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.

Random plane generators may use various types of the random number algorithms to create multidimensional planes. At the same time, the discrete Descartes random planes have to be uniform. The matter is that using the concept of the uncontrolled random generation may lead to a result of weak quality due to initial sequences having either insufficient uniformity or skipping of the random numbers. This article offers a new approach for creating the absolute twisting uniform two-dimensional Descartes planes based on a model of complete twisting sequences of uniform random variables without repetitions or skipping. The simulation analyses confirm that the resulted random planes have an absolute uniformity. Moreover, combining the parameters of the original complete uniform sequences allows a significant increase in the number of created planes without using additional random access memory.

The widely known generators of Poisson random variables are associated with different modifications of the algorithm based on the convergence in probability of a sequence of uniform random variables to the created stochastic number. However, in some situations, this approach yields different discrete Poisson probability distributions and skipping in the generated numbers. This article offers a new approach for creating Poisson random variables based on the complete twister generator of uniform random variables, using cumulative frequency technology. The simulation results confirm that probabilistic and frequency distributions of the obtained stochastic numbers completely coincide with the theoretical Poisson distribution. Moreover, combining this new approach with the tuning algorithm of basic twister generation allows for a significant increase in length of the created sequences without using additional RAM of the computer.

Twisting generators of the pseudorandom normal variables can use uniform random sequences as a basis. However, such technique could provide poor quality result in cases where the original sequences have insufficient uniformity or skipping of random values. This work offers a new approach for creating the random normal variables using the Box-Muller model as a basis together with the twisting generator of uniform planes. The simulation results confirm that the random variables obtained have a better approximation to normal Gaussian distribution. Moreover, combining this new approach with the tuning algorithm of basic twisting generation allows for a significantly increased the length of created sequences without using any additional random access memory of the computer.

Photomatrix therapeutic systems (PMTS) are widely used for the tasks of preventive, stimulating and rehabilitation medicine. They consist of low-intensity light-emitting diodes (LEDs) having the quasi-monochromatic irradiation properties. Depending on the LED matrix structures, PMTS are intended to be used for local and large areas of bio-objects. However, in the case of non-uniform irradiation of biological tissues, there is a risk of an inadequate physiological response to this type of exposure. The proposed approach considers a novel technique for designing this type of biomedical technical systems, which use the capabilities of stochastic algorithms for LED switching. As a result, the use of stochastic photomatrix systems based on the technology of uniform twisting generation of random variables significantly expands the possibilities of their medical application.Algorithms 2020, 13, 41 2 of 21 occurs at the molecular, cellular, tissue, organ, and systemic levels in the bio-object. The main effects of phototherapy should be considered a systemic improvement in metabolism, as well as the normalization of blood flow components, for example, blood viscosity, microcirculation and rheology parameters, immunologic responses, and secondary regenerative processes, among others [21][22][23][24][25][26][27]. As a result, expressed therapeutic effects are achieved, such as biostimulatory, anti-inflammatory, analgesic, and decongestant effects, and many others.Several typical medical PMTS are presented in Figure 1. In particular, Figure 1A shows a cylindrical apparatus for photomatrix action on extremities of hands and feet, and Figure 1B presents a semicylindrical apparatus for the integral irradiation of extended skin surfaces, such as the abdomen or back. In addition to devices for the LED exposure alone, there are also combinations with other various sources of low-intensity physiotherapy. In particular, Figure 1C shows an apparatus that combines both LED irradiation and negative low-intensity pressure for the treatment of copulative dysfunction; Figure 1D displays a photo-ultrasound tool for treating the infected and purulent-necrotic wounds, which consists of a spherical segment of PMTS and a low-frequency ultrasonic waveguide; Figure 1E demonstrates a device combining LEDs of various wavelengths and a low-intensity magnetic field to affect various systems of the human body, for example, nervous, circulatory, musculoskeletal, etc., in order to enhance metabolic processes. In addition to the rigid frames in which the LEDs are fixed, there are also many PMTS based on flexible substrates, which provide a more accurate correspondence to the reliefs of biological tissues. Therefore, Figure 1F presents a semi-flexible construction of PMTS designed for various medical tasks based on LED phototherapy. In general, over thirty different types of PMTS are presently available on the market or known as laboratory prototypes.Algorithms 2020, 13, x FOR PEER REVIEW 2 of 21