Source: http://agorban.narod.ru/cv.htm
Timestamp: 2019-04-19 16:45:38+00:00

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Institute of Computational Modeling, Russian Academy of Sciences, Krasnoyarsk-36, 660036, Russia.
Architecture of neurocomputers and training algorithms for neural networks.
� Novosibirsk Special School for Physics & Mathematics, 1965-1967.
� Advisor of the Omsk Physical & Mathematical School, 1972-1976.
� Swiss Federal Institute of technology (ETH, Zurich, Switzerland), 05.1999-06.1999, 08.2000-09.2000, 03.2002-06.2002.
� Member of Jury of USSR National competition in mathematics for students of technical universities (1986-1990).
� Member of Society for Mathematical Biology (2003).
Participant of 61 conferences, including 15 international, positions as a member of organizing committee or a (co-)chairman at 22 conferences, including 7 international.
� Russian National Workshops �Modeling of Nonequilibrium Systems�, I-V, Krasnoyarsk, October 1999- October 2003.
� Russian National Conference �Problems of Regional Informatization�, Krasnoyarsk, 1998-2003.
� Soviet Union National competition in Neuroinformatics and Neurocomputers for students and young scientists, 1991.
� 1994-1996 American Mathematical Society Fellowship.
� V.A. Okhonin, Kinetic equations for population dynamics (PhD, Biophysics, 1986).
"Critical Situations in a Transfer to Market" (Krasnoyarsk, December 1990).
Organizer of 2 Tobolsk Summer Schools for Talented Children.
4. Neuroinformatics, Novosibirsk, Nauka Publ., 1998, 258 p. (With W.L.Dunin-Barkovskii, D.A.Rossiev, S.A.Terehov).
7. New methods for solving the Boltzmann Equations, AMSE Press, Tassin, France, 1993, ISBN: 2-909214-51-6, 166 p. (With I.V.Karlin).
8. Kinetic Models of Catalytic Reactions (Comprehensive Chemical Kinetics, V.32, ed. by R.G. Compton), Elsevier, Amsterdam, 1991, 396p. (With G.S.Yablonskii, V.I.Bykov and V.I.Elokhin). (Review on this book: Journal of American Chemical Society (JAChS), V.114, n 13, 1992; sections �Reviews on the book�, W. Henry Weinberg, review on the book "Comprehensive Chemical Kinetics", Volume 32, Kinetic Models of Catalytic Reactions, Elsevier, 1991).
13. Kinetic models of heterogeneous catalytic reactions, Novosibirsk, Nauka Publ., 1983, 256 p. (With V.I.Bykov, G.S.Yablonskii).
1. A.N. Gorban, T.G.Popova, A.Yu. Zinovyev, Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences �Physica A: Statistical and Theoretical Physics, 353C (2005), 365-387.
2. A.N. Gorban, T.G.Popova, A.Yu. Zinovyev, Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences, In Silico Biology, 5 (2005), 0039.
3. A.N. Gorban, P.A.Gorban, and I. V. Karlin, Legendre Integrators, Post-Processing and Quasiequilibrium, J. Non-Newtonian Fluid Mech. 120 (2004) 149-167.
4. A.N. Gorban, I.V. Karlin, A.Yu. Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Physics Reports, V. 396, N 4-6 (2004), p. 197-403.
5. A.N. Gorban, I.V. Karlin, A.Yu. Zinovyev, Invariant grids for reaction kinetics, Physica A, 333 (2004), 106--154.
6. A.N. Gorban, I.V. Karlin, Uniqueness of thermodynamic projector and kinetic basis of molecular individualism, Physica A, 336, 3-4 (2004), 391-432.
7. A.N. Gorban, I.V. Karlin, Methods of nonlinear kinetics, in: Encyclopedia of Life Support Systems, Encyclopedia of Mathematical Sciences,� EOLSS Publishers, Oxford, 2004.
8. A.N. Gorban, T. G. Popova, and A. Yu. Zinovyev: Self-organizing approach for automated gene identification. Open Sys. Information Dyn. 10 (2003) 1-13.
10. A.N. Gorban, I. V. Karlin and H. C. Ottinger, The additive generalization of the Boltzmann entropy. Phys. Rev. E. (2003), V. 67. E-print: http:, arXiv.org/abs/cond-mat/0209319.
11. A.N. Gorban, I. V. Karlin, Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 58 (2003) 4751-4768.
12. I.V. Karlin, L. L. Tatarinova, A. N. Gorban, and H. C. �ttinger, Irreversibility in the short memory approximation, Physica A 327 (2003) 399-424.
13. A. Gorban, A. Zinovyev, T. Popova. Seven clusters in genomic triplet distributions. In Silico Biology. V.3 (2003), 471-482.
15. A. Gorban', Braverman M., Silantyev V. Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow� turbines. Math. Comput. Modelling 35 (2002), No. 13, 1371-1375.
16. �A. Gorban', Silantyev V. Riabouchinsky Flow with Partially Penetrable Obstacle. Math. Comput. Modelling 35 (2002), no. 13, 1365-1370.
17. I.V. Karlin, M. Grmela, and A.N. Gorban: Duality in nonextensive statistical mechanics, Phys. Rev. E 65 (2002) 036128.
18. A.N. Gorban and I. V. Karlin, Reconstruction lemma and fluctuation-dissipation theorem, Revista Mexicana de Fisica, 2002. V. 48 Suplemento 1,� PP. 238-242.
19. A.N. Gorban and I. V. Karlin, Geometry of irreversibility, in: Recent Developments in Mathematical and Experimental Physics, Volume C:� Hydrodynamics and Dynamical Systems, Ed. F. Uribe (Kluwer, Dordrecht, 2002), pp. 19-43.
20. A.N. Gorban and I. V. Karlin, Macroscopic dynamics through coarse-graining: A solvable example, Phys. Rev. E. V 65. 026116(1-5) (2002).
22. A.N. Gorban, Zinov'ev A.Y., Pitenko A.A., Data vizualization. The method of elastic maps, Neirocompjutery, 2002, 4, 19-30.
23. A.N. Gorban, A.A Rossiev, Iterative modeling of data with gaps via submanifolds of small dimension, Neirocompjutery, 2002, 4, 40-44.
24. A. Gorban, Rossiev A., Makarenko N., Kuandykov Y., Dergachev V. Recovering data gaps through neural network methods. International Journal of� Geomagnetism and Aeronomy, 2002, Vol. 3, No. 2, December 2002.
25. A.N. Gorban, V.T. Manchuk, A.V.Perfil�eva, E.V.Smirnova, E.P. Cheusova, The mechanism of increasing the correlation between physiological parameters for high adaptation tension, Siberian Ecological Journal, 2001, No 5, 651-655.
26. A.N. Gorban, Gorlov A.M., Silantyev V.M. Limits of the turbin efficiency for free fluid flow,� ASME Journal of Energy Resourses Technology, Dec.� 2001, V. 123, Iss. 4, pp. 311-317.
27. A.N. Gorban, Pitenko A.A., Zinov'ev A.Y., Wunsch D.C. Vizualization of any data uzing elastic map method ,� Smart Engineering System Design.� 2001, V.11, p. 363-368.
28. A.N. Gorban, Popova T.G., Sadovsky M.G., Wunsch D.C. Information content of the frequency dictionaries, reconstruction, transformation and� classification of dictionaries and genetic texts. Smart Engineering System Design, 2001, V.11, p. 657-663.
29. A.N.Gorban, I.V.Karlin, P.Ilg and H.C.Ottinger Corrections and enhancements of quasi-equilibrium states, J. Non-Newtonian Fluid Mech., 2001,� V.96(1-2), PP. 203-219.
30. A.N. Gorban, Karlin I.V., Ottinger H.C., Tatarinova L.L. Ehrenfest's argument extended to a formalism of nonequilibrium thermodynaics, Phys. Rev. E. 2001, V. 63. 066124.
31. A.N. Gorban, Gorbunova K.O., Wunsch D.C. Liquid Brain: The Proof of Algorithmic Universality of Quasichemical Model of Fine-Grained Parallelism, Neural Network World, 2001, No. 4. P P. 391-412.
32. A.N. Gorban, Zinovyev A. Yu. Method of Elastic Maps and its Applications in Data Visualization and Data Modeling. International Journal of Computing Anticipatory Systems, CHAOS. 2001. V. 12. PP. 353-369.
33. V.A. Dergachev, Gorban A.N., Rossiev A.A., Karimova L.M., Kuandykov E., Makarenko N.G., Steier. The filling of gaps in geophysical time series by artificial neural networks, Radiocarbon, 2001, V. 43, No. 2, PP. 343-348.
34. A.N.Gorban, V.P.Torchilin, M.V.Malyutov, M. Lu Modeling polymer brushes protective action ,� Simulation in Industry' 2000. Proceedings of 12-th� European Simulation Symposium ESS'2000. September 28-30, 2000, Hamburg, Germany. A publication of the Society of Computer Simulation� International. Printed in Delft, The Netherlands, 2000. PP. 651-655.
35. A.N.Gorban, Neuroinformatics: What are us, where are we going, how to measure our way? Informacionnye technologii, 2000, 4. - С. 10-14.
36. A.N. Gorban, K. O. Gorbunova, Liquid Brain: Kinetic Model of Structureless Parallelism, Internation Journal of Computing Anticipatory Systems, CHAOS, V. 6, 2000, P.117-126.
37. A.N. Gorban, I.V. Karlin, V.B. Zmievskii and S.V. Dymova, Reduced description in reaction kinetics, Physica A, 2000. V. 275, No. 3-4, PP. 361-379.
39. A.N. Gorban, A.A Rossiev, Neural network iterative method of principal curves for data with gaps, �J Comput Sys Sc Int, 38 (5): 825-830, 1999.
40. A.N. Gorban, I.V.Karlin and� V.B.Zmievskii, Two-step approximation of space-independent relaxation, Transp.Theory Stat.Phys., 1999. V. 28(3), PP. 271-296.
41. A.N. Gorban, Approximation of Continuous Functions of Several Variables by an Arbitrary Nonlinear Continuous Function of One Variable, Linear Functions, and� Their Superpositions. Appl. Math. Lett., 1998. V. 11, No. 3, pp. 45-49.
44. A.N. Gorban, Neuroinformatics and applications, Otkrytye sistemy (Open Systems), 1998, No. 4-5. pp. 36-41.
45. A.N. Gorban, I.V. Karlin, Sroedinger operator in a overfull set ,� Europhys. Lett., 1998, V. 42, No.2, pp. 113-117.
46. I.V. Karlin, A. N. Gorban, S. Succi, V.� Boffi, Maximum Entropy Principle for Lattice Kinetic Equation ,� Physical Review Letters, 1998, V. 81, No. 1, pp. 6-9.
47. �A.N. Gorban, Yeugenii M. Mirkes and Donald Wunsch, High Order Orthogonal Tensor Networks: Information Capacity and Reliability, Proc. IEEE/INNS International Conference on Neural Networks, Houston, IEEE, 1997, pp. 1311-1314.
48. A.N. Gorban, Masha Yu. Senashova and Donald Wunsch, Back-Propagation of Accuracy, Proc. IEEE/INNS International Conference on Neural Networks, Houston, IEEE, 1997, pp. 1998-2001.
49. N.N. Bugaenko, A. N. Gorban, M.G.Sadovskii, Information content of nucleotid sequences and their fragments. Biofizika. 1997. V. 42, Iss. 5, pp. 1047-1053.
51. A.N. Gorban, I.V.Karlin, Scattering rates versus moments: Alternative Grad equations, Phys. Rev. E, 1996, 54(4), R3109.
52. A.N. Gorban, I.V.Karlin, Short-Wave Limit of Hydrodynamics: A Soluble Example, Phys. Rev. Lett., 1996, V. 77, N. 2, P. 282-285.
53. N.N. Bugaenko, A.N. Gorban, M.G. Sadovskii, Information content in nucleotide sequences, Mol Biol, 30 (3): 313-320, 1996.
54. A.N. Gorban, T.G. Popova, M.G. Sadovskii, Human virus genes are less redundant than human genes, Genetika, 32 (2), 289-294, 1996.
55. A.N. Gorban, I.V.Karlin, V.B.Zmievskii, T.F.Nonnenmacher, Relaxational trajectories: global approximations, Physica A, 1996, V.231, No.4, p.648-672.
56. A.N. Gorban, D.N.Golub, Multi-Particle Networks for Associative Memory, Proc. of the World Congress on Neural Networks, Sept. 15-18, 1996, San Diego, CA, Lawrence� Erlbaum Associates, 1996, pp. 772-775.
57. S.E. Gilev, A. N. Gorban, On Completeness of the Class of Functions Computable by Neural Networks, Proc. of the World Congress on Neural Networks, Sept. 15-18, 1996,� San Diego, CA, Lawrence Erlbaum Associates, 1996, pp. 984-991.
58. A.N. Gorban, D.A. Rossiyev, E.V. Butakova, S.E. Gilev, S.E. Golovenkin, S.A. Dogadin, D.A. Kochenov, E.V. Maslennikova, G.V. Matyushin, Y.E. Mirkes, B.V. Nazarov, Medical and Physiological Applications of MultiNeuron Neural Simulator. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.
59. M.G. Dorrer, A.N. Gorban, A.G. Kopytov, V.I. Zenkin, Psychological Intuition of Neural Networks. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.
60. A.N. Gorban, C. Waxman, Neural Networks for Political Forecast. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.
61. A.N. Gorban, T.G. Popova, M.G. Sadovskii, Redundancy of genetic texts, Mol Biol, 28 (2), 206-213, 1994.
62. A.N. Gorban, T.G. Popova, M.G. Sadovskii, Correlation approach to comparing nucleotide-sequences, Zh Obshch Biol, 55 (4-5), 420-430, 1994.
63. A.N. Gorban, I.V. Karlin, General approach to constructing models of the Boltzmann equation, Physica A, 206 (1994), 401-420.
64. A.N. Gorban, I.V. Karlin, Method of invariant manifolds and regularization of acoustic spectra, Transport Theory and Stat. Phys., 23, 559-632, 1994.
65. A.N. Gorban, E.M. Mirkes, T.G. Popova, M.G. Sadovskii, A new approach to the investigations of statistical properties of genetic texts, Biofizika 38 (5), 762-767, 1993.
66. A.N. Gorban, E.M. Mirkes, T.G. Popova, M.G. Sadovskii, The comparative redundancy of genes of various organisms and viruses, Genetika 29 (9), 1413-1419, 1993.
67. A.N. Gorban, I.V.Karlin, Structure and Approximations of the Chapman-Enskog Expansion for Linearized Grad Equations, Transport Theory and Stat.Phys, V.21, No 1&2,� P.101-117, 1992.
68. V.I. Verbitskii, A.N. Gorban, Jointly dissipative operators and their applications, Siberian Math J, 33 (1), 19-23, 1992.
69. A.N. Gorban, E.M. Mirkes, A.P. Svitin, Method of multiplet covering and its application for the prediction of atom and molecular-properties, Zh Fiz Khim, 66 (6): 1504-1510, 1992.
70. V.I. Bykov, V.I. Verbitskii, A.N. Gorban, Evaluation of cauchy-problem solution with inaccurately given initial data and the right part, Izv Vuz Mat, (12), 5-8, 1991.
71. A.N. Gorban, V.I.Verbitsky, Simultaneously Dissipative Operators and Quasi-Thermodynamicity of the Chemical Reactions Systems, Advances in Modelling and Simulation, 1992, V.26,� N1, p.13-21.
72. N.N. Bugaenko, A. N. Gorban, I.V.Karlin� Universal Expansion of the Triplet Distribution Function, Teoreticheskaya i Matematicheskaya Fisica, V.88, No.3, P.430-441(1991).
73. A.N. Gorban, I.V.Karlin, Approximations of the Chapman-Enskog Expansion, Zh.Exp.Teor.Fis., V.100, No.4(10), P.1153-1161(1991); Sov. Phys. JETP, V.73(4),� P.637-641.(1991).
74. S.Ye. Gilev, A. N. Gorban and E.M. Mirkes, Small Experts and Internal Conflicts in Learnable Neural Networks, Doklady Acad. Nauk SSSR, V.320, No.1, (1991) P.220-223.
75. A.N. Gorban, E.M. Mirkes, A.N. Bocharov, V.I. Bykov,� Thermodynamic consistency of kinetic data, Combust Explosion & Shock, 25 (5), 593-600, 1989.
76. V.I. Verbitskii, A.N. Gorban, G.S. Utiubaev, Y.I. Shokin, Moores effect in interval spaces, Dokl Akad Nauk SSSR, 304 (1), 17-21 1989.
77. A.N. Gorban, M.G. Sadovskii, Optimal strategies of spatial-distribution - Olli effect, Zh Obshch Biol 50 (1), 16-21, 1989.
78. A.N. Gorban, K.R.Sedov and� E.V.Smirnova, Correlation Adaptometry as a Method for Measuring the Health, Vestnik Acad. Medic. Nauk SSSR, No.5, P.69-75(1989).
79. V.I.Bykov, A. N. Gorban, A Model of Autooscillations in Association Reactions, Chem.Eng.Sci., V.42, No.5, P.1249-1251(1987).
80. A.N. Gorban, M.G.Sadovskii, Evolutionary Mechanisms of Creation of Cellular Clusters in Flowrate Cultivators, Biotechnology and Biotechnics, No.5, P.34-36(1987).
81. V.I.Bykov, A. N. Gorban, G.S.Yablonskii. Thermodynamic Function Analogue for Reactions Proceeding Without Interactions of Various Substances, Chem.Eng.Sci., V.41, No.11, P.2739-2745 (1986).
82. V.I. Bykov, S.E. Gilev, A.N. Gorban, G.S. Yablonskii, Imitation modeling of the diffusion on the surface of a catalyst, Dokl Akad Nauk SSSR, 283 (5): 1217-1220 1985.
84. V.I. Bykov, A.N. Gorban, T.P. Pushkareva, Autooscillation model in reactions of the association, Zh Fiz Khim, 59 (2): 486-488, 1985.
85. A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Description of non-isothermal reactions using equations of nonideal chemical-kinetics, Kinet Catal, 24 (5), 1055-1063, 1983.
87. V.I. Bykov, A.N. Gorban, Quasithermodynamic characteristic of reactions without the reaction of different substances, Zh Fiz Khim, 57 (12), 2942-2948, 1983.
88. V.I. Bykov, A.N. Gorban, G.S. Yablonskii, Description of non-isothermal reactions in terms of Marcelin-De-Donder kinetics and its generalizations, React Kinet Catal Lett, 20 (3-4), 261-265, 1982.
89. S.E. Gilev, A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Simulative modeling of processes on a catalyst surface, Dokl Akad Nauk SSSR, 262 (6), 1413-1416, 1982.
90. V.I. Elokhin, G.S. Yablonskii, A.N. Gorban, V.M. Ceresiz, Dynamics of chemical-reactions and non-physical steady-states, React Kinet Catal Lett, 15 (2), 245-250, 1980.
91. A.N. Gorban, G.S. Yablonskii, On one unused possibility in the kinetic experiment design, Dokl Akad Nauk SSSR, 250 (5): 1171-1174, 1980.
92. A.N. Gorban, V.I. Bykov, G.S. Yablonskii, The Path to Equilibrium, Intern. Chem. Eng. V.22, No.2, P.386-375(1982).
93. A.N. Gorban, V.M.Ceresiz, Slow Relaxations of Dynamical Systems and Bifurcations of Omega-Limit Sets, Soviet Math. Dokl., V.24, P.645-649(1981).
94. A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Macroscopic Clusters Induced by Diffusion in Catalytic Oxidation Reactions, Chem. Eng. Sci., 1980. V. 35, N. 11. P. 2351-2352. .
95. A.N. Gorban, V.I.Bykov, V.I.Dimitrov. Marcelin-De Donder Kinetics Near Equilibrium, React. Kinet. Catal. Lett., V.12, No.1, P.19-23(1979).
97. A.N. Gorban, Invariant Sets for Kinetic Equations, React. Kinet. Catal. Lett., 1979, V.10, P.187-190.
98. A.N. Gorban, Sets of Removable Singularities and Continuous Mappings, Siberian Math. Journ., V.19, P.1388-1391(1978).
99. A.N. Gorban, V.B. Melamed, Certain properties of Fredholm analytic sets in Banach-spaces, Siberian Math J, 17 (3), 523-526, 1976.
A collection of methods for construction of slow invariant manifolds has been developed, in particular the analogue of Kolmogorov-Arnold-Moser methods for dissipative systems. The nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from reversible dynamics, for Knudsen numbers� near one, was obtained.
The theory of simultaneously dissipative operators and tools for global stability analysis were developed. An explicitly solvable mathematical model for estimating the maximum efficiency of turbines in a free (non-ducted) fluid was obtained. This result can be used for hydropower turbines where construction of dams is impossible or undesirable.
A family of fast training algorithms for neural networks and generalized technology of extraction of explicit knowledge from data was developed. These algorithms are now in use in medical expert systems and in anti-terrorism security systems in Russia (the system "Voron").
The geometric seven-cluster structure of the genome was discovered.
The Geometry of Irreversibility. A new general geometrical framework of nonequilibrium thermo-dynamics will be developed. Our approach is based on constructive methods of invariant manifolds elaborated during the past two decades. The new methods allow us to solve the problem of macro-kinetics even when there are no autonomous equations of macro-kinetics. These methods will be elaborated together with computational algorithms. Each step of these algorithms should be physically consistent. The notion of the invariant film of non-equilibrium states, and the method of its approximate construction transform the problem of nonequilibrium kinetics into a series of problems of equilibrium statistical physics. The main specific problem for application of developed methods will be the problem of dynamic memory appearance in macromolecular complexes. Such memory effects may be important for chromatin dynamics and its role in functional nuclear organization. Spatio-temporal organization of chromatin will be studied.
Two scientific contacts determined my scientific work during 1971-1975: Prof. V.P. Mikheev (technical sciences) and Prof. V.B. Melamed (functional analysis). With Prof. Mikheev we created models of contact net and contact devices and developed new stations for technical diagnosis. Perhaps the main results of our collaboration are: stations for technical diagnosis that were in use on the USSR railways, new methods for modeling of� the dynamics of contact net and contact devices, and applied software for implementation of these methods.
Prof. Melamed was from the Voronezh mathematical school. We introduced the notion of a Fredholm analytic subset of Banach space as a subset that admits a local representation by a set of zeros of an analytic mapping whose differential is Fredholm. The maximum modulus principle and an analogue of the Remmert-Stein theorem were proved.
Global constraints for the dynamics of systems follow from the well-known local thermodynamic constraints.� If a chemical system is one-dimensional (the number of different substances is equal to the number of independent balances plus one), then the equilibrium encircling is impossible. Such systems move monotonically to their equilibrium states, if external conditions are equilibrium.� If the dimension of the system is greater than one, then this monotonicity may be broken.� The effects of �equilibrium encircling� appear. The exact thermodynamic boundaries for the maximal amplitudes of these effects were found. The search for boundaries of the equilibrium encircling is based on the analysis of Lyapunov function trees in the balance polyhedra. The constructive theory of trees of convex functions in convex polyhedra was developed. These results were summarized in the book Equilibrium Encircling: Equations of Chemical Kinetics and their Thermodynamic Analysis (Novosibirsk, Nauka Publ., 1984).
A systematic analysis of singularities of transition processes in general dynamical systems was also undertaken.� Dynamical systems depending on parameter were studied and a system of relaxation times was constructed. Each relaxation time depends on three variables: initial conditions, parameters of the system and accuracy e of relaxation. The singularities of the relaxation times as functions of initial data and parameters under fixed e were studied, leading to a classification of different bifurcations (explosions). The relationship between the singularities of relaxation times and bifurcations of limit sets was investigated. The peculiarities of transition processes under perturbations were studied. It was shown that perturbations simplify the situation: the interrelations between the singularities of relaxation times and other peculiarities of dynamics for general dynamical system under small perturbations are the same as for smooth two-dimensional structurally stable systems. These results were summarized in my PhD thesis (1980).
Does the dynamics of distributed systems which models biological evolution always lead to a discrete distribution? (In the biological context this question can be reformulated as follows: is natural selection really effective if the initial diversity is sufficiently rich?)� In order to answer this question, a theory of special dynamical systems in the space of Radon measures on compact space was developed.� These are systems with a specific conservation law: the conservation of support of measures. There are characterization theorems for omega-limit points, and different theorems about efficiency of natural selection. The qualitative picture of these results was summarized in the book: Demon of Darwin. The Idea of Optimality and Natural Selection, A.N. Gorban, R.G. Khlebopros (Nauka Pub. Moscow, 1988, 208 pp). A short review of these results was given in the talk �Optimality, adaptation and natural selection - the mathematical way to separate sense from nonsense�, available on-line at http://mystic.math.neu.edu/gorban/evolution.pdf .
This abstract theory has found very practical application. My former PhD student, E. V. Smirnova (now Professor Smirnova) discovered that the approximate dimension of the cloud of physiological data of a group precisely characterizes the level of adaptation of this group to the living conditions: when the group members exhaust their adaptation resource then the dimension usually decreases.� It decreases usually, but not always.� Sometimes the dimension goes another way. We explained the effect, and, on the other hand, predicted the exclusions. The results were confirmed by thousands of experiments with different populations and groups: from human to plants and fungi. Now the developed concept of correlation adaptometry is in use for monitoring needs in Siberia and Far North.
In 1985 I stated the problem of effective parallelism as a main problem for our group for the next decade. In 1986 V. Okhonin (former PhD student) published a new algorithm for training neural networks (for synchronized and non-synchronized networks, for discrete and continuous time, for systems with delays in time, and for many other cases).� The central idea was the flexible use of duality (it is a rather usual step in optimization methods). (At the same time, Rumelhart D.E., Hinton G.E., Williams R.J. published a particular case of this algorithm that became famous under the name �back propagation of errors�.) For several years we tried to make the training algorithms faster, and network skills more stable. During an interval of fifteen years (1987-2002) we developed a generalized technology of extraction of explicit knowledge from data.� This technology was implemented in a series of software libraries and allowed us to create dozens of knowledge-based expert systems in medical and technical diagnosis, ecology and other fields.
On the base of this approach, the Russian Close Corporation "Applied Radiophysics - Security Systems" developed neural network-based security systems (1997 � 2003). This Russian system "Voron" was the laureate of the international exhibition "Frontier-2000" (see http://etic-m.narod.ru/company.htm, http://www.grand-prix.ru/catalogue/perimeter/voron/solution/ (in Russian).
The results were summarized in several monographs, 16 PhD theses were submitted, and 3 scientists prepared Doctor of Science degrees. The developed software is in widespread use in the former USSR, and our lab in Krasnoyarsk now serves as the Russian National Center for Neuroinformatics and Neurocomputing.
The concept of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We developed constructive methods of invariant manifolds for model reduction in physical and chemical kinetics. The physical problem of a reduced description is studied in the most general form as a problem of constructing the slow invariant manifold. A collection of methods to derive analytically and to compute numerically the slow invariant manifold is elaborated. Among them, iteration methods based on incomplete linearization, relaxation methods and the method of invariant grids have been developed. The systematic use of thermodynamic structures and of the quasi-chemical representation allows us to construct approximations which are consistent with physical restrictions at each step.
Is it possible to study the genetic text on the same way as A. Kolmogorov studied poetry? Is there a footprint of biological sense in statistical features of the genome? This question needs to be carefully solved. The result may be positive or negative.� Nevertheless, we should study this problem.� We have investigated a numbe of questions in this direction.
Some positive results have been obtained and published during the past fourteen years. In particular, the clear seven-cluster structure of genome was identified. We studied cluster structure of several genomes in the space of olygomer frequencies. The result: many complete genomic sequences were analyzed, using visualization of tables of triplet counts in a sliding window. The distribution of 64-dimensional vectors of triplet frequencies displays a well-detectable cluster structure. The structure was found to consist of seven clusters, corresponding to protein-coding information in three possible phases in one of the two complementary strands and in the non-coding regions. Awareness of the existence of this structure allows development of methods for the segmentation of sequences into regions with the same coding phase and non-coding regions. This method may be completely unsupervised.

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