Исследования Александра Горбаня

Research interests of Alexander Gorban:

  • 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.

Events: Previous and Forthcoming

Vox PopuliVox Dei!

“Глас народа – глас божий»”

Список статей из мировой базы,

ISI Web of Knowledge database,

Цитирующих статьи и книги А.Н.Горбаня


E-prints: Электронные оттиски работ

Some of Books, Recent Talks & Major Papers:


·          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. (Review on this book)


Review papers

·                   A.N. Gorban, H.P. Sargsyan and H.A. WahabQuasichemical Models of Multicomponent Nonlinear Diffusion

, Mathematical Modelling of Natural Phenomena, Volume 6 / Issue 05, (2011), 184−262.

·                   A.N. Gorban, A. ZinovyevPrincipal 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. GorbanA. Y. ZinovyevPrincipal 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])

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

·                   A.N. Gorban, A. Zinovyev, Elastic Principal Graphs and Manifolds and their Practical Applications, Computing 75, 359–379 (2005), (DOI) 10.1007/s00607-005-0122-6 , GorbZin2005Computing.pdf

·                   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, Singularities of transition processes in dynamical systems: Qualitative theory of critical delays, Electron. J. Diff. Eqns., Monograph 05, 2004, (55 pages). Online: http://ejde.math.txstate.edu/Monographs/05/abstr.html

·                   Gorban, A.N.;Karlin, I.V., Method of invariant manifold for chemical kinetics, Chem. Eng. Sci.. 58, 2003, 4751-4768  ChemEngSci2003.pdf NEW: Elsevier Most Cited Paper Award for this paper DIPLOMA (jpg)





·                   A.N. Gorban, G.S.YablonskyExtended 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

·                   N. GorbanO. RadulescuA. Y. ZinovyevAsymptotology of chemical reaction networks, Chemical Engineering Science 65 (2010) 2310–2324

·                   Andrei Zinovyev, Nadya Morozova, Nora Nonne, Emmanuel Barillot, Annick Harel-Bellan, Alexander N GorbanDynamical modeling of microRNA action on the protein translation process,  BMC Systems Biology 2010, 4:13 (24 February 2010)Description: http://www.biomedcentral.com/bmcimages/browse/highlyaccessed.gif

·                   O. Radulescu, A. N. Gorban, A. Y. Zinovyev, and A. LilienbaumRobust simplifications of multiscale biochemical networksBMC Systems Biology 2008, 2:86 doi:10.1186/1752-0509-2-86 Description: http://www.biomedcentral.com/bmcimages/browse/highlyaccessed.gifThe most accessed paper in BMC Systems Biology in November 2008

·                   A.N. Gorban and O. Radulescu, Dynamical robustness of biological networks with hierarchical distribution of time scales, IET Syst. Biol., 2007, 1, (4), pp. 238–246 Gorban2007IEESystemsBiology.pdf

·                   A.N. Gorban and A.Y. Zinovyev, The Mystery of Two Straight Lines in Bacterial Genome Statistics, Bulletin of Mathematical Biology (2007) DOI 10.1007/s11538-007-9229-6 (Online First) GorbanZinovyev2007BMB1.pdf

·                   R. A. Brownlee, A. N. Gorban, and J. Levesley, Stability and stabilization of the lattice Boltzmann method, Phys. Rev. E 75, 036711 (2007) (17 pages) BGJPhyRev2007.pdf

·                   A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological grammars for data approximation, Applied Mathematics Letters Volume 20, Issue 4 (2007), 382-386 GorSummnZinAML2006.pdf

·                   A.N. Gorban, Order–disorder separation: Geometric revision, Physica A Volume 374, Issue 1 , 15 January 2007, Pages 85-102 GorPhysA2006Order.pdf

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

·                   Gorban, A.N.;Karlin, I.V.;Zinovyev, A.Y. Invariant grids for reaction kinetics Physica A, 333, 2004 106-154 ChemGrPhA2004.pdf Online: http://arxiv.org/abs/cond-mat/0307076

·                   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. GorbanThermodynamic Tree: The Space of Admissible PathsarXiv:1201.6315 [cond-mat.stat-mech]

·         A. N. GorbanD. PackwoodPossibility and Impossibility of the Entropy Balance in Lattice Boltzmann CollisionsarXiv:1111.5994 [physics.comp-ph]

·         A. N. GorbanD. PackwoodAdd-ons for Lattice Boltzmann Methods: Regularization, Filtering and LimitersarXiv:1110.0270 [physics.comp-ph]

·         A. ZinovyevA.N. GorbanNonlinear Quality of Life IndexarXiv:1008.4063 [cs.NE]

·         A. GorbanI. TyukinE. SteurH. NijmeijerPositive Invariance Lemmas for Control Problems with Convergence to Lyapunov-unstable SetsarXiv:0901.3577 [math.DS]


For other publications see:

Selected Publications, Preprints & Abstracts


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