Parametrical Tuning of Twisting Generators

Abstract

Generators of uniformly distributed random numbers are broadly applied in simulations of stochastic processes that rely on normal and other distributions. In a point of fact, the uniform random numbers are actively used for applications that range from, modeling different phenomena such as theoretical mathematics and technical designing, to evidence-based medicine. This paper proposes a novel approach which consists of a combination of global twister with circular technique and initial congruential generation with complete stochastic sequences. It has been experimentally confirmed that for complete sequences this type of generation provides uniformity in distribution of random numbers. The offered program codes include the tuning methods for the generation technique where random numbers may take any bit length. Moreover, the automatic switching of generator parameters such as initial congruential constants depending on intervals for generated numbers is considered as well. Demonstrated results of testing confirm the uniformity of distribution without any repeated or skipped generated elements.

Designing the Uniform Stochastic Photomatrix Therapeutic Systems

“…Moving further, it could be be noted that Expression (28) also has some limitations. The first of which concerns the number N. Our mathematical studies [46][47][48][49][50][51] show that uniform generation is achieved only at the condition of N = 2 w . The exponent w exactly matches the quantity of the required binary bits, which are needed for representing the decimal number N − 1.…”

“…Particularly for the current issue, i.e., in case of PMTS influence on biological tissue, this means an accurate understanding of the uniform operation of randomly turned on LEDs. The term 'uniform random variables' means that in the allotted time, all the exposure elements (LEDs or their analogues) are switched on precisely the same number of times [46][47][48][49][50][51]. Thus, it should be started with this, i.e., by checking the ability of standard tools to ensure the uniform generation of irradiation from point light sources.…”

Uniform Twister Plane Generator

“…These sequences V can be interpreted as the left circular shift (Deon and Menyaev, 2016b) of the original sequence <3, 2, 1, 0>. Figure 2 shows four tracks of an interaction of the pairs of sequences on the U and V axes.…”

“…In our previous studies (Deon and Menyaev, 2016a;2016b; there were proposed several pseudorandom number generators, particularly nsDeonYuliTwist32D, which offers a technique of using no congruential twisting array. This generator allows the creation of absolutely complete twister uniform sequences having various lengths.…”

“…Without loss of generality and in order to visualize the result, we assign the amount of discrete coordinates by given sets U = V = {0, 1, 2, 3, 4, 5, 6, 7}, which in the binary representation corresponds to the length w = 3 bits for each coordinate. According to the previous studies (Deon and Menyaev, 2016b;, let's choose a twister generator nsDeonYuliTwist32D, which operates on the basis of congruential model x i+1 = (ax i + c) &maskW with constants a = 5, c = 1. The initial values of the twisting sequences are taken here as x 0 = 1 ∈ U and x 0 = 4 ∈ V. Any other choice of parameters for generation is possible; the essence of the obtained results will not be changed.…”