Alexander Gorban

Professor of Applied Mathematics

 Director of the Mathematical Modelling Centre

phone: +44 (0) 116 223 1433
email: ag153(at)
Google Scholar Profile scholar_results

Personal web page


Data mining

Online resources:
PCA, SOM and GSOM applet, K-means and K-medoids applet, kNN and Potential energy applet and
Data cartography: Political Atlas of the World (to be continued)

Leicester students win international data analytics competition

Research Interests
Dynamics of systems of physical, chemical and biological kinetics;
Data Mining;
Human adaptation to hard living conditions.

More details: please see link at left.


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.

Current grants

Prof A.N. Gorban is 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.

Media reaction on the work about Hilbert Sixth Problem

QuantaMagazine, July 21, 2015 
Famous Fluid Equations Are Incomplete
A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

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. 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
  2. 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)
  3. 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
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. 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
  11. 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]
  12. 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].
  13. A.N. Gorban, D.J. Packwood, Enhancement of the stability of lattice Boltzmann methods by dissipation control, Physica A 414 (2014) 285–299.
  14. 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.
  15. A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 1438-1456.
  16. A.N. Gorban, G.S. Yablonsky, Grasping Complexity, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 1421-1426.
  17. 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.
  18. 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
  19. A.N. Gorban, Local equivalence of reversible and general Markov kinetics, Physica A 392 (2013) 1111–1121.
  20. A.N. Gorban, E.M. Mirkes, G.S. Yablonsky, Thermodynamics in the limit of irreversible reactions, Physica A 392 (2013) 1318–1335.
  21. 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.
  22. A.N. Gorban and D. Packwood, Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions, Physical Review E 86, 025701(R) (2012).
  23. 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.
  24. A.N. Gorban, G.S.Yablonsky, Extended detailed balance for systems with irreversible reactions, Chem. Eng. Sci. 66 (2011) 5388–5399.
  25. 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.
  26. 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.
  27. 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.
  28. A.N. Gorban, O. Radulescu, A. Y. Zinovyev, Asymptotology of chemical reaction networks, Chem. Eng. Sci. 65 (2010) 2310–2324.
  29. 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.
  30. R.A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, (2-3) (2008), 385-406.
  31. A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 1-45.
  32. A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological grammars for data approximation, Applied Mathematics Letters, 20 (4)  (2007),  382-386.
  33. 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.
  34. A.N. Gorban, I.V. Karlin, A.Y Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Phys. Rep., 396, 2004, 197-403.
  35. A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58, 2003, 4751-4768.

Recent preprints

  1. A.N. Gorban, I.Y. Tyukin, Stochastic Separation Theorems, arXiv:1703.01203 [cs.LG]
  2. E.M. Mirkes, A.N. Gorban, J. Levesley, P.A.S. Elkington, J.A. Whetton, Pseudo-Outcrop Visualization of Borehole Images and Core Scans, arXiv:1702.02633 [physics.geo-ph]
  3. A.N. Gorban, I. Romanenko, R. Burton, I.Y. Tyukin, One-Trial Correction of Legacy AI Systems and Stochastic Separation Theorems, arXiv:1610.00494 [stat.ML]
  4. 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]
  5. 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].
  6. 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]

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Department of Mathematics
University of Leicester
University Road
Leicester LE1 7RH
United Kingdom

Tel.: +44 (0)116 252 3917
Fax: +44 (0)116 252 3915

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