Alexander N. Gorban'


       E-mail: ag153(at) 

       Leicester Mathematics on Google scholar

 Related pages:



The Artist Anna Gorban


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.

See Selected Publications and Preprints for more publications and their abstracts.

Events: Previous and Forthcoming

Teaching: Data Mining
(The online course is in preparation. See PCA, SOM and GSOM applet, K-means and K-medoids applet  and kNN and Potential energy applet prepared by E.M. Mirkes)
Data cartography: Political Atlas of the World, Mining Historical Data


Vox Populi – Vox Dei!

“The voice of the people is the voice of God”

Here are citations from the scientific journals,

which belong to the ISI Web of Knowledge database,

to papers and books by A. N. Gorban.

My Citations in Google Scholar

Web of Science Research ID


Some of Books, Recent Talks & Major Papers:


·          A. 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)

·          Model Reduction and Coarse--Graining Approaches for Multiscale Phenomena, Ed. by Alexander N. Gorban, Nikolaos  Kazantzis, Ioannis G. Kevrekidis, Hans Christian Öttinger, Constantinos Theodoropoulos, Springer, Berlin-Heidelberg-New York, 2006.

·          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.

·          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

·          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)


Review papers

·           A.N. Gorban, I. Karlin, Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the American Mathematical Society, 51(2), 2014, 186-246

·           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), 184262.

·           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.

·           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 (and also arXiv:0809.0490v1 [cs.LG])

·           A. N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 1-45. The original publication is available at

·           A.N. Gorban, I.V. Karlin, A.Y. Zinovyev, Constructive methods of invariant manifolds for kinetic problems Phys. Rep., 396, 2004, 197-403 PhysRepCorr.pdf

·           A. N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci.. 58, 2003, 4751-4768: Elsevier Most Cited Paper Award for this paper DIPLOMA (jpg)

·           A.N. Gorban, Singularities of transition processes in dynamical systems: Qualitative theory of critical delays, Electron. J. Diff. Eqns., Monograph 05, 2004, (55 pages).


Selected Talks



·          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

·          A.N. Gorban, E.M. Mirkes, G.S. Yablonsky, Thermodynamics in the limit of irreversible reactions, Physica A 392 (2013) 1318–1335.

·          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, doi:10.1261/rna.032284.112

·          Gorban A.N., Gorban P.A., Judge G. Entropy: The Markov Ordering Approach. Entropy. 2010; 12(5):1145-1193 (corrected postprint). NEW: Entropy Best Paper Award” for 2014.

·          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. Number 9 in the Top Hottest Articles in the Journal, April to June 2010

·          A. N. Gorban, O. Radulescu, A. Y. Zinovyev, Asymptotology of chemical reaction networks, Chemical Engineering Science 65 (2010) 2310–2324

·          O. Radulescu, A. N. Gorban, A. Y. Zinovyev, and A. Lilienbaum, Robust simplifications of multiscale biochemical networks, BMC Systems Biology 2008, 2:86 doi:10.1186/1752-0509-2-86 most accessed paper in BMC Systems Biology in November 2008

·          R.A. Brownlee, A.N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A:, 387, Issues 2-3, 15 January 2008,

·          A.N. Gorban, A.N. Gorlov, V.M. Silantyev, Limits of the Turbine Efficiency for Free Fluid Flow, Journal of Energy Resources Technology - December 2001 - Volume 123, Issue 4, pp. 311-317. [PDF] [Abstract] CITED BY



·          A. N. Gorban, I. Karlin, Hilbert's 6th Problem: Exact and Approximate Hydrodynamic Manifolds for Kinetic Equations, arXiv:1310.0406 [math-ph]

·          E. M. Mirkes, I. Alexandrakis, K. Slater, R. Tuli, A. N. Gorban, Computational Diagnosis of Canine Lymphoma, arXiv:1305.4942 [q-bio.QM]

·           A. Zinovyev, A.N. Gorban, Nonlinear Quality of Life Index, arXiv:1008.4063 [cs.NE]

For other publications see:

Selected Publications, Preprints & Abstracts

Centre for Mathematical Modelling

Geomathematical Consortium

The Mirrow

Last modified: November 20, 2013


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"Russian Scientists"