of entropy, Kolmogorov-Sinai entropy that at least theoretically can identify chaos., The equations for information entropy form the basis of another type of entropy, Kolmogorov-Sinai entropy that at least theoretically can identify chaos. ???? Shannon’s entropy (information entropy) cannot by itself identify chaos. Its value is always positive and finite, and can vary a lot, depending on the control parameter, number and size of compartments and other factors., Over three consecutive measurements with two possible states there are eight possible routes. For each of the eight sequence probabilities we calculate and the add up the resulting eight values. That sum is the information entropy for time 3. ???? Sequence probabilities in chaos analysis usually are based on lagged values of a single variable. That means pseudo phase space. As with attractor reconstruction, the two aspects that we can vary are the lag itself and the number of phase space dimensions.