Russian Mathematicians Discover Universal Approach to Analyzing 'Memory Processes'
Scientists have proposed a new mathematical approach to the analysis and forecasting of complex systems to improve the quality and simplify the modeling of a huge number of processes in science, telecommunications and industry.
A scientific team from Russia's Samara University has created a new mathematical apparatus to describe long-term memory processes, which may revolutionize robotics and nuclear reactor processes, among others.
According to the authors, the discovery can significantly refine the models used to calculate physicochemical, electromagnetic, and mechanical processes in many areas of modern technology and science.
Fundamental laws similar to physical laws cannot be found in all fields of science and technology, scientists explained. Mathematical statistics can identify dependencies that are not fundamental laws, but allow the modeling of real systems and processes with great accuracy.
According to specialists, the most difficult part is identifying patterns in the case of so-called long-term memory processes, in which long-standing events have a strong influence on current developments. These include, for example, computer network traffic or the charge-discharge process of a supercapacitor.
"Mathematical identification of a system involves creating a model based on a huge amount of data. Our approach to identification based on a model with fractional-order derivatives allows us to obtain more accurate results with a much smaller data set," Dmitry Ivanov, associate professor at the SNRU’s Department of Information Systems Security, said.
The scientific team primarily intends to use the results to improve the efficiency of computer security systems, as well as to improve the controllability of asynchronous motors, the experts noted.
The scientists also claimed that the use of the new model would be in demand for the calculation of processes in nuclear reactors, the design of new polymers, and a wide range of other problems in the chemical industry, as well as in mechatronics, and robotics. The results of their study were published in the Mathematics
In the future, researchers at Samara University intend to develop a set of new process optimization algorithms based on the proposed mathematical model and implement them in methods for solving various engineering problems.
The work was carried out with the participation of specialists from the University of Gabes and the University of Sfax (Tunisia). The research was conducted within the framework of the Moscow Technical University of Communications and Informatics (MTUCI) grant on information security. Samara University is a member of the "Priority 2030" program of the Ministry of Education and Science of the Russian Federation.