Address: Department of Mathematics, University of Leicester, University
Road, Leicester LE1 7RH, United Kingdom
Institute of Computational Modeling, Russian Academy of Sciences,
Krasnoyarsk-36, 660036, Russia.
E-mail: ag153@le.ac.uc , gorban@icm.krasn.ru
Full Professor in Modeling & Simulation
Russian State Certificate of Professorship, 1993
Research interests:
Dynamics of systems of
physical, chemical and biological kinetics;
Bioinformatics;
Human adaptation to hard
living conditions;
Architecture of
neurocomputers and training algorithms for neural networks.
Education:
·
Doctor of Physics & Math (Biophysics), (Advanced doctoral degree,
Dr. Sc., analogue of Dr Habilit.), 1990, Institute of Biophysics, Krasnoyarsk.
Thesis: "Extremal Principles and a priori Estimations in Biological and
Formal Kinetics";
·
PhD in Physics & Math (Differential Equations & Math.Phys),
1980, Kuibyshev State University and Pedagogical Institute. Thesis: "Slow
Relaxations and Bifurcations of Omega-Limit Sets of Dynamical Systems";
·
Diploma, 1973 (Master degree equivalent), Omsk Pedagogical Institute
(Physical Department and Mathematics Department). Thesis: Sets of Removable
Singularities in Banach Spaces and Continuous Mappings;
·
Novosibirsk State University (Physics), 1967-1970;
·
Novosibirsk Special School for Physics & Mathematics, 1965-1967.
Current Employment
Applied Mathematics Chair, University of Leicester
|
Name and
Address of Current Employe |
Job Title |
|
Dept. of Mathematics, University of Leicester, University Road, LE1
7RH, United Kingdom |
Chair in Applied Mathematics (2004-present) |
|
Institute of
Computational Modeling, Russian Academy of Sciences, Akademgorodok,
Krasnoyarsk-36, 660036, Russia |
Head of
Nonequilibrium Systems Laboratory (1989 – present) and Computer Sciences
Department (1995 – present), Deputy Director (1995 – 2004) |
|
Krasnoyarsk
State Technical University, 26 Kirensky St., Krasnoyarsk, 660074, Russia |
Professor, Head
of Neurocomputers Chair (part-time, 50%) (1993 – present) |
Employment History:
Institute of Computational Modeling, Russian Academy of Sciences,
Siberian Branch (formerly Computing Center of the USSR Academy of Sciences,
Siberian Branch), Krasnoyarsk, Russia:
·
Deputy Director and Head of the Computer Sciences Department, 1995 –
present;
·
Head of the Nonequilibrium Systems Laboratory, 1989 - present
·
Senior researcher, 1983-1989;
·
Junior researcher, 1978-1983;
Institute of Catalysis, USSR Academy of Sciences, Siberian Branch,
Novosibirsk, Russia:
·
Engineer, 1977-1978;
Institute of Theoretical & Applied Mechanics, USSR Academy of
Sciences, Siberian Branch, Novosibirsk, Russia:
·
Engineer, 1978;
Tomsk Polytechnic Institute, Laboratory of Kinetics, Tomsk, , Russia:
·
Junior researcher, 1977;
Omsk State University, Laboratory of Kinetics, Omsk, Russia:
·
Junior researcher, 1976;
Omsk Railway Engineering Institute, Research Division, Omsk, Russia:
·
Engineer, 1973-1976.
Part-time:
Krasnoyarsk State Technical University, Krasnoyarsk, Russia:
·
Head of Neurocomputers Chair, 1993-present;
Swiss Federal Institute of technology (ETH), Zurich, Switzerland):
·
Senior Researcher, 2003-2004;
Krasnoyask State Technological University, Krasnoyarsk, Russia::
·
Professor, Department of Automatization and Robots, 1993-2003;
Krasnoyarsk State University, Krasnoyarsk, Russia:
·
Professor, Psychological Department, 1998-2001;
·
Associate professor, Higher Mathematics Chair, 1981-1989;
·
Associate professor, Psychological Department, 1989-1991;
Omsk Pedagogical Institute, Omsk, Russia:
·
Advisor of the Omsk Physical & Mathematical School, 1972-1976.
Visiting:
·
Clay Mathematics Institute (Cambridge, USA), 03.2000-08.2000;
·
Northeastern University (Boston, USA), 03.2000-05.2000;
·
Courant Mathematics Institute (New York, USA), 04.2000;
·
Institut des Hautes Etudes Scientiques (IHES, Paris, France),
10.2000-12.2000, 07.2001-08.2001,11.2002-12-2002, 09.2003;
·
Swiss Federal Institute of technology (ETH, Zurich, Switzerland),
05.1999-06.1999, 08.2000-09.2000, 03.2002-06.2002.
Expert positions:
·
Vice-Chairman of Scientific Council at Krasnoyarsk State Technical
University (direction: Software and tools for mathematical modeling)
(1999-present);
·
Head of Workgroup on Neurocomputing, Ministry of Science and Technology
Russian Federation (1998-2000);
·
Vice-Chairman of Expert Council Krasnoyarsk Regional Science Foundation
(1993-1996);
·
Chairman of the Analytic Games Committee, Krasnoyarsk (1989-1994);
·
Member of Jury of USSR National competition in mathematics for students
of technical universities (1986-1990).
·
Full member of Russian Psychological Association (1989);
·
Director of Krasnoyarsk International AMSE Center (Association for the Advancement
of Modeling and Simulation Techniques in Enterprises) (1990);
·
Active member of International Informatization Academy (1994);
·
Member of Advisory Board of the Russian Neural Networks Society
(1990-present);
·
Associated Member of ASME (American Society of Mechanical Engineers)
(1997);
·
Member of Association CHAOS (Centre for Hyperincursion and Anticipation
in Ordered Systems) (2000);
·
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.
Organizer of:
·
International Workshop "Invariance and Model Reduction for
Multiscale Phenomena", Zurich, August, 2003;
·
USA-NIS Neurocomputing Opportunities Workshop, Washington, DC, July
1999, (Sponsored by the National Science Foundation of the USA and Applied
Computational Intelligence Lab, TTU) (Co-Chair);
·
Russian National Conference “Neurionformatics” (1998-2003);
·
Russian National Workshops “Neuroinformatics and Application” I-XII,
Krasnoyarsk, October 1992- October 2003);
·
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.
Grants and awards:
·
Prigogine Prize and Medal (2003, International Informatization Academy,
this Academy is in general consultative status of the United Nations from 1995,
Headquarters: New York, Geneva, Moscow, Montreal);
·
Clay Scholar, (Clay Mathematics Institute, Cambridge, USA, 2000);
·
Russian Federal Grant of the “Integration” program, 4 times
(1998-2003);
·
Grant of Russian Federal subprogram “New Information Processing
Technology” (1999);
·
Soros Professor (grant of International Science Foundation) (1998);
·
Russian Federal Fellowship for outstanding scientists, twice (6 years);
·
Grant of Russian Foundation of Basic Research (1996-1998);
·
Grants of Regional Scientific Foundation, Krasnoyarsk, Russia, 4 times
(1997-2001);
·
1994-1996 American Mathematical Society Fellowship.
Scientific advisor of 22 PhD thesis
and 3 Dr. Habilit. (Dr. Sc.), including:
·
E.M. Mirkes, The structure and functioning of ideal neurocomputer (Dr.
Habilt., Computer Science, 2002);
·
E.V. Smirnova, Measurement and modeling of adaptation (Dr. Habilt.,
Modeling in Biophysics, 2001);
·
D.A. Rossiev, Neural networks based expert systems for medical diagnostics (Dr. Habilt., Biophysics, 1997);
·
A.Yu. Zinovyev, Method of Elastic Maps for Data Visualization:
Algorithms, Software and Applications in Bioinformatics (PhD, Computer Science,
2001);
·
V.G. Tzaregorodtzev, Algorithms, technology and software for knowledge
extraction using trainable neural networks (Ph. D., Computer Science, 2000);
·
A.A. Pitenko, Neural networks for geoinformatics (Ph. D., Computer
Science, 2000);
·
A.A. Rossiev, Neural network modeling of data with gaps (Ph. D.,
Computer Science, 2000);
·
M.Yu. Senashova, Accuracy estimation for neural networks (Ph. D.,
Computer Science, 1999);
·
M.A.Dorrer, Psychological intuition of neural networks (Ph. D.,
Computer Science, 1999);
·
I.V. Karlin, Method of invariant manifold in physical kinetics, (PhD,
Physics, 1991);
·
V.I.Verbitsky, Simultaneously dissipative operators and global
stability (PhD, Mathematical Analysis, 1989);
·
M.G. Sadovskii, Optimization in space distributions of populations,
(PhD, Biophysics, 1989);
·
V.A. Okhonin, Kinetic equations for population dynamics (PhD,
Biophysics, 1986).
Leader of 18 full-scale
Analytic Games, including:
"Project of a Free Economic Zone for the Leningrad Region"
(Leningrad, September 1990);
"Problems of Russian Culture" (Krasnoyarsk, June 1991);
"Critical Situations in a Transfer to Market" (Krasnoyarsk,
December 1990).
Co-organizer of 15
Krasnoyarsk Summer Schools for Talented Children,
Organizer of 2 Tobolsk
Summer Schools for Talented Children.
Selected Publications
Monographs (in reverse
chronological order):
1. Invariant
Manifolds for Physical and Chemical Kinetics, Springer Verlag, Lecture Notes in
Physics, Berlin-Heidelberg-NewYork, 2004. 498 p. (With I.V. Karlin);
2. Singularities of
transition processes in dynamical systems: Qualitative theory of critical
delays, Electron. J. Diff. Eqns., Monograph 05, 2004, (55 pages). Online: http://ejde.math.swt.edu/Monographs/05/abstr.html
3. Thermodynamic
equilibria and extremes: Analysis of thermodynamic accessible regions and
partial equilibria in physical, chemical, and technical systems. Novosibirsk,
Nauka Publ., 2001, 296 p. (With B.M. Kaganovich, S.P. Fillipov)
4. Neuroinformatics,
Novosibirsk, Nauka Publ., 1998, 258 p. (With W.L.Dunin-Barkovskii, D.A.Rossiev,
S.A.Terehov).
5. Methods of
neuroinformatics, Krasnoyarsk State University Press, 1998, 205 p. (A.N.Gorban
ed.)
6. Neural networks
on PC, Novosibirsk, Nauka Publ., 1996, 276 p. (With D.A.Rossiev). [In Russian,
Russian title “Neironnye seti na personal’nom komp’yutere”]
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).
9. Training of
Neural Networks, Moscow, USSR-USA JV "ParaGraph", 1990, 160 p. [In
Russian, Russian title “Obuchenie neironnyh setei”]
10. Demon of Darwin.
The Idea of Optimality and Natural Selection, Nauka Pub., Moscow, 1988, 208p.
(With R.G.Khlebopros). http://ddarwin.narod.ru
11. Essays on
Chemical relaxation, Novosibirsk, Nauka Publ., 1986, 316 p. (With V.I.Bykov,
G.S.Yablonskii);
12. Equilibrium
Encircling. Equations of Chemical Kinetics and their Thermodynamic Analysis,
Novosibirsk, Nauka Publ., 1984, 256 p. [In Russian, Russian title “Obkhod
Ravnovesiya”]
13. Kinetic models of
heterogeneous catalytic reactions, Novosibirsk, Nauka Publ., 1983, 256 p. (With
V.I.Bykov, G.S.Yablonskii).
Articles
(in
reverse chronological order):
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.
9. A.N. Gorban and
I. V. Karlin, Family of additive entropy functions out of thermodynamic limit, Phys. Rev. E. 2003, V.67, 016104,
E-print: http:, arXiv.org/abs/cond-mat/0205511
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. Öttinger, 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.
14. A.N. Gorban, T.G
Popova, M.G Sadovsky, Classification of nucleotide sequences over their
frequency dictionaries reveals a relation between the structure of sequences
and taxonomy of their bearers, Zh Obshch
Biol 64 (1), 65-77. 2003
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).
21. I.V. Karlin and
A.N. Gorban, Hydrodynamics from Grad's equations: What can we learn from exact
solutions? Ann. Phys. (Leipzig) 10-11
(2002), pp. 783-833. E-print: http:,
arXiv.org/abs/cond-mat/0209560
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.
38. A.N Gorban, The
generalized Stone approximation theorem for arbitrary algebras of continuous
functions, Dokl Akad Nauk, 365 (5),
586-588, 1999
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.
42. S.E. Gilev, A.N.
Gorban, The completeness theorem for semigroups of continuous functions, Dokl Akad Nauk, 362 (6): 733-734, 1998
43. N.N.Bugaenko, A.
N. Gorban, M.G.Sadovskii, Maximum entropy method in analysis of genetic text
and measurement of its information content , Open systems and information
dynamics. #5, 1998. - pp.265-278.
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.
50. V.I. Bykov, A.N.
Gorban, S.V. Dymova, Method of invariant manifolds for the reduction of kinetic
description, ACH-Models Chem 134 (1):
83-95 1997
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.
83. V.I. Bykov, A.N.
Gorban, Simplest model of self-oscillations in association reactions, React Kinet Catal Lett, 27 (1): 153-155
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.
86. V.I. Bykov, A.N.
Gorban, L.P. Kamenshchikov, G.S. Yablonskii, Inhomogeneous stationary states in
reaction of carbon-monoxide oxidation on platinum, Kinet Catal, 24 (3), 520-524, 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).
96. A.N. Gorban,
Priori evaluation of the region of linearity for kinetic-equations, React Kinet Catal Lett, 10 (2), 149-152,
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.
Past Achievements and Future
Research
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.
Results
and Projects (1971-2004)
1.
The beginning (1971-1975)
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.
2.
Chemical kinetics and topological dynamics (1975-1980)
3.
Biological kinetics and functional analysis (1980-1990)
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.
4.
Neural networks (1985-now)
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.
5.
Physical Kinetics and Invariant Manifolds (1977-present)
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.
There are many
examples of applications: nonperturbative derivation of physically consistent
hydrodynamics from the Boltzmann equation and from reversible dynamics, for
Knudsen numbers Kn near one; construction of the moment equations for
nonequilibrium media and their dynamical correction in order to gain more
accuracy in the description of highly nonequilibrium flows; the kinetic theory
of phonons; model reduction in chemical kinetics; derivation and numerical
implementation of constitutive equations for polymeric fluids. A review of this
direction of work is now published in Physics Reports, and is available
on-line: http://arXiv.org/abs/cond-mat/0311017
6.
Bioinformatics and Geometry of Genome (1990-now)
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.