Alexander N. Gorban'


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       E-mail: ag153(at) 


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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
kNN and Potential energy applet
Data cartography: Political Atlas of the World)


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

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, 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, G.S.Yablonsky, Extended detailed balance for systems with irreversible reactions, Chemical Engineering Science 66 (2011) 5388–5399.

·          Gorban A.N., Gorban P.A., Judge G. Entropy: The Markov Ordering Approach. Entropy. 2010; 12(5):1145-1193

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

·          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)Description: Description:

·          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 Description: Description: most accessed paper in BMC Systems Biology in November 2008

·          A.N. Gorban and A.Y. Zinovyev, The Mystery of Two Straight Lines in Bacterial Genome Statistics, Bulletin of Mathematical Biology 69 (2007), 2429–2442. DOI 10.1007/s11538-007-9229-6

·          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,  T.G.Popova, and A.Y. Zinovyev, Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences Physica A 353C (2005), 365-387. CodonPhysA2005.pdf , Internet site CLUSTER STRUCTURE IN GENOME with analysis of all available bacterial genomes.

·          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. Zinovyev, N. Morozova, A. N. Gorban, A. Harel-Belan, Mathematical modeling of microRNA-mediated mechanisms of translation repression, arXiv:1202.1243 [q-bio.MN].

·          A. N. Gorban, Thermodynamic Tree: The Space of Admissible Paths, arXiv:1201.6315 [cond-mat.stat-mech]

·          A. N. Gorban, D. Packwood, Possibility and Impossibility of the Entropy Balance in Lattice Boltzmann Collisions, arXiv:1111.5994 [physics.comp-ph]

·          A. N. Gorban, D. Packwood, Add-ons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters, arXiv:1110.0270 [physics.comp-ph]

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

·          A. Gorban, I. Tyukin, E. Steur, H. Nijmeijer, Positive Invariance Lemmas for Control Problems with Convergence to Lyapunov-unstable Sets, arXiv:0901.3577 [math.DS]

For other publications see:

Selected Publications, Preprints & Abstracts

Centre for Mathematical Modelling

Geomathematical Consortium


Last modified: March 8, 2011


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