Address: Department of Mathematics, University of Leicester, University
Road, Leicester LE1 7RH, United Kingdom
Institute of Computational Modeling,
E-mail:
Full Professor in
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,
·
PhD in Physics & Math (Differential Equations
& Math.Phys), 1980,
·
Diploma, 1973 (Master degree equivalent), Omsk
Pedagogical Institute (Physical Department and Mathematics Department). Thesis:
Sets of Removable Singularities in Banach Spaces and Continuous Mappings;
·
·
Current Employment
Applied Mathematics Chair,
Name and
Address of Current Employe |
Job Title |
Dept. of Mathematics, |
Chair in Applied Mathematics (2004-present) Director of the Centre for Mathematical Modelling (2006-present) |
Employment History:
·
Chief Scientist, 2008-present (on leave);
·
Deputy Director and Head of the Computer Sciences
Department, 1995 – 2005;
·
Head of the Nonequilibrium Systems Laboratory, 1989
– 2008;
·
Senior researcher, 1983-1989;
·
Junior researcher, 1978-1983;
Institute of
·
Engineer, 1977-1978;
Institute of Theoretical & Applied
·
Engineer, 1978;
Tomsk Polytechnic Institute, Laboratory of Kinetics,
·
Junior researcher, 1977;
·
Junior researcher, 1976;
Omsk Railway Engineering Institute, Research Division,
·
Engineer, 1973-1976.
Part-time:
·
Head of Neurocomputers Chair, 1993-2006; Professor,
1993-2006 (and now on leave);
Swiss Federal Institute of technology (ETH),
·
Senior Researcher, 2003-2004;
·
Professor, Department of Automatization and Robots,
1993-2003;
·
Professor, Psychological Department, 1998-2001;
·
Associate professor, Higher Mathematics Chair,
1981-1989;
·
Associate professor, Psychological Department,
1989-1991;
·
Advisor of the
Visiting:
·
Clay Mathematics Institute (
·
Northeastern University (
·
Courant Mathematics Institute (
·
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,
Expert positions:
·
Vice-Chairman of Scientific Council at
·
Head of Workgroup on Neurocomputing, Ministry of
Science and Technology
·
Vice-Chairman of Expert Council
·
Chairman of the Analytic Games Committee,
·
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
·
Active member of
·
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 Research workshop: “Principal manifolds for data
cartography and dimension reduction” August 24-26, 2006,
·
International Workshop “Geometry of Genome: Unravelling of Structures Hidden in Genomic
Sequences,”
·
International Workshop “Model
Reduction and Coarse-Graining Approaches for Multiscale Phenomena,”
·
International Workshop "Invariance and Model
Reduction for Multiscale Phenomena,"
·
USA-NIS Neurocomputing Opportunities Workshop,
·
Russian annual National Conference
“Neurionformatics” (1998-present);
·
Russian annual National Workshops “Neuroinformatics
and Application,”
·
Russian annual National Workshops “Modeling of
Nonequilibrium Systems,”
·
Russian National Conference “Problems of Regional
Informatization”,
·
Soviet Union National competition in
Neuroinformatics and Neurocomputers for students and young scientists, 1991.
Grants and awards:
·
Elsevier
Most Cited in 2003-2006 Paper Award for the paper: Gorban, A.N.;Karlin, I.V., Method
of invariant manifold for chemical kinetics, Chem.
·
Mathematical
Modelling of Adaptation and Decision-Making in Neural Systems, The Royal
·
Modularity,
Abstraction and Robustness of Network Models in Molecular Biology,
·
EPSRC and LMS grants for the International Workshop “Model Reduction and Coarse-Graining
Approaches for Multiscale Phenomena,”
·
Prigogine Prize and Medal (2003,
·
Clay Scholar, (Clay Mathematics Institute,
·
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,
·
1994-1996 American Mathematical Society Fellowship.
Scientific advisor of 28 PhD thesis
and 3 Dr. Habilit. (Dr. Sc.), including:
·
David
Packwood Non-equilibrium dynamics of lattice-Boltzmann systems (Ph. D., Applied
Mathematics, University of Leicester, UK, 2012);
·
Jian
X. Zhang, nonequilibrium entropic filters for lattice Boltzmann methods and
shock tube case studies (Ph. D., Applied Mathematics, University of Leicester,
UK, 2011);
·
Hafiz Abdul Wahab, Quasichemical Models of
Multicomponent Nonlinear Diffusion (Ph. D., Applied Mathematics, University of Leicester, UK, 2011);
·
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
"Problems of Russian Culture" (Krasnoyarsk, June 1991);
"Critical Situations in a Transfer to Market" (Krasnoyarsk,
December 1990).
Co-organizer of 15
Organizer of 2 Tobolsk
Summer Schools for Talented Children.
Selected Publications
Monographs (in reverse
chronological order):
11. Kinetic
Models of Catalytic Reactions (Comprehensive
Chemical Kinetics, V.32, ed. by R.G. Compton), Elsevier,
Articles
(in
reverse chronological order):
1.
A.N. Gorban, G.S.Yablonsky, Extended
detailed balance for systems with irreversible reactions, Chemical Engineering Science 66 (2011)
5388–5399.
2.
A.N.
Gorban, H.P. Sargsyan and H.A. Wahab, Quasichemical
Models of Multicomponent Nonlinear Diffusion, Mathematical Modelling of Natural Phenomena, Volume 6 / Issue 05, (2011), 184−262.
3.
A.Gorban and S. Petrovskii, Collective dynamics: when one plus one does
not make two, Mathematical
Medicine and Biology (2011) 28, 85−88.
4.
A.N. Gorban and M. Shahzad, The Michaelis-Menten-Stueckelberg Theorem. Entropy 2011, 13, 966-1019.
5.
G. S. Yablonsky, A. N. Gorban, D. Constales, V. V. Galvita and G. B.
Marin, Reciprocal relations between kinetic curves, EPL,
93 (2011) 20004.
6.
A.N. Gorban, Self-simplification in Darwin’s Systems, In: Coping with Complexity: Model
Reduction and Data Analysis, A.N. Gorban and D. Roose (eds.), Lecture Notes in
Computational Science and Engineering, 75, Springer: Heidelberg – Dordrecht -
London -New York, 2011, pp. 311-344.
7.
D.J. Packwood, J. Levesley, and A.N. Gorban, Time
step expansions and the invariant manifold approach to lattice Boltzmann models,
In: Coping with Complexity: Model Reduction and Data Analysis, A.N. Gorban and
D. Roose (eds.), Lecture Notes in Computational Science and Engineering, 75,
Springer: Heidelberg – Dordrecht - London -New York, 2011, pp. 169-206.
8.
A.N. Gorban, Kinetic
path summation, multi-sheeted extension of master equation, and evaluation of
ergodicity coefficient, Physica A 390
(2011) 1009–1025.
9.
A.N. Gorban, L.I. Pokidysheva,·E,V. Smirnova, T.A.
Tyukina, Law of the Minimum Paradoxes, Bull
Math Biol 73(9) (2011), 2013-2044.
10.
A.N. Gorban, E.V. Smirnova, T.A. Tyukina, Correlations, risk and crisis: From physiology to
finance, Physica A, Vol. 389, Issue 16, 2010, 3193-3217.
11.
A.N. Gorban, A. Zinovyev, Principal manifolds and graphs in practice:
from molecular biology to dynamical systems, International Journal of
Neural Systems, Vol. 20, No. 3 (2010) 219–232.
12.
E. Chiavazzo, I.V. Karlin, A.N. Gorban, K. Boulouchos,
Coupling
of the model reduction technique with the lattice Boltzmann method, Combustion and Flame 157 (2010)
1833–1849
13.
Gorban A.N., Gorban P.A., Judge G. Entropy: The Markov Ordering Approach. Entropy. 2010; 12(5):1145-1193.
14.
AN. Gorban and V. M. Cheresiz, Slow Relaxations and Bifurcations of the
Limit Sets of Dynamical Systems. I. Bifurcations of Limit Sets, Journal
of Applied and Industrial Mathematics, 2010, Vol. 4, No. 1, pp. 54–64.
15.
A.N. Gorban and V. M. Cheresiz, Slow Relaxations and Bifurcations of the
Limit Sets of Dynamical Systems. II. Slow Relaxations of a Family of Semiflows, Journal
of Applied and Industrial Mathematics, 2010, Vol. 4, No. 2, pp. 182–190
16.
E. Chiavazzo, I.V. Karlin, and A.N. Gorban, The Role of Thermodynamics in Model Reduction
when Using Invariant Grids, Commun. Comput. Phys., Vol. 8, No. 4 (2010), pp. 701-734.
17.
Andrei Zinovyev, Nadya Morozova, Nora Nonne,
Emmanuel Barillot, Annick Harel-Bellan, Alexander N Gorban, Dynamical
modeling of microRNA action on the protein translation process, BMC Systems
Biology 2010, 4:13
(24 February 2010).
18.
A.N. Gorban, O. Radulescu, A. Y. Zinovyev, Asymptotology
of chemical reaction networks, Chemical Engineering Science 65 (2010)
2310–2324.
19.
A.N. Gorban, E.V. Smirnova, T.A. Tyukina, General
Laws of Adaptation to Environmental Factors: from Ecological Stress to
Financial Crisis. Math. Model.
Nat. Phenom. Vol. 4, No. 6, 2009, pp. 1-53.
20.
A.N. Gorban, A. Y. Zinovyev, Principal
Graphs and Manifolds, Chapter 2 in: Handbook of Research on Machine Learning
Applications and Trends: Algorithms, Methods, and Techniques, Emilio Soria
Olivas et al. (eds), IGI Global, Hershey, PA, USA,
2009, pp. 28-59.
21.
E. Chiavazzo, I. V. Karlin, A. N. Gorban and K
Boulouchos, Combustion simulation via lattice Boltzmann
and reduced chemical kinetics, J. Stat. Mech. (2009) P06013,
22.
Ovidiu Radulescu, Alexander N Gorban, Andrei
Zinovyev, and Alain Lilienbaum Robust simplifications of
multiscale biochemical networks, BMC Systems Biology 2008, 2:86 doi:10.1186/1752-0509-2-86.
23.
A.N. Gorban and O. Radulescu, Dynamic and Static Limitation
in Multiscale Reaction Networks, Revisited, Advances in Chemical Engineering 34 (2008), 103-173.
24.
A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No.
4, 2007, pp. 1-45.
25.
R. A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice
Boltzmann methods, Physica
A: Statistical Mechanics and its Applications Volume 387, Issues 2-3, 15 January 2008, Pages 385-406 .
26.
A.N. Gorban and O.
Radulescu, Dynamical robustness of biological networks
with hierarchical distribution of time scales, IET Syst. Biol., 2007, 1, (4), pp. 238–246.
27.
R. A. Brownlee, A. N. Gorban, and J.
Levesley, Stability and stabilization of the lattice Boltzmann method, Phys. Rev. E 75, 036711 (2007) (17 pages)
28.
A.N. Gorban and A.Y. Zinovyev The Mystery of Two
Straight Lines in Bacterial Genome Statistics, Bulletin of Mathematical Biology (2007)
29.
E. Chiavazzo, A.N. Gorban, and I.V. Karlin, Comparison
of Invariant Manifolds for Model Reduction in Chemical Kinetics, Commun. Comput. Phys. Vol. 2, No. 5 (2007),
pp. 964-992
30.
A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological
grammars for data approximation, Applied Mathematics Letters Volume
20, Issue 4 (2007), 382-386
31.
A.N. Gorban, Order–disorder
separation: Geometric revision, Physica A Volume
374, Issue 1 , 15 January 2007, Pages 85-102
32.
A.N. Gorban and O. Radulescu, Dynamical
robustness of biological networks with hierarchical distribution of time scales,
IET Syst. Biol., 2007, 1, (4), pp. 238–246
33.
R.A. Brownlee, A.N. Gorban, and J.
Levesley, Stabilization of the lattice Boltzmann method using the Ehrenfests'
coarse-graining idea, Phys. Rev. E 74, 037703 (2006)
34.
A.Gorban, I. Karlin, A. Zinovyev, Invariant Grids: Method of Complexity Reduction
in Reaction Networks, Complexus, V.
2, 110–127.
35.
A.N. Gorban, I.V. Karlin,
Quasi-Equilibrium Closure Hierarchies for the Boltzmann Equation, Physica A 360 (2006) 325–364
36.
A.Gorban, A. Zinovyev, Elastic Principal
Graphs and Manifolds and their Practical Applications, Computing 75, 359–379 (2005),
37.
A.N. Gorban, I.V. Karlin, Invariance correction to Grad's equations:
Where to go beyond approximations? Continuum
Mechanics and Thermodynamics, 17(4) (2005), 311–335,
38.
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.
39.
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.
40.
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.
41.
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.
42.
A.N. Gorban,
I.V. Karlin, A.Yu. Zinovyev, Invariant grids for reaction kinetics, Physica A, 333 (2004), 106--154.
43.
A.N. Gorban,
I.V. Karlin, Uniqueness of thermodynamic projector and kinetic basis of
molecular individualism, Physica A,
336, 3-4 (2004), 391-432.
44.
A.N. Gorban,
I.V. Karlin, Methods of nonlinear kinetics, in: Encyclopedia of Life Support
Systems, Encyclopedia of Mathematical
Sciences, EOLSS Publishers, Oxford,
2004.
45.
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.
46.
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
47.
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.
48.
A.N. Gorban,
I. V. Karlin, Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 58 (2003) 4751-4768.
49.
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.
50.
A.Gorban, A. Zinovyev,
T. Popova. Seven clusters in genomic triplet distributions. In Silico Biology. V.3 (2003), 471-482.
51.
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
52.
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.
53.
Gorban', Silantyev V. Riabouchinsky Flow with
Partially Penetrable Obstacle. Math.
Comput. Modelling 35 (2002), no. 13, 1365-1370.
54.
I.V. Karlin, M. Grmela, and A.N. Gorban: Duality in
nonextensive statistical mechanics, Phys.
Rev. E 65 (2002) 036128.
55.
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.
56.
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.
57.
A.N. Gorban and I. V. Karlin, Macroscopic dynamics
through coarse-graining: A solvable example, Phys. Rev. E. V 65. 026116(1-5) (2002).
58.
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
59.
A.N. Gorban, Zinov'ev A.Y.,
Pitenko A.A., Data vizualization. The method of elastic maps, Neirocompjutery, 2002, 4, 19-30.
60.
A.N. Gorban, A.A Rossiev, Iterative modeling of data
with gaps via submanifolds of small dimension, Neirocompjutery, 2002, 4, 40-44.
61.
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.
62.
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.
63.
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.
64.
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.
65.
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.
66.
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.
67.
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.
68.
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.
69.
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.
70.
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.
71.
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.
72.
A.N.Gorban, Neuroinformatics: What are us, where are
we going, how to measure our way? Informacionnye
technologii, 2000, 4. - С. 10-14.
73.
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.
74.
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.
75.
A.N Gorban, The generalized Stone approximation
theorem for arbitrary algebras of continuous functions, Dokl Akad Nauk, 365 (5), 586-588, 1999
76.
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.
77.
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.
78.
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.
79.
S.E. Gilev, A.N. Gorban, The completeness theorem
for semigroups of continuous functions, Dokl
Akad Nauk, 362 (6): 733-734, 1998
80.
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.
81.
A.N. Gorban, Neuroinformatics and applications, Otkrytye sistemy (Open Systems), 1998,
No. 4-5. pp. 36-41.
82.
A.N. Gorban, I.V. Karlin, Sroedinger operator in a
overfull set , Europhys. Lett., 1998, V. 42, No.2, pp. 113-117.
83.
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.
84.
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.
85.
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.
86.
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.
87.
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
88.
A.N. Gorban, I.V.Karlin, Scattering rates versus
moments: Alternative Grad equations, Phys.
Rev. E, 1996, 54(4), R3109.
89.
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.
90.
N.N. Bugaenko, A.N. Gorban, M.G. Sadovskii,
Information content in nucleotide sequences, Mol Biol, 30 (3): 313-320, 1996.
91.
A.N. Gorban, T.G. Popova, M.G. Sadovskii, Human
virus genes are less redundant than human genes, Genetika, 32 (2), 289-294, 1996.
92.
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.
93.
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.
94.
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.
95.
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.
96.
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.
97.
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.
98.
A.N. Gorban, T.G. Popova, M.G. Sadovskii, Redundancy
of genetic texts, Mol Biol, 28 (2), 206-213,
1994.
99.
A.N. Gorban, T.G. Popova, M.G. Sadovskii,
Correlation approach to comparing nucleotide-sequences, Zh Obshch Biol, 55 (4-5), 420-430, 1994.
100. A.N. Gorban, I.V.
Karlin, General approach to constructing models of the Boltzmann equation, Physica A, 206 (1994), 401-420.
101. A.N. Gorban, I.V.
Karlin, Method of invariant manifolds and regularization of acoustic spectra, Transport Theory and Stat. Phys., 23,
559-632, 1994.
102. 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.
103. 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.
104. 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.
105. V.I. Verbitskii,
A.N. Gorban, Jointly dissipative operators and their applications, Siberian Math J, 33 (1), 19-23, 1992.
106. 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.
107. 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.
108. 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.
109. 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).
110. 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).
111. 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.
112. 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.
113. 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.
114. A.N. Gorban, M.G.
Sadovskii, Optimal strategies of spatial-distribution - Olli effect, Zh Obshch
Biol 50 (1), 16-21, 1989.
115. 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).
116. V.I.Bykov, A. N.
Gorban, A Model of Autooscillations in Association Reactions, Chem.Eng.Sci., V.42, No.5,
P.1249-1251(1987).
117. 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).
118. 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).
119. 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.
120. V.I. Bykov, A.N.
Gorban, Simplest model of self-oscillations in association reactions, React Kinet Catal Lett, 27 (1): 153-155
1985
121. V.I. Bykov, A.N.
Gorban, T.P. Pushkareva, Autooscillation model in reactions of the association,
Zh Fiz Khim, 59 (2): 486-488, 1985.
122. 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.
123. 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
124. V.I. Bykov, A.N.
Gorban, Quasithermodynamic characteristic of reactions without the reaction of
different substances, Zh Fiz Khim, 57
(12), 2942-2948, 1983.
125. 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.
126. 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.
127. 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.
128. A.N. Gorban, G.S.
Yablonskii, On one unused possibility in the kinetic experiment design, Dokl Akad Nauk SSSR, 250 (5):
1171-1174, 1980.
129. A.N. Gorban, V.I.
Bykov, G.S. Yablonskii, The Path to Equilibrium, Intern. Chem. Eng. V.22, No.2, P.386-375(1982).
130. 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).
131. 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. .
132. 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).
133. A.N. Gorban,
Priori evaluation of the region of linearity for kinetic-equations, React Kinet Catal Lett, 10 (2), 149-152,
1979
134. A.N. Gorban,
Invariant Sets for Kinetic Equations, React.
Kinet. Catal. Lett., 1979, V.10, P.187-190.
135. A.N. Gorban, Sets
of Removable Singularities and Continuous Mappings, Siberian Math. Journ., V.19, P.1388-1391(1978).
136. 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
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
Prof. Melamed was from the
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
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
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
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.
A new approach to
the lattice Boltzmann method is developed. Beginning from thermodynamic
considerations, the LBM can be recognised as a discrete dynamical system
generated by entropic involution and free-flight and the stability analysis is
more natural. We solve the stability problem of the LBM on the basis of this
thermodynamic point of view. The main instability mechanisms are identified.
The simplest and most effective receipt for
stabilisation adds no artificial dissipation, preserves the second-order
accuracy of the method, and prescribes coupled steps: to start from a local
equilibrium, then, after free-flight, perform the overrelaxation collision, and
after a second free-flight step go to new local equilibrium. Two other
prescriptions (“salvation rules”)
add some artificial dissipation locally and prevent the system from loss of
positivity and local blow-up.
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.