On identifiability of mathematical models of evolutionary processes from data of discrete measurements of state vector

Volkov, I. K.; Zuyev, S. M.

doi:10.1515/rnam.1994.9.4.395

Cited by 3 publications

(4 citation statements)

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“…The existence of a minimum value of the sum of squares of deviations Φ(α|£7) is intuitively understandable and theoretically justified [2,4,6,[9][10][11][12]. However, in any case the question arises of whether a point of minimum is unique for the considered functional Φ(α|ί/).…”

Section: G T [X(t) -X (T A)}mentioning

confidence: 99%

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Conditions for identifiability of autonomous systems of ordinary differential equations

Volkov¹,

Zuev²

1999

Russian Journal of Numerical Analysis and Mathematical Modelling

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We consider the problem of parametric identification of mathematical models in evolutionary processes, which are a Cauchy problem for a normal autonomous system of ordinary differential equations. We propose a criterion for choosing the observable variables of a model and the number of moments of measurements, which ensures the sufficient conditions for uniqueness of the solution to the original problem. The results obtained are extended to the case in which the mathematical model has a system of stochastic differential equations.

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Section: G T [X(t) -X (T A)}mentioning

confidence: 99%

“…The generalization to the case of indirect measurements can be found in our previous publications [10,11]. Besides, it should be noted that in the subsequent discussion the observational data is interpreted as realisations of a random process for the reason that the data is measurement results [9,[10][11][12].…”

Section: G T [X(t) -X (T A)}mentioning

confidence: 99%

Conditions for identifiability of autonomous systems of ordinary differential equations

Volkov¹,

Zuev²

1999

Russian Journal of Numerical Analysis and Mathematical Modelling

Self Cite

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“…Unfortunately, the system of genetic ecological monitoring has not been developed in Russia [4]. Therefore it is necessary to schedule the measures intended for collecting and processing the experimental data in order for the conditions for the identifiability of the mathematical model used [14,15,17] to be satisfied.…”

Section: U(t) « Ui ^ Tto V(£) « VI £ Vqmentioning

confidence: 99%

“…Using different approaches to the solution of problems of the parametric identification of mathematical models of evolutionary processes with lumped parameters by the limited experimental data on the state vector [14,15,17], we can determine not only the estimate of the extended parameter vector α of the mathematical model (1.1) but also its a posteriori distribution law. Thus, having solved the parametric identification problem, the state vector of the population X(t,a,Xo) is a vector random process, and according to conventional terminology [11] we obtain a problem of taking dicisions under risk conditions.…”

Section: U(t) « Ui ^ Tto V(£) « VI £ Vqmentioning

confidence: 99%

On one concept of the construction of an ecological risk criterion for populations

Volkov¹

1998

Russian Journal of Numerical Analysis and Mathematical Modelling

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We propose a possible version of the concept of the construction of an ecological risk criterion for populations and analyse problems of its practical realization.The progress in the scientific and technological revolution at this stage is accompanied by a considerable increase in the spectrum of harmful factors in the environment. In spite of the obvious danger of environmental pollution the sanitary standards are not infrequently violated, and the impact of the new harmful factors on human health, as a rule, needs a prolonged and detailed study. This primarily refers to genetic changes which have no threshold effect and manifest themselves with a certain, sometimes considerable, lag. This problem becomes even more important because mutation changes often lead to hereditary pathology. Having originated once, the pathological mutations persist over prolonged periods and are passed on from one generation to another.A lot of publications both of a theoretical and of an experimental character deal with the development of a mutageneity estimate [2,6]. Attempts have been made to consider the impact of environmental mutagens on cells, organisms, and populations in the context of genetics and sanitary with the aim to develop and use the system of genetic monitoring in practice. Moreover we should emphasize that on the background of fundamental investigations in this area [7,8] the so-called ecological risk criterion for the people is used in increasing frequency in the scientific literature and science fiction. The use of this criterion, which sometimes has no distinct meaning [4], implies the realization of optimal measures intended to improve the ecology and human health in concrete regions.The aim of this research is to develop the concept of the construction of an ecological risk criterion for populations and quantitative methods of its determination under real conditions.

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Technique of rationalizing of identification in experimental studies of dynamic objects in aircrafts

Kashin

Лапин

Mokaeva

et al. 2019

XLIII ACADEMIC SPACE CONFERENCE: Dedicated to the Memory of Academician S.P. Korolev and Other Outstanding Russian Scientists –

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On identifiability of mathematical models of evolutionary processes from data of discrete measurements of state vector

Cited by 3 publications

References 0 publications

Conditions for identifiability of autonomous systems of ordinary differential equations

Conditions for identifiability of autonomous systems of ordinary differential equations

On one concept of the construction of an ecological risk criterion for populations

Technique of rationalizing of identification in experimental studies of dynamic objects in aircrafts

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