## ISSUE 179, article 7

Kibern. vyčisl. teh., 2015, Issue 179, pp 81-92.

Pashinskaia Svetlana L., Junior researcher of the Medical Informatics Department of the Marzeev’s Institute of Hygiene and Medical Ecology of the National Medical Academy of Sciences of Ukraine, Popudrenko st., 50, Kiev, 02094, Ukraine, email: pashynska_sv@gmail.com

Antomonov Mikhail Yu., Dr (Biology), Prof., Head of Medical Informatics Department of Marzeev’s Institute of Hygiene and Medical Ecology of the National Medical Academy of Sciences of Ukraine, Popudrenko st., 50. Kiev, 02094, Ukraine, email: antomonov@gmail.com

INVERSE PROBLEMS OF INTEGRATED EVALUATION: IDENTIFICATION OF CRITICAL COMPONENTS OF HEALTH AND ECOLOGICAL SITUATION

Introduction. Integrated assessment of environmental quality in medical ecological research used different mathematical structures that are often weighted sum of expression of all reported hazards. The problem of optimal formation of integrated indicators is the direct problem of integral evaluation.

The purpose of paper is to develop methods, algorithms, computational formulas and software implementation for solving the inverse problem of the integral evaluation — identifying destabilizing factors in the assessment of ecological and hygienic objects.

Results. Realization of this aim requires the formulation and solution of problems phased: express processing of data array; the selection of informative features; construction of an integrated evaluation.

Algorithm of construction integrated evaluation is implemented as follows: the calculation of the normalized equivalents of selected indicators; calculation of weighted average grade of the objects on the normalized equivalents; calculation shifted integrated evaluation, as the square root of the product of the minimum and weighted average; comparison of average and shifted integrated evaluation; identification of critical elements.

The paper presents an automated technology analysis and evaluation of the primary indicators in order to optimize their list to calculate the integral evaluation. The technology allows working with arrays having outliers and missing data. We consider a phased construction of an integrated assessment. The nonlinear algorithm of integration indicator formation and the method for identifying critical elements were developed.

Conclusions. The proposed technology allows to quickly implementing the processing of the data array, to bring it to a format suitable for further, more detailed analysis and to form an integrated assessment. The results of processing may be performed within the environmental and medical objects; identify objects with the most adverse environmental conditions and disease. Calculation of displaced integral indicators shows destabilizing elements in the system of indicators.

Keywords: integrated evaluation, ecological and hygienic objects, medical and ecological research.

References

1. Lemeshko B.Yu., Rogozhnikov A.P. Investigation of the features and power of some of the criteria of normality. Metrologiya, 2009, no 4, pp. 3–24 (in Russian).
2. Vasil’yev V.I.., Shevchenko A.I. Recovery of missing data in empirical tables. Iskusstvennyy intellect, 2003, no 3, pp. 317–324 (in Russian).
3. Zloba Ye., Yatskiv I. Statistical methods for recovery of missing data. Computer Modeling & New Technologies, 2002. Vol. 6. no 1. pp. 51–61 (in Russian).
4. Bakumenko L.P., Korotkov P.A. Integral assessment of the quality and environmental sustainability of the region (on the example of the Republic of Mari El). Prikladnaya ekonometrika. 2008, no 1(9), pp. 73–92 (in Russian).
5. Pavlov S. B. Ekologіchny rizik for Health Protection of the population. Meditsinskiye issledovaniya, 2001. T. 1, issue 1, pp. 16–19 (in Ukrainian).
6. Antomonov M.Yu. Mathematical processing and analysis of medical and biological data. Kiev: Malyi druk, 2006. 558 p (in Russian).
7. Shuyskiy V.F., Zantsinskaya T.P., Petrov D.S. Quantification and valuation of complex anthropogenic impact on macrozoobenthos. Sb. nauch. tr. GosNIORKH, issue 326. 2000, pp. 137–144 (in Russian).
8. Faynzilberg L.S. Plausible, but wrong decisions in the construction of diagnostic rules. Materialy vosmoy distantsionnoy nauchno-prakticheskoy konferentsii s mezhdunarodnym uchastiyem. «Sistemy podderzhki prinyatiya resheniy. Teoriya i praktika. SPPR ’2012». Kiev, IPMMS NAN Ukrainy, 2012, pp. 31–34 (in Russian).

## ISSUE 179, article 6

Kibern. vyčisl. teh., 2015, Issue 179, pp 70-80.

Najafian Toomajani Mohamadali, Junior Researcher of Medical Information Systems Department of the International Research and Training Center for Information Technologies and Systems of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Glushkov ave., 40, Kiev, 03187, Ukraine, email: Najafian@mail.ru

Budnyk Mykola M., Dr (Engineering), Leading Researcher of Department of Sensor Instruments, Systems and Technologies of Non-Contact Diagnostics of the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Glushkov ave., 40, Kiev, 03187, Ukraine, email: budnyk@meta.ua

Kovalenko Alexander S., Dr (Medicine), Prof., Head of Medical Information Systems Department of the International Research and Training Center for Information Technologies and Systems of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Glushkov ave., 40, Kiev, 03187, Ukraine, e-mail: askov49@gmail.com

EVALUATION OF INHOMOGENEITY DEGREE OF ELECTRICAL PROCESSES INTO THE HEART VENTRICLES BASED ON MAGNETOCARDIOGRAPHY

Introduction. Methods for analysis of the current density distribution (CDD) maps as cross-sections of the human heart into the frontal plane were considered. Degrees of non-homogeneity of regional and global kinds are determined based on degree of difference between CDD maps and normal quasi-dipole map. Method for estimation of the abnormality degree of CDD maps caused by failures of electric processes into the heart ventricles has been proposed. Evaluation of regional and global inhomogeneity for each map is determined according to small, medium and large grades.

Purpose of the article is to assess the degree of abnormality of electrical processes in the ventricles of the heart through the MCG mapping, analysis of sets of CDD maps beginning of the QRS complex to the end of the T wave, the calculation of the degree of their differences from normal quasi-dipole map.

Methods. Method of assessing the degree of abnormality of the CDD maps.

Results. In order to achieve reliable classification of the degree of regional (global) maps inhomogeneity is assessed by a 3-point scale (small, medium, large), For a more detailed stratification of patients a total degree of inhomogeneity (abnormality) has developed on a 5-value scale: low (normal), below average (small abnormality), the average (intermediate abnormality), above average (mild abnormality), large (severe abnormality).

First determine the level of regional inhomogeneity. For each map, it is determined according to the 3-value scale – small, mild and severe degree.

Conclusion. This method can be applied to the analysis of not only CDD maps, but also for the magnetic field maps. In this case, it is needed to solve the inverse problem, and instead of the current areas, area of the extreme of the magnetic field were analyzed. However, the magnetic field gives a fairly indirect distribution pattern of excitation into the myocardium, so informative value is much lower for medical analysis.

In addition, method is preferable for using relatively cheap device, which allow make examination under normal condition without magnetically shielded room. Above factor greatly simplifies and reduces the cost of implementation of the MCG technology into clinical practice.

Keywords: current density distribution (CDD) map, estimation of regional inhomogeneity, estimation of global inhomogeneity.

References

1 Connolly D.C., Elveback L.R., Oxman H.A. Coronary heart disease in residents of Rochester, Minnesota: Prognostic value of the resting electrocardiogram at the time of initial diagnosis of angina pectoris. MayoClin. Proc., 1984; Vol. 59, p. 247–50. https://doi.org/10.1016/S0025-6196(12)61257-9

2 Vinogradova T.S. Akulova F.D., Belotserkovskiy Z.B. et al., Instrumental methods for studing the cardiovascular system. Moscow: Medicine, 1986. 416 p. (in Russian).

3 Lant J., Stroink G., Voorde B. et al. Complementary Nature of Electrocardiografic and Magnetocardiografic Data in Patients with Ischemic Heart Disease. J. Electrocardiology. 1990. V.23, p.315–322. https://doi.org/10.1016/0022-0736(90)90121-H

4 Budnyk M.M., Voytovych I.D., Kozlovsky V.I et al. Diagnostic criteria for chronic ischemic heart disease based on registration and analysis magnitokardiogram. Preprint 2002-5, NAS of Ukraine. Kiev: Glushkov Institute of Cybernetics. 2002, No 5. 49 p. (in Ukrainian).

5 Bakharev A. Ischemia identification, quantification and partial localization in MCG. Int. Patent Application WO 0217769. Cardiomag Imaging Inc., USA, 2002.

6 Kozlovsky V., M. Budnyk, Stadnyuk L., Ryzhenko T. Method of diagnosis of ischemic heart disease. Patent UA 74466. Application No. a 2004 021 170, published 15.12.2005, Bulletin No. 12 (in Ukrainian).

7 Zahrabova A., Budnyk M., Stadnyuk L. et al. Method of estimation of processes of the heart electrical excitation and recovery. Patent UA 13427. Application No. u2006 01007, published 15.03.2006, Bull. No. 3 (in Ukrainian).

8 Chaikovsky I., Budnyk M. Method for estimating abnormality of currents distribution into the heart. Patent UA 83050. Application No. a2006 00 584, published 10.06. 2008,Bulletin No. 11 (in Ukrainian).

9 Chaikovsky I., Budnyk M. Method for estinating abnormality process of ventricular repolarization. Patent UA 83061. Application No. a2006 02821, published 10.06.2008, Bull.No. 11 (in Ukrainian).

10 Wilson at al. The T deflection of the electrocardiogram. Trans. Assoc. Am. Physicians,vol. 46; No. 2, – p. 19–31.

11 Chaikovsky I., Budnyk M., Vasetsky Yu., Najafian M. Method of estimation of the degree of abnormality of electrical processes into the heart ventricles, Patent UA 90701. Application No. a 2007 08 616, published 25.05.2010, Bulletin No. 10 (in Ukrainian).

## ISSUE 179, article 5

Kibern. vyčisl. teh., 2015, Issue 179, pp 56-69.

Gorodetskyi Victor G., PhD (Physics & Mathematics), Associate Professor of the National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave., 37, Kiev, 03056, Ukraine , e-mail: v.gorodetskyi@ukr.net

Osadchuk Mykola P., Assistant of the National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave., 37, Kiev, 03056, Ukraine, email: 13717421@ukr.net

ALGORITHM FOR RECONSTRUCTING THE DYNAMICAL SYSTEMS USING ONE OBSERVABLE VARIABLE

Introduction. We consider the problem of reconstructing the system of ordinary differential equations by using one observable variable. The data under investigation is a scalar time series of some process data. It is assumed that the dynamics of the process can be described by an original system of ordinary differential equations with polynomial right-hand sides. We replace the original system by standard system of known type in which the unknown variables are replaced by derivatives of the observable variable, and one of the variables of the standard system is the same as observable variable. We use standard systems which have the ratio of polynomials with unknown coefficients in the right-hand sides.

The purpose of this work is to simplify and improve the accuracy of G. Gouesbet algorithm for determining the coefficients of the standard system.

Methods. As well as in the prototype algorithm, the time series is differentiated to find all the variables of the standard system. Then we form the system of linear algebraic equations which are solved with respect to the unknown coefficients of the standard system. The algorithm uses such novelties: ability to assign the known values for any coefficient of the standard system, solving the over determined algebraic system by using least square method, possibility to use different methods of differentiation.

Results. Algorithm was utilized to reconstruct standard system by use of one variable of Rossler system and other systems with chaotic evolution. All the results confirmed the effectiveness of the algorithm improvements.

Conclusion. The proposed novelties allow to improve the accuracy of computing the coefficients of the standard system and simplify the algorithm.

Keywords: original system, standard system, reconstructing, least square method, observable variable.

References

1 Cremers J., Hubler A. Construction of differential equations from experimental data. Naturforsch, 1987, vol. 42a, pp. 797–802.

2 Breeden J.L., Hubler A. Reconstructing equations of motion from experimental data with unobserved variables. Phys. Rev. A, 1990, vol. 42, pp. 5817–5826. https://doi.org/10.1103/PhysRevA.42.5817

3 Gouesbet G. Reconstruction of standard and inverse vector fields equivalent to the Rossler system. Phys. Rev. A, 1991, vol. 44, pp. 6264–6280. https://doi.org/10.1103/PhysRevA.44.6264

4 Takens F. Detecting strange attractors in turbulence. In: D.A. Rand, L.S. Young (Eds.), Dynamical System and Turbulence, Lecture Notes in Mathematics. Springer, New York. 1981, no. 898, pp. 366–381. https://doi.org/10.1007/BFb0091924

5 Gouesbet G. Reconstruction of the vector fields of continuous dynamical systems from numerical scalar time series. Phys. Rev. A, 1991, vol. 43, pp. 5321–5331. https://doi.org/10.1103/PhysRevA.43.5321

6 Gouesbet G., Letellier C. Global vector-field reconstruction by using a multivariate polynomial L2 approximation on nets. Phys. Rev. E, 1994, vol. 49, no. 6, pp. 4955–4972. https://doi.org/10.1103/PhysRevE.49.4955

7 Maquet J., Letellier C., Aguirre L. A. Scalar modelling and analysis of a 3D biochemical reaction model. Journal of Theoretical Biology, 2004, vol. 228, pp. 421–430. https://doi.org/10.1016/j.jtbi.2004.02.004

8 Gorodetskyi V., Osadchuk M. Reconstruction of chaotic systems of a certain class. International Journal of Dynamics and Control. Available at: DOI 10.1007/s40435-014-0100-y.

9 Le Sceller L., Letellier C., Gouesbet G. Structure selection for Global vector field reconstruction by using the identification of fixed points. Phys. Rev. E, 1999, vol. 60, no. 2, pp. 1600–1606. https://doi.org/10.1103/PhysRevE.60.1600

10 Strang G. Linear Algebra and Its Applications. Thomson Brooks/Cole, 2006, 487 p.

11 Rossler O.E. An equation for continuous chaos. Phys. Lett. A, 1976, vol. 57, pp. 397–398. https://doi.org/10.1016/0375-9601(76)90101-8

12 Forsythe G. E., Moler C.B. Computer solution of linear algebraic systems. N. J.: Prentice-Hall, Inc., Englewood Cliffs, 1967, 148 p.

## ISSUE 179, article 4

Kibern. vyčisl. teh., 2015, Issue 179, pp 43-55.

Romanenko Victor D., Dr (Engineering), Prof., Deputy Director for Scientific and Pedagogical Work, Institute for Applied Systems Analysis of National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave. 37, Kiev, 03056, Ukraine, email: ipsa_mmsa@ukr.net

Milyavskiy Yurii L., PhD (Engineering),Assistant of the Department of Mathematical Methods of System Analysis of the Institute for Applied Systems Analysis of National Technical University of Ukraine “Kiev Polytechnic Institute”, Peremogy Ave. 37, Kiev, 03056, Ukraine, email: yuriy.milyavsky@gmail.com

IMPULSE PROCESSES STABILISATION IN COGNITIVE MAPS OF COMPLEX SYSTEMS BASED ON MODAL STATE REGULATORS

Introduction. Cognitive modelling is one of the most widespread approaches for ill-structured socio-economic systems research nowadays. It is usually used when subject of enquiry is a complex high-dimensional system; in fact, most of financial, economical, social, political systems belong to this category. Cognitive map (CM) is a directed graph, where vertices represent concepts, directed edges represent the causal effect relationships between concepts, and the weights of edges represent the degree of the causal effect. When CM switches to transition process as a result of external or internal impulse, so called «impulse process» is described by difference first-order equation for increments. It was previously shown by the authors that impulse process can also be equivalently expressed by state-space model. One of the most important questions is how to stabilise unstable CM. For this purpose control inputs should be added to the system. Then the problem of regulators design arises.

Purpose of the paper is to investigate possibility of applying modal control methods for state regulators design (with single and multiple controls) to stabilise unstable impulse process in CM.

Results. Different methods of modal control were investigated and applied for CM impulse process stabilisation. CM dynamics was presented by state space model. Problem of external control inputs for CM was discussed. It was demonstrated that as opposed to «input — output» models, state space models allow to use smaller number of controls for stabilisation (if the system is controllable). Cases with single and multiple inputs were discussed. Impulse process in the CM for commercial bank was simulated, and different approaches to modal regulators design were applied for this cognitive model. Simulation results demonstrated efficiency of the proposed approach to CM stabilisation. It was also shown that modal control with multiple inputs is preferable where possible because it allows to get quicker response and smoother transition process with lower amplitude of control inputs.

Conclusion. Applying of modal control methods allows effective stabilising of CM. Using multiple control inputs helps to increase performance and make transition process smoother and easier to implement.

Keywords: cognitive map, modal control, impulse process stabilisation, closed loop pole placement.

References

1 Axelrod R. The Structure of Decision: Cognitive Maps of Political Elites. Princeton University Press. 1976. 404 p.

2 Roberts F. Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems. Englewood Cliffs, Prentice-Hall. 1976. 559 p.

3 Avdeeva Z.K., Kovriga S.V., Makarenko D.I., Maksimov V.I. Cognitive approach in control. Control problems, 2002, no. 3, pp. 2–8 (in Russian).

4 Maksimov V.I. Structural–target analysis of socio-economic situations development. Control problems, 2005, no. 3, pp. 30–38 (in Russian).

5 Gorelova G.V., Zakharova E.N., Radchenko S.A. Research of semi-structured problems in socio-economic systems. Cognitive approach. Rostov-na-Donu: Publisher RSU, 2006, 332 p. (in Russian).

6 Romanenko V.D., Milyavskiy Y.L. Stabilizing of impulse processes in cognitive maps based on state-space models. System research & information technologies, 2014, no. 1, pp. 26–42 (in Russian).

7 Isermann R. Digital control systems. Berlin: Springer-Verlag. 1981. 566 p. https://doi.org/10.1007/978-3-662-02319-8

8 Yegupov N.D., ed. Methods of classic and modern automatic control theory. Handbook. Vol. 2: Regulators design and optimization theory of automated control systems. Moscow: MSTU, 2000. 736 p. (in Russian).

9 Ackermann J. Sampled-Data Control Systems. Berlin: Springer-Verlag. 1985. 596 p. https://doi.org/10.1007/978-3-642-82554-5

10 Valasek M., Olgac N. Efficient Eigenvalue Assignments for General Linear MIMO Systems. Automatica, 1995, vol. 31, pp. 1605–1617. https://doi.org/10.1016/0005-1098(95)00091-A

11 Romanenko V.D., Milyavskiy Y.L., Reutov A.A. Adaptive Control Method for Unstable Impulse Processes in Cognitive Maps Based on Reference Models. Journal of Automation and Information Sciences, 2015, no. 2, pp. 35–45 (in Russian). https://doi.org/10.1615/JAutomatInfScien.v47.i3.20

## ISSUE 179, article 3

Kibern. vyčisl. teh., 2015, Issue 179, pp 35-42.

Norkin Bogdan V., PhD (Phys. & Math.), Researcher of the Department of Methods for Discrete Optimization of Mathematical Modeling for Analysis of Complex Systems of the Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Acad.Glushkov ave., 40, Kiev, 03187, Ukraine, email: bogdan.norkin@gmail.com

ON THE APPROXIMATION OF VECTOR OPTIMIZATION PROBLEMS

Introduction. Vector optimization has a great variety of applications. Such problems naturally appear in stochastic optimization, where the optimization problem contains random parameters. In the latter case the vector objective function may include mean value, median, variance, quantiles and other characteristics of the random objective function. The difficulty is that these quantities usually cannot be calculated exactly and are non-convex as functions of variable parameters. These circumstances set additional difficulties for solving corresponding vector optimization problems.

The purpose of this paper is to study conditions for convergence of the approximation method when the objective functions and the feasible set are replaced by their more and more fine approximations.

Results. We consider an approximation approach to solving vector optimization problems. The standard approach to such problems is to optimize one criterion under constraints on the others or to scalarize the problem, i.e. to combine all criteria into one scalar criterion. This paper describes a completely different approach, where the feasible set is approximated by a discrete grid (deterministic or random) and the vector function is approximately calculated on this grid. The obtained discrete problem is exactly solved by Pareto type optimization.

Conclusions. Sufficient conditions are established for Pareto-optimal solutions of the approximate problems to converge in set convergence sense to the Pareto optimal solution of the original problem (with some accuracy). Namely, it is required for the approximate functions to converge uniformly to the original function and for the feasible set approximations (possibly discrete) to converge to elements of the original feasible set, at least, in the vicinity of the solution. The result confirms a natural hypothesis that the approximation accuracy should increase when approaching to the solution.

Keywords: vector optimization, stochastic multicriteria optimization, Pareto optimality, discrete approximation, epsilon-dominance.

References

1 Miettinen K. Nonlinear multiobjective optimization. Boston,London,Dordrecht: Kluwer Academic Publishers, 1999. 298 p.

2 Sobol I.M., Statnikov R.B. Vybor optimalnyh parametrov v zadachah so mnogimi kriteriyami (Selection of optimal parameters in problems with multiple criteria). 2-nd ed, revised and supplemented. Moscow: Drofa, 2006. 176 p. (In Russian).

3 Deb K. Multi-objective optimization using evolutionary algorithms. Chichester: John Willey & Sons, 2001. 497 p.

4 Hanne T. On the convergence of multiobjective evolutionary algorithms. European J. of Operational Research. 1999. 117. P. 553–564. https://doi.org/10.1016/S0377-2217(98)00262-8

5 Li Z., Li Zhe, Rudolph G. On the convergence properties of quantum-inspired multi-objective evolutionary algorithms. In: Advanced intelligent computing theories and applications. With aspects of contemporary intelligent computing techniques. Berlin, Heidelberg: Springer, 2007. P. 245–255. https://doi.org/10.1007/978-3-540-74282-1_28

6 Laumanns M., Zenklusen R. Stochastic convergence of random search methods to fixed size Pareto front approximations. European J. of Operational Research. 2011. 213. P. 414–421. https://doi.org/10.1016/j.ejor.2011.03.039

7 Ben Abdelaziz F. Solution approaches for the multiobjective stochastic programming. European J. of Operational Research. 2012. 216. P. 1–16. https://doi.org/10.1016/j.ejor.2011.03.033

8 Gutjahr W., Pichler A. Stochastic multi-objective optimization: a survey on non-scalarizing methods. Annals of Operations Research. 2013. P. 1–25.

9 Shapiro A., Dentcheva D., Ruszczycnski A. Lectures on stochastic programming: Modeling and theory. Second Edition. Philadelphia: SIAM, 2014. 494 p.

10 Koenker R. Quantile Regression. Cambridge, New York: Cambridge University Press, 2005. https://doi.org/10.1017/CBO9780511754098

11 Ermoliev Y.M. Metody stochasticheskogo programmirovaniya (Methods of stochastic programming). Moscow: Nauka, 1976. 240 p. (in Russian).

12 Rockafellar R.T., Wets R.J-B. Variational Analysis. Berlin: Springer, 1998 (3rd Printing in 2009). 734 p. https://doi.org/10.1007/978-3-642-02431-3

13 Norkin B.V. Sample approximations of multiobjective stochastic optimization problems. www://optimization-online.org. Electronic preprint. November 2014. Access: http://www.optimization-online.org/DB_HTML/2014/11/4655.html

## ISSUE 179, article 2

Kibern. vyčisl. teh., 2015, Issue 179, pp 20-34.

Dotsenko Sergey I., PhD (Phys. & Math.), Associate Professor, Department of Operations Research, Faculty of Cybernetics of the Taras Shevchenko National University of Kyiv, Ave. Acad. Glushkov, 4 D, Kyiv, 03187, Ukraine, e-mail: sergei204@ukr.net

ON GAME-THEORETICAL APPROACH IN ACTION COORDINATION PROBLEMS WITH INFORMATION EXCHANGE

Introduction. Cooperative game theory is integral part of modern economics. The founder of this theory is Lloyd Shapley, who became Nobel prize winner in economics in 2012. In classical cooperative game theory the characteristic function of the game is rigidly defined and remains unchanged.. The extra players don’t participate in the game immediately, but they provide the connection between the origin players and so, may change the characteristic function of the game. For the extended game the Shapley values are calculated for origin and extra players equally well.

The purpose of this research is aimed at so-called extended games, when the extra players may be inducted into the game.

Results. The Shapley values for extended communication games, based on both forces, coordination game and secretary problem are obtained in explicit form. As accessory result, the theorem on stochastic inequality for Shapley values in the case of player’s non-uniform joining times to coalition is proved and then illustrated by vivid example.

Conclusions. The considered examples vividly illustrate winnings increment effect, stipulated by extra agent induction. This agent is aimed to provide the connection between the other players and is called a connector. Connector’s Shapley value characterizes his fair salary for connection provision. A linear extension function’s method provides the analysis of Shapley value calculation for problems of more sophisticated structure, than delivered above.

Keywords: cooperative game, communicative extension, Shapley value, stochastic inequality, optimal choice problem.

References
1 Tijs S. Introduction to game theory. Hindustan book agency. 2003.

2 Owen G. Multilinear Extensions of Games. Management Science. 1972, pp. 64–79. https://doi.org/10.1287/mnsc.18.5.64

3 Owen G. Values of Graph-Restricted Games. SIAM J Alg. Disc. Math. 1986, pp. 210–220.

4 Myerson R. Graphs and Cooperation in Games. Math. Op. Res. 1977, pp. 225–229.

5 Shapley L. A value for n-person games. Contributions to the Theory of Games. Princeton University Press. 1953, pp. 307–317.

6 Mazalov V.V. Mathematical game theory and it’s applications. Saint Petersburg: “Lan” 2010, 446 p. (in Russian).

## ISSUE 179, article 1

Kibern. vyčisl. teh., 2015, Issue 179, pp 5-19.

Vovk Maiia I.,PhD (Biology), Head of Bioelectronic Control and Medical Cybernetics Department of the International Research and Training Center for Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, av. Acad. Glushkova, 40, Kiev, 03187, Ukraine, e-mail: dep140@irtc.org.ua

Galyan Yevgeniya B., Junior Researcher of Bioelectronic Control and Medical Cybernetics Department of International Research and Training Center for Information Technologies and Systems of National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, av. Acad. Glushkova, 40, Kiev, 03187, Ukraine, e-mail: galevbor@mail.ru

PERSONАLIZED BIOTECHNICAL SYSTEM TO RESTORE SPEECH

Introduction. In previous studies, we proposed a new method and technology to restore speech based on biotechnical system of hand movement control. To support operator’s choice of personalized control actions we had to include the information component in the technical subsystem.

The purpose of this research is to develop the structural and functional model of personalized biotechnical system to restore speech, to determine functionality and relationship of the system components and to describe the structure, content and functions of the information component.

Methods. We used information and structural modeling, structural and functional modeling, Unified Modeling Language (UML).

Results. In this paper we present a structural and functional model of personalized biotechnical system of hand movement control to restore speech and define structure and functionality of its components. The functional relationships between the components of the system, transformation and orderliness of information circulating within and between components are described. We paid a particular attention to the information component. It provides support for the operator activity to choice personalized parameters of rehabilitation course and gives tools for operator’s learning of technology to restore speech in online and for storage of clinical information. The structure of information component, its content and the realization in PC architecture are described. Peculiarities of algorithmic and logical implementation of operations performed by informational component are represented in the activity diagram of decision support block in UML notation. Elements of information component such as electronic library, decision support block, a database of medical records are realized using software Swish Max 4.0, Sony Vegas Pro 9.0, Visual Studio 2013.

Conclusions. Personalized biotechnical system to restore speech under consideration is an intellectual, logical thinking, teaching system due to information component that is included into its structure.

Keywords: personalized biotechnical system, speech restoring, information system, hand movement control, structural and functional model, decision support block.

References
1. Semenova К.А. Cerebral Palsy. Moscow: «Meditsina», 1968. 259 p. (in Russian).

2. Danilova L.А. Correction methods for speech and mental development in children with cerebral palsy. Moscow: «Meditsina», 1977. 95 p. (in Russian).

3. Mishchenko Т.S. Risk factors and clinical features of patients with different subtypes of ischemic stroke. International medical journal. 2011, vol. 17, no 3, pp. 27–32. (in Russian).

4. Vovk M.I., Galyan Ye.B., Podoprigora Ye.N. Information technology for movement control of the hand used to restore the motor component of speech. Cybernetics and Computer Engineering, 2014, no 175, pp.20–30. (in Russian).

5. Vovk M.I., Galyan Ye.B. Restoring of motor component of speech based on muscle movement control. Theoretical grounding. Cybernetics and Computer Engineering, 2012,no 167, pp.51–60. (in Russian).

6. Vovk M.I., Galyan Ye.B., Podoprigora Ye.N. Method for the treatment of speech disorders. Ukraine patent for utility model № 95347. Bul. No 24. 25.12.14. (in Ukrainian).

7. Antomonov Yu. G., Kotova A. B. Functional load of human in the structure of biotechnical system. Cybernetics and Computer Engineering, 1989, no. 84, pp. 66–73. (in Russian).

8. Gritsenko V.І., Kotova A.B., Vovk M.I., Kozak L.M. Information technology in biology and medicine. Lectures: Tutorial. Kyiv: Nauk. Dumka, 2007. 381 p. (in Russian).

9. Vovk M.I. Bioinformation technology of motor control of a person. Cybernetics and Computer Engineering, 2010, no. 161, pp. 42–52. (in Russian).

10. Galyan Ye.B. The information component of hand movements training technology for speech restoration. Biomedical Engineering and Electronics , 2014, no 2. Available at: www.es.rae.ru/biofbe/199-958 (date: 18.08.2014) (in Russian).

11. Galyan Ye.B. Algorithm of parameter selection for hand movement training to restore speech. Biological and Medical Informatics and Cybernetic for Health Care: materials of annual science and technology seminar. Kiev: Zhukin Physical and Mathematical School, 18–22 June 2012. K: Acad. of Sciences of Ukraine, ITRC of IT and S, 2014. — available at http://www.irtc.org.ua /Inform/135_2014.pdf (in Russian).

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