Moscow Institute of Physics and Technology (Phystech)
Faculty of Applied Mathematics and Control
1992 – Ph.D. in applied mathematics “Methods and algorithms for reconstructing the displacement field” in Samara Aerospace University
Prepared and teaches several computer courses such as Linux programming, Databases, C programming language, Python language, mathematical models in economics.
Now scientific research/interest is concerned with:
1.Mathematical models of financial crises and macroeconomic models of general equilibrium
2.Complexity of finite automata and formal languages and application to Image processing and Big Data
List of some publication
Krainiukov N.I. Samara Aerospace University
Thesis
?Methods and algorithms for reconstructing the displacement field from holographic interferometry data?
[1] Krainiukov N.I., Melnikov B.F. State markup function and basic words for finite state machines // International conference 'Modern problems of mathematics, computer science and bioinformatics' dedicated to the 100th anniversary of the birth of Aleksey Andreevich Lyapunov, Corresponding Member of the USSR Academy of Sciences
International Conference "Modern Problems of Mathematics, Informatics and Bioinformatics", devoted to the 100th anniversary of professor Alexei A. Lyapunov Novosibirsk, Russia, 2011, October 11-14
[2] Krainiukov N.I. Parallel algorithms for minimization of finite state machines for subregular languages // All-Russian scientific conference 'Modern problems of mathematical modeling of supercomputing and information technologies', Taganrog, 2012
[3] Krainiukov NI, Melnikov B.F. Osnovy system of computer algebra GAP. Methodical recommendations and laboratory practice, Togliatti 2012
[4] Krainiukov N.I. Analysis and generation of musical phrases by finite automata // First International Conference 'Mathematics, Music, Natural Science', Moscow, 2013
[5] Krainiukov N.I., Pivneva S.V. Computing the automaton complexity of Boolean functions as a discrete optimization problem. Vector of Science, TSU, 4 (22), 2012
[6] Krainiukov N.I. Minimization of finite state machines in the case of subregular languages. 'Vector of Science' TSU, no. 2 (24), 2013
[8]. Zubova T.N., Krainiukov N.I., Melnikov B.F.
On one approach to mathematical modeling of managerial impact on an organization
[8] Stanik N.A., Krainiukov N.I. Equilibrium Shifts and Shocks in Dynamic Systems, January 2020
Journal of Physics Conference Series 1441:012172
DOI:
[9] Stanik N.A., Krainiukov N.I. . January 2020
DOI:
[10] Stanik N.A., Krainiukov N.I. Approaches to assessing the short-term equilibrium of the exchange rate Financial markets and banks. 2019.No. 1.P. 55-58.
[11] Stanik N.A., Krainiukov N.I. Economic Dynamics: Estimating the Sensitivity of Economic Variables in Macroeconomic Models
Dynamics of systems, mechanisms and machines. 2019.Vol. 7.No. 4.P. 147-150.
[12] Stanik N.A., Krainiukov N.I. Methods and indicators for clustering commercial banks
Financial markets and banks. 2020. No. 1. S. 69-76.
[13] Stanik N.A., Krainiukov N.I. A Feeling of a financial apocalypse. Financial markets and banks 2021 № 3
Now scientific research is concerned with two main topics:
1 Complexity theory of non-deterministic finite automata, in particular, “flower automata” and regular languages, which are admitted by such a class of automata and сomplexity of rationa (regular)l
sets of regular languages. We study the connection between obtaining a copresentation of the submonoid M in 
with the basis C of generators and definig relations, in the case when C is not a code, and the complexity of the representation of the submonoid M in using codes (in particular, prefix codes) using the "flower" machines.
2. Mathematical models of financial crises and macroeconomic models of general equilibrium. Economic dynamics and assessment of the sensitivity of macroeconomic models to emerging shocks, which can "knock" the system out of the equilibrium position, followed by a return to another stationary state with structural changes in the dynamics of the financial and economic system.
В настоящее время научные исследования касаются двух основных тем:
1.Теория сложности недетерминированных конечных автоматов, в частности ?цветочных автоматов? и регулярных языков, которые допускаются таким классом автоматов и изучения сложности рационального (регулярного) множества регулярных языков..
Изучается связь получения копредставления подмоноида M в A^* с базисом С образующих и определяющих соотношений, том случае, когда С не является кодом и сложность представления подмоноида M в A^* с помощью кодов (в частности, префиксных кодов) с помощью ?цветочных? автоматов.
2.Математические модели финансовых кризисов и макроэкономические модели общего равновесия. Экономическая динамика и оценка чувствительности макроэкономических моделей к возникающим шокам, которое могут ?выбить? систему из положения равновесия с последующим возвращением к другому стационарному состоянию со структурным изменениям динамики финансово-экономической системы.
