THE THEORY AND ALGORITHM FOR DIAGNOSIS OF BIOLOGICAL SYSTEMS WITH AN INFINITE NUMBER
OF STATES ON THE BASIS OF APPLICABLE Q-MATRICES AND TRANSITION PROBABILITY MATRICES

Ryzhakov Viktor Vasil'evich, Doctor of technical sciences, professor, head of sub-department of technical quality control, Honoured Scientist of the Russian Federation, Penza State Technological Academy
(Penza, 1a Baydukova passage), rvv@pgta.ru
Ryzhakov Mikhail Viktorovich, Senior lecturer, sub-department of applied mechanics, head of the laboratory
of applied nanotechnologies, Moscow Institute of Physics and Technology (State University)
(Moscow Region, Dolgoprydny, 9 Institutsky Lane), mryzhakov@applmech.mipt.ru

519.21.248+57+574

Background. Biological systems (populations) of living organisms are characterized by massive population of particular territories. Under certain environmental violations there may occur corresponding violations in this community that can be used as a measure of environmental violations for their quantitative assessment.
Materials and methods. When developing the procedures for diagnosing biological systems with an infinite number of individuals and their states the peculiarities of specimen existence were taken into account according to some known publications. Therefore, the paper proposes a theory and algorithms which are based on a certain probabilistic approach. This approach uses triangular matrices with an infi-nite number of transition probabilities that allow taking into consideration an infinite number of specimens and their states. For the acquisition of probability matrix elements for system transitions from one state to another Q-matrices and known Kolmogorov equation were used.
Results. Based on the use of the transition probability matrix there were suggested algorithms and sampling control technique over the states of specimen system (population), which considers the peculiarities of using binomial and Poisson laws affecting the accuracy of control.
Conclusions. The re-sults obtained are characterized by substantial utility for practical purposes.

biological system, theory, algorithm, diagnosis, Q-matrix, transition probabilities.

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