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We propose a measure of compactness of a letter (symbol) or group of letters in a symbolic sequence showing how compact the appearance of the letter is in the sequence. The compactness of data with different nature (deterministic-chaotic and/or stochastic) is computed and is compared with the compactness of an ideal random sequence. We also discuss some applications of the compactness in dealing with...
Using Takens's theorem we show that any pair of uni-directionally coupled dynamical systems can be synchronised via almost all scalar observations of the driving system's state. Moreover, the values of the scalar observation at only a finite number of times are sufficient for synchronisation purposes.
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