Alexander Gorban

Director of the Mathematical Modelling Centre and Professor of Applied Mathematics

Tel: +44(0) 116 223 1433

New: Nomination for the Research Impact Award

Pattern Recognition in Big Data
Researchers: Professor Alexander Gorban, Professor Jeremy Levesley, Dr Ivan Tyukin, Dr Evgeny Mirkes, Dr Andrey Mudrov, Department of Mathematics

LtoR: I. Tyukin, J. Levesley, A. Gorban, E. Mirkes

LtoR: I. Tyukin, J. Levesley, A. Gorban, E. Mirkes




Data mining

Online resources:


Workshop "Hilbert's Sixth Problem'', University of Leicester, May 02-04, 2016. The original Hilbert's formulation (in English translation) was: "6. Mathematical Treatment of the Axioms of Physics. ...(continued here)

Preface to the special issue “Model reduction across disciplines” of Math. Model. Nat. Phenom. (Vol. 10, No. 3, 2015, pp. 1–5) dedicated to 60th birthday of A. Gorban, by Guest Editors: G. Fridman, J. Levesley, I. Tyukin, D. Wunsch

Lifetime Achievement Award

MaCKIE-2015, Mathematics in (bio)Chemical Kinetics and Engineering
Lifetime Achievement Award in recognition of outstanding contributions to the research field of (bio)chemical kinetics.


Press release in EurecAlert

Press releases in ScienceDaily:


Selected books

  1. A.N. Gorban and D. Roose (eds.), Coping with Complexity: Model Reduction and Data Analysis,  Lecture Notes in Computational Science and Engineering, 75, Springer: Heidelberg – Dordrecht - London -New York, 2011.
  2.  A.N. Gorban, B. Kegl, D. Wunsch, A. Zinovyev  (Eds.), Principal Manifolds for Data Visualisation and Dimension Reduction, Lecture Notes in Computational Science and Engineering, Vol. 58, Springer, Berlin – Heidelberg – New York, 2007. (ISBN 978-3-540-73749-0)
  3.  A.N. Gorban, N.  Kazantzis, I.G. Kevrekidis, H.C. Öttinger, C. Theodoropoulos (eds), Model Reduction and Coarse--Graining Approaches for Multiscale Phenomena, Springer, Berlin-Heidelberg-New York, 2006.
  4.  A.N. Gorban, B.M. Kaganovich, S.P. Filippov, A.V. Keiko, V.A. Shamansky, I.A. Shirkalin, Thermodynamic Equilibria and Extrema: Analysis of Attainability Regions and Partial Equilibria, Springer, Berlin-Heidelberg-New York, 2006.
  5.  A.N. Gorban, I.V. Karlin, Invariant Manifolds for Physical and Chemical Kinetics, Lect. Notes Phys. 660, Springer, Berlin, Heidelberg, 2005. [Review in Bull. London Math. Soc. 38 (2006) (pdf)] [Review in Zentralblatt Math. (2006) (pdf)] [Abstract(txt)] [Preface-Contents-Introduction(pdf)] [Editorial Reviews (htm)][Authors(gif)] Russian web-site with this book
  6.  A.N. Gorban, Singularities of transition processes in dynamical systems: Qualitative theory of critical delays, Electron. J. Diff. Eqns. Monograph 5, 2004, 55 p.
  7. G.S.Yablonskii, V.I.Bykov, A.N. Gorban, and V.I.Elokhin,  Kinetic Models of Catalytic Reactions (Comprehensive Chemical Kinetics, V.32, ed. by R.G. Compton), Elsevier, Amsterdam, 1991, 396p. (Reviews on this book: (1) W.H. Weinberg in J. Am. Chem. Soc. 114 (13) (1992), 5484-5485; (2) G. Wedler in Chem.-Ing.-Tech. 64 (1992) (8), 767-768)

Selected papers

  1. E.M. Mirkes, A.N. Gorban, J. Levesley, P.A.S. Elkington, J.A. Whetton, Pseudo-outcrop Visualization of Borehole Images and Core Scans , Mathematical Geosciences, 2017, Online first,   

  2. Gorban A.N., Tyukin I.Y. Stochastic Separation Theorems, Neural Networks, 94, October 2017, 255-259.
  3. A.N. Gorban, I.V. Karlin, Beyond Navier–Stokes equations: capillarity of ideal gas, Contemporary Physics 58(1) (2017), 70-90, DOI:10.1080/00107514.2016.1256123. arXiv e-print
  4. E. Moczko, E.M. Mirkes, C. Ceceres, A.N. Gorban, S. Piletsky, Fluorescence-based assay as a new screening tool for toxic chemicals, Scientific Reports 6, Article number: 33922 (2016)
  5. A.N. Gorban, E.M. Mirkes, A. Zinovyev, Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning, Neural Networks 84 (2016), 28-38
  6. E.M. Mirkes, T.J. Coats, J. Levesley, A.N. Gorban, Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes, Computers in Biology and Medicine 75 (2016), 203-216.
  7. A.N. Gorban, T.A. Tyukina, E.V. Smirnova, L.I. Pokidysheva, Evolution of adaptation mechanisms: Adaptation energy, stress, and oscillating death, Journal of Theoretical Biology 405 (2016), 127-139.
  8. A.N. Gorban, I.Yu. Tyukin, D.V. Prokhorov, K.I. Sofeikov, Approximation with random bases: Pro et Contra, Information Sciences 364-365, (2016), 129-145.
  9. A. N. Gorban,·A. Zinovyev, Fast and user-friendly non-linear principal manifold learning by method of elastic maps, in Proceedings DSAA 2015 -- IEEE International Conference on Data Science and Advanced Analytics, Paris; 10/2015.
  10. A.N. Gorban, V.N. Kolokoltsov, Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes, Math. Model. Nat. Phenom. Vol. 10, No. 5, 2015, pp. 16–46.
  11. A.N. Gorban, I.Yu. Tyukin, H. Nijmeijer, Further Results on Lyapunov-Like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems, Proceedings of 53rd IEEE Conference on Decision and Control, December 15-17, 2014. Los Angeles, California, USA, IEEE, 2014, pp. 1557-1562.
  12. A.S. Manso, M.H. Chai, J.M. Atack, L. Furi, M. De Ste Croix, R. Haigh, C. Trappetti, A.D. Ogunniyi, L.K. Shewell, M. Boitano, T.A. Clark, J. Korlach, M. Blades, E. Mirkes, A.N. Gorban, J.C. Paton, M.P. Jennings, M.R. Oggioni, A random six-phase switch regulates pneumococcal virulence via global epigenetic changes, Nature Communications 5 (2014), Article number: 5055. Supplementary Information
  13. A.N. Gorban, I. Karlin, Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the American Mathematical Society,  Vol. 51, Issue 2, 2014, 186-246. arXiv:1310.0406 [math-ph]
  14. E.M. Mirkes, I. Alexandrakis, K. Slater, R. Tuli, A.N. Gorban, Computational diagnosis and risk evaluation for canine lymphoma, Computers in Biology and Medicine, Volume 53, 1 October 2014, 279-290. arXiv:1305.4942 [q-bio.QM].
  15. A.N. Gorban, D.J. Packwood, Enhancement of the stability of lattice Boltzmann methods by dissipation control, Physica A 414 (2014) 285–299.
  16. A.N. Gorban, I. Tyukin, E. Steur, and H. Nijmeijer, Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems, SIAM J. Control Optim., Vol. 51, No. 3, 2013, pp. 2306-2334.
  17. A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 1438-1456.
  18. A.N. Gorban, G.S. Yablonsky, Grasping Complexity, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 1421-1426.
  19. R.A. Brownlee, J. Levesley, D. Packwood, A.N. Gorban, Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters, Progress in Computational Physics, 2013, vol. 3, 31-52.
  20. A.N. Gorban, Thermodynamic Tree: The Space of Admissible Paths, SIAM J. Applied Dynamical Systems, Vol. 12, No. 1 (2013), pp. 246-278. DOI: 10.1137/120866919 arXiv e-print
  21. A.N. Gorban, Local equivalence of reversible and general Markov kinetics, Physica A 392 (2013) 1111–1121.
  22. A.N. Gorban, E.M. Mirkes, G.S. Yablonsky, Thermodynamics in the limit of irreversible reactions, Physica A 392 (2013) 1318–1335.
  23. Zinovyev, N. Morozova, A.N. Gorban, and A. Harel-Belan, Mathematical Modeling of microRNA-Mediated Mechanisms of Translation Repression, in U. Schmitz et al. (eds.), MicroRNA Cancer Regulation: Advanced Concepts, Bioinformatics and Systems Biology Tools, Advances in Experimental Medicine and Biology Vol. 774, Springer, 2013, pp. 189-224.
  24.  A.N. Gorban and D. Packwood, Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions, Physical Review E 86, 025701(R) (2012).
  25.  N. Morozova, A. Zinovyev, N. Nonne, L.-L. Pritchard, A.N. Gorban, and A. Harel-Bellan, Kinetic signatures of microRNA modes of action, RNA, Vol. 18, No. 9 (2012), 1635-1655.
  26. A.N. Gorban, G.S.Yablonsky, Extended detailed balance for systems with irreversible reactions, Chem. Eng. Sci. 66 (2011) 5388–5399.
  27.  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.
  28. 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.
  29. 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.
  30. A.N. Gorban, O. Radulescu, A. Y. Zinovyev, Asymptotology of chemical reaction networks, Chem. Eng. Sci. 65 (2010) 2310–2324.
  31. 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.
  32. R.A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, (2-3) (2008), 385-406.
  33. A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 1-45.
  34. A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological grammars for data approximation, Applied Mathematics Letters, 20 (4)  (2007),  382-386.
  35. A.N. Gorban,  T.G.Popova, A.Yu. Zinovyev, Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences Physica A 353C (2005), 365-387.
  36. A.N. Gorban, I.V. Karlin, A.Y Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Phys. Rep., 396, 2004, 197-403.
  37. A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58, 2003, 4751-4768.

Recent preprints

  1. I.Y. Tyukin, A.N. Gorban, K. Sofeikov, I. Romanenko, Knowledge Transfer Between Artificial Intelligence Systems, arXiv:1709.01547 [cs.AI] 
  2. D.L. Crane, R.L. Davidchack, A.N. Gorban, Minimal cover of high-dimensional chaotic attractors by embedded coherent structures, arXiv:1607.02180 [nlin.CD]
  3. E. Fehrman, A.K. Muhammad, E.M. Mirkes, V. Egan, A.N. Gorban , The Five Factor Model of personality and evaluation of drug consumption risk, arXiv:1506.06297 [stat.AP].
  4. E. M. Mirkes, T. Walsh, E. J. Louis, A. N. Gorban, Long and short range multi-locus QTL interactions in a complex trait of yeast, arXiv:1503.05869 [q-bio.GN]

Scientific achievements


I developed a family of methods for model reduction and coarse-graining: method of invariant manifold, method of natural projector, relaxation methods. I have solved problems in gas kinetics, polymer dynamics, chemical reaction kinetics and biological kinetics. For this series of work I received the I. Prigogine prize and medal. I have been Clay Scholar (Cambridge, USA, 2000).

Solution of Hilbert problem

My student Karlin and I recently received the recognition of the scientific community for solving an important part of the Hilbert Sixth problem about the irreducibility of continuum mechanics to physical kinetics that remained unsolved almost for 100 years.

Stable Lattice Boltzmann methods

New family of numerical methods is developed. They are based on the ideas of lattice Boltzmann models (LBM) in combination with methods of invariant manifold and specific entropic stabilisers. Standard test examples demonstrate that the new methods erase spurious oscillations without blurring of shocks, and do not affect smooth solutions.


The methods of genome analysis based on frequency dictionaries are elaborated and applied to various biological problems (genome redundancy, mosaic structure of genome, genetic species signature, etc.). For example, existence of a universal 7-cluster structure in all available bacterial genomes is proved.

Data mining and rules extraction

A general neural networks based technology of extraction of explicit knowledge from data was developed. 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.

For example new tools were developed for differential diagnosis of allergic and pseudoallergic reactions, for anticipation of myocardial infarction complications, and for evaluation of the accumulated radiation dose based on parameters of human blood.

Revealing and visualisation of hidden structure of complex systems

A system of methods is developed to reveal the hidden intelligible models in complex systems: complex datasets and complex reaction networks. First of all, this is revealing of hidden geometry.

New special tools have been proposed and elaborated, the grammars of elementary transformations which allow us to create the intelligible models of complex systems by the chains of simple steps and dominant systems that represent the complex networks by the simple networks, which dynamics can be studied analytically. Several biological and medical centres now use these methods and algorithms, for example, Institute Curie (France).

MicroRNAs kinetic signatures

MicroRNAs are key regulators of all important biological processes, including development, differentiation and cancer. Although remarkable progress has been made in deciphering the mechanisms used by miRNAs to regulate translation, many contradictory findings have been published that stimulate active debate in this field. I, with with co-authors, have developed computational tools for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures). They have found sensitive parameters of the translation process for various conditions.

The crises anticipation

I invented a new method to measure the stress caused by environmental factors. In particular, this is a possibility to measure the health of the groups of healthy people. This method is based on a universal effect discovered by me in my study of human adaptation. This effect is supported by hundreds of experiments and observations and extended to systems of different nature. Now, this method is used for monitoring of Far North populations, for analysis of crises in national financial systems and in companies. It becomes a part of the modern approach to crises anticipation.

Research interests

  • Architecture of neurocomputers and training algorithms for neural networks
  • Dynamics of systems of physical, chemical and biological kinetics
  • Human adaptation to hard living conditions
  • Methods and technologies of collective thinking

Current grants

I'm the Lead Academic in three Knowledge Transfer Partnership (KTP) grants funded by Innovate UK foundation:

  • KTP009890 between Apical Ltd and the University of Leicester (Visual Intelligence), 2015-2017, Knowledge Base Supervisor Dr I.Y. Tyukin
  • KTP010522 between Visual Management Systems Limited and the University of Leicester (Visual Intelligence), 2017-2019, Knowledge Base Supervisor Dr I.Y. Tyukin
  • KTP010604 between Dataffirm Limited and the University of Leicester (Mining of Big Text Data), 2017-2019, Knowledge Base Supervisor Dr E.M. Mirkes

Other grants and awards

  • International Research Workshop: Hilbert's Sixth Problem, LMS, 2016;
  • International Research Workshop: Hilbert's Sixth Problem, EPSRC, 2016;
  • Weatherford Contract Research, 07.2013-06.2015
  • Data Mining for Geological Information, NERC (Natural Environment Research Council), 07.2013-10.2013
  • Development Fund, 2012; Mathematical Modelling of Adaptation and Decision-Making in  Neural Systems, The Royal Society, UK: International Joint UK-Japan Project
  • Modularity, Abstraction and Robustness of Network Models in Molecular Biology, Alliance : Franco-British Research Partnership Programme
  • EPSRC and LMS grants for the International Workshop: Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, Leicester, UK August 24-26 2005
  • Prigogine Award and Medal (2003)
  • 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)
  • Russian Federal Fellowship for outstanding scientists, twice (6 years)
  • Grant of Russian Foundation of Basic Research (1996-1998)
  • 1994-1996 American Mathematical Society Fellowship.

Personal details

Appointments history

2004-present, University of Leicester

  • 2006-present, Director of the Centre for Mathematical Modelling
  • 2004-present, Chair in Applied Mathematics

2003-2004, Swiss Federal Institute of technology (ETH), Zurich, Switzerland)

  • Senior Researcher

1983-2005, Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, Krasnoyarsk, Russia (last year was on leave)

  • 1995-2005: Deputy Director and Head of the Computer Sciences Department
  • 1989-2006 Head of the Nonequilibrium Systems Laboratory
  • 1983-1989: Senior researcher
  • 1978-1983: Junior researcher

1977-1978, Institute of Catalysis, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia

  • Engineer

1978, Institute of Theoretical & Applied Mechanics, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia

  • Engineer

1977, Tomsk Polytechnic University, Laboratory of Kinetics, Tomsk, Russia

  • Junior researcher

1976, Omsk State University, Laboratory of Kinetics, Omsk, Russia

  • Junior researcher

1973-1976, Omsk Railway Engineering Institute, Research Division, Omsk, Russia

  • Engineer

Part-time teaching

1993-2006, Krasnoyarsk State Technical University, Krasnoyarsk, Russia: (last years was on leave)

  • Head of Neurocomputers Department and Professor

1993-2003, Krasnoyask State Technological University, Krasnoyarsk, Russia

  • Professor, Department of Automatization and Robots, 1993-2003;

1981-2001, Krasnoyarsk State University, Krasnoyarsk, Russia

  • Professor, Psychological Faculty, 1998-2001
  • Associate Professor, Higher Mathematics Chair, 1981-1989

Visiting positions

  • Isaac Newton Institute for Mathematical Sciences (Cambridge, UK), 2010
  • Institut des Hautes Etudes Scientiques (IHES, Bures-sur-Yvette, France), 2000, 2001, 2002, 2003, 2009
  • Courant Mathematics Institute (New York, USA), 2000, 2007, 2008
  • Clay Mathematics Institute (Cambridge, USA), 2000 (Clay Scholar)
  • ETH, Zurich, Switzerland: 1999, 2000, 2002

Expert positions

  • Vice-Chairman of Scientific Council at Krasnoyarsk State Technical University (direction: Software and tools for mathematical modelling) (1999-2006)
  • 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)

Membership of associations

  • SIAM
  • LMS
  • Russian Society of Artificial Intelligence (Chair of Krasnoyarsk Regional Branch)
  • Russian Neural Networks Society
  • Associated Member of ASME (American Society of Mechanical Engineers) (1997)

Organiser of:

  • International Research Workshop: Hilbert's Sixth Problem, University of Leicester, Leicester, UK, May 2-May 4, 2016
  • International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis, Ambleside, Lake District, UK August 31-September 4, 2009
  • International Research workshop: Mathematics of Model Reduction, University of Leicester, Leicester, UK August 28-August 30, 2007
  • International Research Workshop: Lattice Boltzmann at all-scales: from turbulence to DNA translocation, 15 November 2006, University of Leicester, Leicester, UK
  • International Research Workshop: Principal manifolds for data cartography and dimension reduction, August 24-26, 2006, Leicester University, Leicester, UK
  • International Research Workshop: Geometry of Genome: Unravelling of Structures Hidden in Genomic Sequences,Leicester University, Leicester, UK, 22/09/2005-24/09/2005
  • International Research Workshop: Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena, Leicester University, Leicester, UK August 24-26 2005
  • International Research 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 annual National Conference: Neurionformatics (1998-present)
  • Russian annual National Workshops: Neuroinformatics and Application, Krasnoyarsk, 1992- present
  • Russian annual National Workshops: Modeling of Nonequilibrium Systems,Krasnoyarsk, 1999- present
  • Russian National Conference: Problems of Regional Informatization, Krasnoyarsk, 1998-2003
  • Soviet Union National competition in Neuroinformatics and Neurocomputers for students and young scientists, 1991


Scientific advisor of 29 PhD thesis and 5 DrSc, including:

  • Y. Shi, kNN predictability analysis of stock and share closing prices, (PhD, Applied Mathematics, University of Leicester, UK, 2016)
  • A. Akinduko, Multiscale Principal Component Analysis (PhD, Applied Mathematics, University of Leicester, UK, 2015)
  • D. Packwood, Non-Equilibrium Dynamics of Discrete Time Boltzmann Systems (PhD, Applied Mathematics, University of Leicester, UK, 2012)
  • Jianxia Zhang, Nonequilibrium Entropic Filters for Lattice Boltzmann Methods and Shock Tube Case Studies (PhD, Applied Mathematics, University of Leicester, UK, 2012)
  • M. Shahzad, Slow Invariant Manifold and its approximations in kinetics of catalytic reactions, (PhD, Applied Mathematics, University of Leicester, UK, 2011)
  • H.A. Wahab, Quasichemical Models of Multicomponent Nonlinear Diffusion (PhD, Applied Mathematics, University of Leicester, UK, 2011)
  • O. Radulescu, Mathematical models of complexity in molecular biology and mechanics of complex fluids, (Dr. Habilitation, Applied Mathematics, Universit de Rennes 1, France, 2006)
  • E.M. Mirkes, The structure and functioning of ideal neurocomputer (DrSc='doctor nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 2002)
  • E.V. Smirnova, Measurement and modeling of adaptation (DrSc='doctor nauk', Modeling in Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia, 2001)
  • A.Yu. Zinovyev, Method of Elastic Maps for Data Visualization: Algorithms, Software and Applications in Bioinformatics (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 2001)
  • V.G. Tzaregorodtzev, Algorithms, technology and software for knowledge extraction using trainable neural networks (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 2000)
  • A.A. Pitenko, Neural networks for geoinformatics (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 2000)
  • A.A. Rossiev, Neural network modeling of data with gaps (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 2000)
  • M.Yu. Senashova, Accuracy estimation for neural networks (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 1999)
  • M.A. Dorrer, Psychological intuition of neural networks (PhD='kandidat nauk', Computer Science, Krasnoyarsk State Technical University, Russia, 1999)
  • D.A. Rossiev, Neural networks based expert systems for medical diagnostics
  • 'doctor nauk', Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia, 1997)
  • I.V. Karlin, Method of invariant manifold in physical kinetics, (PhD, Physics, Krasnoyarsk AMSE Centre, Russia-France, 1991)
  • V.I. Verbitsky, Simultaneously dissipative operators and global stability (PhD='kandidat nauk', Mathematical Analysis, Ural University, Yekaterinburg, Russia, 1989)
  • M.G. Sadovskii, Optimization in space distributions of populations, (PhD=''kandidat nauk', Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia, 1989)
  • V.A. Okhonin, Kinetic equations for population dynamics (PhD='kandidat nauk', Biophysics, Moscow University, Russia, 1986)

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