Raoul R. Nigmatullin
In this presentation the author wants to prove that a trendless sequence (TLS) can be used as an additional source of information. This additional information can be extracted from random noise with the help of 3D-DGIs (discrete geometrical invariants) method that allows to reduce 3N random data points to 13 parameters composed from the combination of integer moments and their intercorrelations up to the fourth order inclusive. Actually, they form a “universal” 13-feature space for comparison of one random sequence with another one. Comparison of these parameters associated with different noise tracks allows to use this set of parameters for calibration and other purposes associated with “standard”/reference equipment. As an example, we considered chemical data taken from different laboratories. This “nano-noise” is associated with random fluctuations generated by available equipment. The new mathematical expressions proposed in this presentation allows to reduce information and then to find a few key parameters that enable to differentiate the given noise and compare one set of measurements expressed in the form of rectangle matrix with another one.
The ideas of information extraction in random fluctuations and search the hidden deterministic components are the logic continuation of the methods collected recently in the book
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