Search

It was found that the distribution of users of social networks by the number of contacts, as well as the statistics of telephone conversations by duration, obtained for different cities on the basis of experimental data, obey the same laws, expressed through a differential equation of the first order. This differential equation contains two phenomenological parameters, one of which is interpreted as the fractal dimension of the communication space, and the second is directly expressed through the Dunbar number or its analogue. Essentially, for all cities under investigation the numerical value of the parameter, interpreted as the fractal dimension of the communication space, remains constant with high accuracy. At the same time, the analogue of the Dunbar number, which describes the distribution of users of social online networks by the number of contacts, correlates with the population of the city. The results obtained are discussed from the point of view of the formation of a global communication network - the noosphere, which, due to the development of telecommunication technologies, is already de facto man-machine system. It is shown that the results obtained confirm the conclusion about the existence of objective laws describing the behavior of human-machine systems, made earlier on the basis of general philosophical considerations.

An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation. [ABSTRACT FROM AUTHOR]

A new approach to ensuring information security is proposed for using in the zone of direct radio visibility. The approach is based on a direct analogy between radio and optical radiation. In the latter case, information protection can be ensured by identifying the point or direction from which the signal comes; all other light sources are cut off by the observer. It is shown that a similar method of information protection can also be implemented in the radio range, which corresponds to modern trends in the development of radio holography. The simplest scheme for detecting the direction to a transmitter, identified as "friend" is presented. Its operability is demonstrated by means of simulation modeling. Ways for the further development of this approach are determined, based on the fact that modern technologies make it possible to implement distributed reception of a radio signal (to use a relatively large number of receivers), which makes it possible to implement direct analogues of such optical elements as a lens, holograms. [ABSTRACT FROM AUTHOR]

Generalized Rademacher functions, constructed as a sequence of elements of Galois fields are intended to find the spectral representation of signals with levels. These functions form a complete basis on the interval corresponding to -1 discrete time intervals and for passing into the classical Rademacher functions. The advantage of such spectra obtained using Galois Fields Fourier Transform is that the range of variation of the spectrum amplitudes remains the same as the range of variation of the original signal, which is modeled on discrete time functions taking values in the Galois field. [ABSTRACT FROM AUTHOR]

An algorithm of digital logarithm calculation for the Galois field G F ( 257 ) is proposed. It is shown that this field is coupled with one of the most important existing standards that uses a digital representation of the signal through 256 levels. It is shown that for this case it is advisable to use the specifics of quasi-Mersenne prime numbers, representable in the form p = 2 n + 1 , which includes the number 257. For fields G F ( 2 n + 1 ) , an alternating encoding can be used, in which non-zero elements of the field are displayed through binary characters corresponding to the numbers + 1 and - 1. In such an encoding, multiplying a field element by 2 is reduced to a quasi-cyclic permutation of binary symbols (the permuted symbol changes sign). Proposed approach makes it possible to significantly simplify the design of computing devices for calculation of digital logarithm and multiplication of numbers modulo 257. A concrete scheme of a device for digital logarithm calculation in this field is presented. It is also shown that this circuit can be equipped with a universal adder modulo an arbitrary number, which makes it possible to implement any operations in the field under consideration. It is shown that proposed digital algorithm can also be used to reduce 256-valued logic operations to algebraic form. It is shown that the proposed approach is of significant interest for the development of UAV on-board computers operating as part of a group., (© 2024. The Author(s).)

An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2n+1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2n+1 to an addition operation., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Suleimenov et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)