Alexander Gorban

Professor of Applied Mathematics

phone: +44 (0) 116 223 1433
email: ag153(at)mcs.le.ac.uk
personal web page

Research Interests

Dynamics of systems of physical, chemical and biologicalkinetics;

Bioinformatics;

Human adaptation to hard living conditions;

Architecture ofneurocomputers and training algorithms for neural networks.

Some of the past achievements

· Physical and chemical kinetics. A. Gorban (AG) has developed a family of methods for model reduction and coarse-graining in 1980s-1990s: method of invariant manifold, method of natural projector, relaxation methods. All these methods create reduced models which satisfy the main physical principles. He has solved problems in gas kinetics, polymer dynamics and chemical reaction kinetics: nonperturbative derivation of physically consistent hydrodynamics from the Boltzmann equation and from reversible dynamics, for Knudsen numbers Kn~1; 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 (more than 50 papers are published, the main results are collected in [1-6]). For this series of work AG received the I. Prigogine prize and medal from the International Informatization Academy (this Academy is in general consultative status of the United Nations from 1995), he was Clay Scholar (Clay Mathematics Institute, Cambridge, USA, 2000).

· Bioinformatics. Existence of a universal 7-cluster structure in all available bacterial genomes is proved [7]. New unsupervised methods of gene finding are developed [8]. The methods of genome analysis based on frequency dictionaries are elaborated [9-14] and applied to various biological problems (genome redundancy, mosaic structure of genome, genetic species signature, etc.)

· Data mining and rules extraction. A general technology of extraction of explicit knowledge from data was developed in 1987-2002 [15-17]. 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.

· The works that improve the quality of life. Among the research aimed at improve the quality of life is the intellectual security counterterrorist system “Voron” (“Corvus”). AG was a scientific consultant of this project.

More details: please see link at left.

References

1. Gorban A.N., Karlin I.V., Zinovyev A.Yu., Constructive methods of invariant manifolds for kinetic problems, Physics Reports, V. 396, N 4-6 (2004), p. 197-403.
2. Gorban A.N., Karlin I.V. Constructive Methods of Invariant Manifolds for Physical and Chemical Kinetics, Springer Verlag, Lecture Notes in Physics 660, Berlin-Heidelberg-NewYork, 2005. 498 p.
3. Yablonskii, G.S., Gorban, A.N., Bykov, V.I., and Elokhin, V.I., Kinetic Models of Catalytic Reactions (Comprehensive Chemical Kinetics, V.32, ed. by R.G. Compton), Elsevier, Amsterdam, 1991, 396 p.
4. 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
5. 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.
6. 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.
7. Gorban AN, Zinovyev AY, Popova TG., Seven clusters in genomic triplet distributions. In Silico Biol. 3(4) (2003):471-482.
8. Zinovyev, A.Yu., Gorban, A.N., Popova, T.G., Self-Organizing Approach for Automated Gene Identification, Open Systems and Information Dynamics 10(4) (2003), 321—333
9. Gorban', A.N., Mirkes, E.M., Popova, T.G., Sadovskii M.G., A new approach to the study of statistical properties of genetic sequences, Biofizika, 38(5) (1993), 762-767.
10. Gorban' AN, Mirkes EM, Popova TG, Sadovskii MG. Comparative redundancy of genes of various organisms and viruses, Genetika. 29(9) (1993), 1413-1419.
11. Gorban' AN, Popova TG, Sadovskii MG., Redundancy of genetic sequences and mosaic structure of a genome, Mol Biol (Mosk), 28(2) (1994):313-322.
12. Gorban, A.N., Popova, T.G., Sadovsky, M.G., Classification of symbol sequences over their frequency dictionaries: towards the connection between structure and natural taxonomy, Open System and Information Dynamics, 7 (2000), 1-17.
13. Gorban A.N., 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, 11 (2001), 657-663.
14. Gorban A.N., Training of Neural Networks, Moscow, USSR-USA JV "ParaGraph", 1990, 160 p.
15. Gorban A.N., Rossiev D.A., Neural networks on PC, Novosibirsk, Nauka Publ., 1996, 276 p.
16. Gorban A.N., Senashova M.Yu., and Wunsch D.C., Back-Propagation of Accuracy, Proc. IEEE/INNS International Conference on Neural Networks, Houston, IEEE, 1997, pp. 1998-2001

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Department of Mathematics

Alexander Gorban

Research Interests