Alexander Gorban

Personal web page

Teaching

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)

Research Interests

Dynamics of systems of physical, chemical and biological kinetics;

Data Mining;

Bioinformatics;

Human adaptation to hard living conditions.

More details: please see link at left.

Press Releases in ScienceDaily

Mathematicians Solve Decade-Old Debate On Regulation of Protein Production by microRNAs in Cells (July 31, 2012)

Plants and Animals Under Stress May Provide the Key to Better Stock Market Predications (Nov. 3, 2010)

References

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. 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, 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

2.        A.N. Gorban, Local equivalence of reversible and general Markov kinetics, Physica A 392 (2013) 1111–1121.

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

4.        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.

5.        A.N. Gorban and Dave Packwood, Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions, Physical Review E 86, 025701(R) (2012).

6.        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). Published in Advance July 31, 2012, doi:10.1261/rna.032284.112

7.        A.N. Gorban, G.S.Yablonsky, Extended detailed balance for systems with irreversible reactions, Chem. Eng. Sci. 66 (2011) 5388–5399.

8.        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.

9.        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.

10.    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.

11.    Zinovyev, N. Morozova, N. Nonne, E. Barillot, A. Harel-Bellan, A.N. Gorban, Dynamical modeling of microRNA action on the protein translation process,  BMC Systems Biology 2010, 4:13 (24 February 2010).

12.    A.N. Gorban, O. Radulescu, A. Y. Zinovyev,  Asymptotology of chemical reaction networks, Chem. Eng. Sci. 65 (2010) 2310–2324

13.    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.

14.    R.A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, (2-3) (2008), 385-406.

15.    A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 1-45.

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

17.    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.

18.    A.N. Gorban, Singularities of transition processes in dynamical systems: Qualitative theory of critical delays, Electron. J. Diff. Eqns. Monograph 5, 2004, 55 p.

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

20.    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, Extremal property of a simple cycle, arXiv:1301.2379 [physics.chem-ph]

2.      E. M. Mirkes, A. Zinovyev, A. N. Gorban, Geometrical complexity of data approximators, arXiv:1302.2645 [stat.ML]

3.      A.N. Gorban, General H-theorem and entropies that violate the second law, arXiv:1212.6767 [cond-mat.stat-mech]

4.      A.N. Gorban, Maxallent: Maximizers of all Entropies and Uncertainty of Uncertainty, arXiv:1212.5142 [physics.data-an]