By Professor Dr. Igor Grabec, Professor Dr. Wolfgang Sachse (auth.)
The digital processing of data allows the development of clever platforms able to accomplishing a synergy of self reliant size, the modeling of average legislation, the regulate of tactics, and the prediction or forecasting of a giant number of typical phenomena. during this monograph, a statistical description of normal phenomena is used to strengthen a knowledge processing procedure in a position to modeling non-linear relationships among sensory facts. The method, according to self-organized, optimum upkeep of empirical details, applies those relationships for prediction and adaptive control.
This monograph is written for college kids, scientists and engineers in academia and who're drawn to experimental paintings on the topic of the adaptive modeling of ordinary legislation, the improvement of sensory-neural networks, clever keep watch over, synergetics and informatics. No particular wisdom of complex arithmetic is presupposed. Examples taken from physics, engineering, medication and economics display the applicability of such clever systems.
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For this purpose, we first perform a set of simultaneous measurements to determine the mass and the size of a number of specimens. Let us assume that the experiments have been carried out on solids in the form of a cube with sides whose dimensions are denoted by a and expressed in units of [cm1. 1 and they represent a set of sample values. The measurements of the mass m of each specimen is listed in the second row of the table. It is evident that the quantity of the mass corresponds to the value of three times a 3 • This observation can be mathematically expressed by the relation .
In actuality, this occurs by transmitting the fundamental building blocks, represented by DNA and RNA molecules, or genetic code from generation to generation. The survival and reproduction of optimally adapted beings in the process of selection has given significance to the information represented by the structure of DNA and RNA molecules and the corresponding genetic code. [17] The complete process of selection and preservation of information about an optimal structure has proceeded from simple organic compounds to the organisms living today by continuation of species as an entity.
The application of mathematical relations for the description of natural laws leads to an interesting possibility. Let us consider again the example of 30 2. A Quantitative Description of Nature the relationship between the volume and mass of an object which has been estimated from a finite number of observations. From a mathematical point of view, there is no difficulty in considering negative values of the variable V or magnitudes of it which, say, are only a few nuclear dimensions or which exceed the size of the galaxy.