Alexander GORBAN

Professor, Chair in Applied Mathematics,
Director of the Centre for Mathematical Modelling,
Department of Mathematics,
University of Leicester,
University Road,
Leicester LE1 7RH,
United Kingdom

Full Professor in Modeling & Simulation
Russian State
Certificate of Professorship, 1993

Research interests:

Dynamics of systems of physical, chemical and biological kinetics;

Data Mining;


Human adaptation to hard living conditions;


Citation information (07.04.2016)

·      Scopus citation score: citations 1788, h-index 23 (07.05.2016)

Scopus Author ID: 7005285942,

  • Google Scholar citation index 6249 h-index 39 (07.04.2016):

Academic degrees

·          1980, PhD in Physics & Math (Differential Equations & Math.Phys), Kuibyshev, USSR. Thesis: "Slow Relaxations and Bifurcations of Omega-Limit Sets of Dynamical Systems";

·          1990, Doctor of Physics & Math (Biophysics), (Advanced doctoral degree, Dr. Sc., analogue of Dr Habilit.), Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, USSR. Thesis: "Extremal Principles and a priori Estimations in Biological and Formal Kinetics".

·          1993, Full Professor in Modelling & Simulation: Russian State Certificate of Professorship.




2004-present, University of Leicester:

·          2006-present, Director of the Centre for Mathematical Modelling;

·          2004-present, Chair in Applied Mathematics;

2003-2004, Swiss Federal Institute of technology (ETH), Zurich, Switzerland):

·          Senior Researcher, 2003-2004;

1983-2005, Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, Krasnoyarsk, Russia (last years was on leave):

·          Deputy Director and Head of the Computer Sciences Department, 1995 – 2005;

·          Head of the Nonequilibrium Systems Laboratory, 1989 – 2006;

·          Senior researcher, 1983-1989;

·          Junior researcher, 1978-1983;

1977-1978, Institute of Catalysis, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia:

·          Engineer, 1977-1978;

1978, Institute of Theoretical & Applied Mechanics, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia:

·          Engineer, 1978;

1977, Tomsk Polytechnic University, Laboratory of Kinetics, Tomsk, Russia:

·          Junior researcher, 1977;

1976, Omsk State University, Laboratory of Kinetics, Omsk, Russia:

Junior researcher, 1976;

1973-1976, Omsk Railway Engineering Institute, Research Division, Omsk, Russia:

·          Engineer, 1973-1976.


Part-time teaching

Krasnoyarsk State Technical University, Krasnoyarsk, Russia: (last years was on leave):

·          Head of Neurocomputers Department, 1993-2006; Professor, 1993-2006;

Krasnoyask State Technological University, Krasnoyarsk, Russia::

·          Professor, Department of Automatization and Robots, 1993-2003;

Krasnoyarsk State University, Krasnoyarsk, Russia:

·          Professor, Psychological Faculty, 1998-2001;

·          Associate professor, Higher Mathematics Chair, 1981-1989.



  • Isaac Newton Institute for Mathematical Sciences (Cambridge, UK), 2010;
  • Institut des Hautes Etudes Scientiques (IHES, Bures-sur-Yvette, France), 2000, 2001, 2002, 2003, 2009.
  • Courant Mathematics Institute (New York, USA), 2000, 2007, 2008;
  • Clay Mathematics Institute (Cambridge, USA), 2000 (Clay Scholar);
  • ETH, Zurich, Switzerland: 1999, 2000, 2002.


Expert positions:

·         Vice-Chairman of Scientific Council at Krasnoyarsk State Technical University (direction: Software and tools for mathematical modelling) (1999-2006);

·         Head of Workgroup on Neurocomputing, Ministry of Science and Technology Russian Federation (1998-2000);

·         Vice-Chairman of Expert Council Krasnoyarsk Regional Science Foundation (1993-1996);

·         Chairman of the Analytic Games Committee, Krasnoyarsk (1989-1994);

·         Member of Jury of USSR National competition in mathematics for students of technical universities (1986-1990).


Membership of Associations

·         Member of SIAM;

·         Member of LMS;

·         Russian Society of Artificial Intelligence (Chair of Krasnoyarsk Regional Branch);

·         Russian Neural Networks Society;

·         Associated Member of ASME (American Society of Mechanical Engineers) (1997);


Some scientific achievements:

·   Kinetics.  A. Gorban has developed a family of methods for model reduction and coarse-graining: method of invariant manifold, method of natural projector, relaxation methods. He has solved problems in gas kinetics, polymer dynamics, chemical reaction kinetics and biological kinetics.  For this series of work AG received the I. Prigogine prize and medal, he has been Clay Scholar (Cambridge, USA, 2000).

·   Solution of Hilbert problem. Gorban with his student Karlin have recently received the recognition of the scientific community for solving an important part of the Hilbert 6th problem about the irreducibility of continuum mechanics to physical kinetics that remained unsolved almost for 100 years.

·   Stable Lattice Boltzmann methods. New family of numerical methods is developed. They are based on the ideas of lattice Boltzmann models (LBM) in combination with methods of invariant manifold and specific entropic stabilisers. Standard test examples demonstrate that the new methods erase spurious oscillations without blurring of shocks, and do not affect smooth solutions.  

·   Bioinformatics. The methods of genome analysis based on frequency dictionaries are elaborated and applied to various biological problems (genome redundancy, mosaic structure of genome, genetic species signature, etc.). For example, existence of a universal 7-cluster structure in all available bacterial genomes is proved.

·   Data mining and rules extraction. A general neural networks based technology of extraction of explicit knowledge from data was developed. This technology was implemented in a series of software libraries and allowed us to create dozens of knowledge-based expert systems in medical and technical diagnosis, ecology and other fields. For example new tools were developed for differential diagnosis of allergic and pseudoallergic reactions, for anticipation of myocardial infarction complications, and  for evaluation of the accumulated radiation dose based on parameters of human blood. 

·   Revealing and visualization of hidden structure of complex systems. A system of methods is developed to reveal the hidden intelligible models in complex systems: complex datasets and complex reaction networks. First of all, this is revealing of hidden geometry. New special tools have been proposed and elaborated, the grammars of elementary transformations which allow us to create the intelligible models of complex systems by the chains of simple steps and dominant systems that represent the complex networks by the simple networks, which dynamics can be studied analytically. Several biological and medical centres now use these methods and algorithms, for example, Institute Curie (France).

·   MicroRNAs kinetic signatures. MicroRNAs are key regulators of all important biological processes, including development, differentiation and cancer. Although remarkable progress has been made in deciphering the mechanisms used by miRNAs to regulate translation, many contradictory findings have been published that stimulate active debate in this field. A. Gorban with co-authors have developed computational tools for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures). They have found sensitive parameters of the translation process for various conditions.

·   The crises anticipation. A. Gorban invented a new method to measure the stress caused by environmental factors. In particular, this is a possibility to measure the health of the groups of healthy people. This method is based on a universal effect discovered by A. Gorban in his study of human adaptation. This effect is supported by hundreds of experiments and observations and extended to systems of different nature. Now, this method is used for monitoring of Far North populations, for analysis of crises in national financial systems and in companies. It becomes a part of the modern approach to crises anticipation.



Organizer of:

·          International Research Workshop: Hilbert’s Sixth Problem, University of Leicester, Leicester, UK, May 2 – May 4, 2016.

·          International Research Workshop: Coping with Complexity:  Model Reduction and Data Analysis, Ambleside, Lake District, UK August 31 – September 4, 2009. 

·          International Research workshop: Mathematics of Model Reduction, University of Leicester, Leicester, UK August 28 – August 30, 2007,

·          International Research Workshop: Lattice Boltzmann at all-scales: from turbulence to DNA translocation, 15 November 2006, University of Leicester, Leicester, UK,

·          International Research Workshop: “Principal manifolds for data cartography and dimension reduction” August 24-26, 2006, Leicester University, Leicester, UK

·          International Research Workshop:Geometry of Genome: Unravelling of Structures Hidden in Genomic Sequences,” Leicester University, Leicester, UK, 22/09/2005 – 24/09/2005;

·          International Research Workshop: “Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena,” Leicester University, Leicester, UK August 24-26 2005;

·          International Research Workshop: "Invariance and Model Reduction for Multiscale Phenomena," Zurich, August, 2003;

·          USA-NIS Neurocomputing Opportunities Workshop, Washington, DC, July 1999, (Sponsored by the National Science Foundation of the USA and Applied Computational Intelligence Lab, TTU) (Co-Chair);

·          Russian annual National Conference “Neurionformatics” (1998-present);

·          Russian annual National Workshops “Neuroinformatics and Application,” Krasnoyarsk, 1992- present;

·          Russian annual National Workshops “Modeling of Nonequilibrium Systems,” Krasnoyarsk, 1999- present.

·          Russian National Conference “Problems of Regional Informatization”, Krasnoyarsk, 1998-2003.

·          Soviet Union National competition in Neuroinformatics and Neurocomputers for students and young scientists, 1991.


Grants and awards:

·         International Research Workshop: Hilbert’s Sixth Problem, LMS, 2016;

·         International Research Workshop: Hilbert’s Sixth Problem, EPSRC, 2016;

·         Lattice Boltzmann methods for analysis of permeability in geophysics, Weatherford Contract Research,  07.2013  06.2015;

·         Data Mining for Geological Information, NERC (Natural Environment Research Council), 07.2013  10.2013;

·         Data Mining for Lymphoma Differential Diagnosis, European Regional Development Fund, 2012;

·         Mathematical Modelling of Adaptation and Decision-Making in  Neural Systems, The Royal Society, UK: International Joint UK-Japan Project;

·         Modularity, Abstraction and Robustness of Network Models in Molecular Biology, Alliance : Franco-British Research Partnership Programme;

·         EPSRC and LMS grants for the International Workshop “Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena,” Leicester, UK August 24-26 2005;

·         Prigogine Award and Medal (2003);

·         Clay Scholar, (Clay Mathematics Institute, Cambridge, USA, 2000);

·         Russian Federal Grant of the “Integration” program, 4 times (1998-2003);

·         Grant of Russian Federal subprogram “New Information Processing Technology” (1999);

·         Russian Federal Fellowship for outstanding scientists, twice (6 years);

·         Grant of Russian Foundation of Basic Research (1996-1998);

·         1994-1996 American Mathematical Society Fellowship.


Scientific advisor of 29 PhD thesis and 5 DrSc, including:

·         Y. Shi, kNN predictability analysis of stock and share closing prices, (PhD, Applied Mathematics, University of Leicester, UK, 2016).

·         A. Akinduko, Multiscale Principal Component Analysis (PhD, Applied Mathematics, University of Leicester, UK, 2015).

·         D. Packwood, Non-Equilibrium Dynamics of Discrete Time Boltzmann Systems (PhD, Applied Mathematics, University of Leicester, UK, 2012).

·         Jianxia Zhang, Nonequilibrium Entropic Filters for Lattice Boltzmann Methods and Shock Tube Case Studies (PhD, Applied Mathematics, University of Leicester, UK, 2012).

·         M. Shahzad, Slow Invariant Manifold and its approximations in kinetics of catalytic reactions, (PhD, Applied Mathematics, University of Leicester, UK, 2011).

·         H.A. Wahab, Quasichemical Models of Multicomponent Nonlinear Diffusion (PhD, Applied Mathematics, University of Leicester, UK, 2011).

·         O. Radulescu, Mathematical models of complexity in molecular biology and mechanics of complex fluids, (Dr. Habilitation, Applied Mathematics, Université de Rennes 1, France, 2006)

·         E.M. Mirkes, The structure and functioning of ideal neurocomputer (DrSc=“doctor nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 2002);

·         E.V. Smirnova, Measurement and modeling of adaptation (DrSc=“doctor nauk”, Modeling in Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia,  2001);

·         A.Yu. Zinovyev, Method of Elastic Maps for Data Visualization: Algorithms, Software and Applications in Bioinformatics (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 2001);

·         V.G. Tzaregorodtzev, Algorithms, technology and software for knowledge extraction using trainable neural networks (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 2000);

·         A.A. Pitenko, Neural networks for geoinformatics (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 2000);

·         A.A. Rossiev, Neural network modeling of data with gaps (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 2000);

·         M.Yu. Senashova, Accuracy estimation for neural networks (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 1999);

·         M.A. Dorrer, Psychological intuition of neural networks (PhD=“kandidat nauk”, Computer Science, Krasnoyarsk State Technical University, Russia, 1999);

·         D.A. Rossiev, Neural networks based expert systems for medical  diagnostics (DrSc=“doctor nauk”, Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia,  1997);

·         I.V. Karlin, Method of invariant manifold in physical kinetics, (PhD, Physics, Krasnoyarsk AMSE Centre, Russia-France, 1991);

·         V.I. Verbitsky, Simultaneously dissipative operators and global stability (PhD=“kandidat nauk”, Mathematical Analysis, Ural University, Yekaterinburg, Russia, 1989);

·         M.G. Sadovskii, Optimization in space distributions of populations, (PhD=“kandidat nauk”, Biophysics, Institute of Biophysics, Russian Academy of Sciences, Krasnoyarsk, Russia, 1989);

·         V.A. Okhonin, Kinetic equations for population dynamics (PhD=“kandidat nauk”, Biophysics, Moscow University, Russia, 1986).


Selected Publications

Monographs (in reverse chronological order):


  1. A.N. Gorban, D Roose (Eds) Coping with Complexity: Model Reduction and Data Analysis (Lecture Notes in Computational Science and Engineering, Springer, 2010.
  2. A.N. Gorban, B. Kegl, D. Wunsch, A. Zinovyev  (Eds.), Principal Manifolds for Data Visualisation and Dimension Reduction, LNCSE 58, Springer, Berlin – Heidelberg – New York, 2007.
  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 (498 pages). [Review in Bull. London Math. Soc. 38 (2006)];
  6. 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:  
  7. A.N.Gorban, W.L.Dunin-Barkovskii, D.A.Rossiev, S.A.Terehov, Neuroinformatics, Novosibirsk, Nauka Publ., 1998, 258 p. (With W.L.Dunin-Barkovskii, D.A.Rossiev, S.A.Terehov). [In Russian]
  8. A.N.Gorban, D.A.Rossiev, Neural networks on PC, Novosibirsk, Nauka Publ., 1996, 276 p. (With D.A.Rossiev). [In Russian];

9.      G.S.Yablonskii, V.I.Bykov, A.N.Gorban, 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: Journal of American Chemical Society (JAChS), V.114, n 13, 1992; sections “Reviews on the book”, W. Henry Weinberg, review on the book "Comprehensive Chemical Kinetics", Volume 32, Kinetic Models of Catalytic Reactions, Elsevier, 1991).

  1. A.N. Gorban, Training of Neural Networks, Moscow, USSR-USA JV "ParaGraph", 1990, 160 p. [In Russian, Russian title “Obuchenie neironnyh setei”]
  2. A.N. Gorban, R.G.Khlebopros,  Demon of Darwin. The Idea of Optimality and Natural Selection, Nauka Pub., Moscow, 1988, 208p. [In Russian]  
  3. A.N. Gorban, V.I.Bykov, G.S.Yablonskii, Essays on Chemical relaxation, Novosibirsk, Nauka Publ., 1986, 316 p. [In Russian]
  4. A.N. Gorban, Equilibrium Encircling. Equations of Chemical Kinetics and their Thermodynamic Analysis, Novosibirsk, Nauka Publ., 1984, 256 p. [In Russian];
  5. G.S.Yablonskii, V.I.Bykov, A.N. Gorban, Kinetic models of heterogeneous catalytic reactions, Novosibirsk, Nauka Publ., 1983, 256 p. [In Russian].


Selected papers in peer-reviewed publications (in reverse chronological order). Rank of Journals in Quartiles for papers 2011-2016 is shown according to Thomson Reuters InCitesTM Journal Citation Report 2014:

1.         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 (2016), In Press, Corrected Proof, Available online 19 January 2016,  Q2 IN MATHEMATICAL & COMPUTATIONAL BIOLOGY

2.         A.A. Akinduko, E.M. Mirkes, A.N. Gorban SOM: Stochastic initialization versus principal components, Information Sciences (2016), Available online 27 October 2015, Q1 IN COMPUTER SCIENCE, INFORMATION SYSTEMS

3.             A.N. Gorban, I.Yu. Tyukin, D.V. Prokhorov, K.I. Sofeikov Approximation with random bases: Pro et Contra Information Sciences (2016), In Press, Corrected Proof, Available online 25 September 2015, Q1 IN COMPUTER SCIENCE, INFORMATION SYSTEMS

4.             A.N. Gorban, N. Jarman, E. Steur, H. Nijmeijer, C. van Leeuwen, I. Tyukin Directed cycles and multi-stability of coherent dynamics in systems of coupled nonlinear oscillators, IFAC-PapersOnLine, 48, (18) (2015), 19–24

5.             A.N. Gorban , A. Zinovyev, Fast and user-friendly non-linear principal manifold learning by method of elastic maps, in Proceedings of DSAA 2015 -- IEEE International Conference on Data Science and Advanced Analytics, Paris; 10/2015.

6.             A.N. Gorban, Forward-Invariant Peeling in Chemical Dynamics: a Simple Case Study, Mathematical Modelling of Natural Phenomena Vol. 10, No. 5, 2015, pp. 126–134. Q2 IN ITERDISCIPLINARY SCIENCES

7.         A.N. Gorban, V.N. Kolokoltsov, Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes, Mathematical Modelling of Natural Phenomena Vol. 10, No. 5, 2015, pp. 16–46. Q2 IN ITERDISCIPLINARY SCIENCES

8.             A.N. Gorban, N. Jarman, E. Steur, C. van Leeuwen, I.Yu. Tyukin, Leaders Do Not Look Back, or Do They? Mathematical Modelling of Natural Phenomena Vol. 10, No. 3, 2015, pp. 212–231. Q2 IN ITERDISCIPLINARY SCIENCES

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, in 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. Q1 IN ITERDISCIPLINARY SCIENCES

11.      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. Q3 IN MATHEMATICAL & COMPUTATIONAL BIOLOGY

12.         A.N. Gorban, Detailed balance in micro- and macrokinetics and micro-distinguishability of macro-processes, Results in Physics, Volume 4, 2014, 142-147.

13.         A.N. Gorban, D.J. Packwood, Enhancement of the stability of lattice Boltzmann methods by dissipation control, Physica A 414 (2014) 285–299. Q2 IN PHYSICS, MULTIDISCIPLINARY

14.         A.N. Gorban, General H-theorem and Entropies that Violate the Second Law. Entropy 2014, 16, 2408-2432, Q2 IN PHYSICS, MULTIDISCIPLINARY

15.         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. Q1 IN MATHEMATICS

16.         Spahn, F., Vieira Neto, E., Guimarães, A.H.F., Gorban, A.N., Brilliantov, N.V.
A statistical model of aggregate fragmentation, New Journal of Physics 16, Article number 013031, 2014.

17.         E M Mirkes, I Alexandrakis, K Slater, R Tuli and A N Gorban, Computational diagnosis of canine lymphoma, J. Phys.: Conf. Ser. 490 012135 (2014)

18.         A A Akinduko and A N Gorban, Multiscale principal component analysis, J. Phys.: Conf. Ser. 490 012081 (2014)

19.         Y Shi, A N Gorban and T Y Yang, Is it possible to predict long-term success with k-NN? Case study of four market indices (FTSE100, DAX, HANGSENG, NASDAQ), J. Phys.: Conf. Ser. 490 012082 (2014)

20.         K.I. Sofeikov, I. Romanenko, I. Tyukin, A.N. Gorban, Scene Analysis Assisting for AWB Using Binary Decision Trees and Average Image Metrics. In Proceedings of IEEE Conference on Consumer Electronics, 10-13 January, Las-Vegas, USA, 2014, pp. 488-491.

21.         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 Journal On Control And Optimization Vol. 51, No. 3, 2013, pp. 2306-2334. Q1 IN MATHEMATICS, APPLIED

22.         E.M. Mirkes, A. Zinovyev, and A.N. Gorban, Geometrical Complexity of Data Approximators, in I. Rojas, G. Joya, and J. Cabestany (Eds.): IWANN 2013, Part I, Advances in Computation Intelligence, Springer LNCS 7902, pp. 500–509, 2013.

23.      A.N. Gorban, G.S. Yablonsky, Grasping Complexity, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 1421-1426. Q1 IN MATHEMATICS, APPLIED

24.         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.

25.         A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty, Computers & Mathematics with Applications 65, Issue 10, May 2013, 1438-1456. Q1 IN MATHEMATICS, APPLIED

26.         A. N. Gorban, Thermodynamic Tree: The Space of Admissible Paths, SIAM Journal On Applied Dynamical Systems, Vol. 12, No. 1 (2013), pp. 246-278. Q1 IN MATHEMATICS, APPLIED

27.         A. 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. Q2 IN BIOLOGY

28.      A.N. Gorban, E.M. Mirkes, G.S. Yablonsky Thermodynamics in the limit of irreversible reactions, Physica A 392 (2013) 1318–1335. Q2 IN PHYSICS, MULTIDISCIPLINARY

29.         A.N. Gorban, Local equivalence of reversible and general Markov kinetics, Physica A 392 (2013) 1111–1121. Q2 IN PHYSICS, MULTIDISCIPLINARY

30.      A.N. Gorban and D. Packwood, Allowed and forbidden regimes of entropy balance in lattice Boltzmann collisions, Physical Review E 86, 025701(R) (2012). Q1 IN PHYSICS, MATHEMATICAL

31.         N. Morozova, A. Zinovyev, N. Nonne, L.-L. Pritchard, A.N. Gorban, and A. Harel-Bellan, Kinetic signatures of microRNA modes of action, RNA-A Publication of the RNA Society, Vol. 18, No. 9 (2012), 1635-1655. Q1 IN BIOCHEMISTRY AND MOLECULAR BIOLOGY

32.         A.N. Gorban, G.S.Yablonsky, Extended detailed balance for systems with irreversible reactions, Chemical Engineering Science 66 (2011) 5388–5399. Q2 IN ENGINEERING, CHEMICAL

33.         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), 184−262. Q2 IN ITERDISCIPLINARY SCIENCES

34.      G. S. Yablonsky, A. N. Gorban, D. Constales, V. V. Galvita and G. B. Marin, Reciprocal relations between kinetic curves, EPL, 93 (2011) 20004. Q2 IN PHYSICS, MULTIDISCIPLINARY

35.         A.N. Gorban and M. Shahzad, The Michaelis-Menten-Stueckelberg Theorem. Entropy 2011, 13, 966-1019. Q2 IN PHYSICS, MULTIDISCIPLINARY

36.         A.N. Gorban, Kinetic path summation, multi-sheeted extension of master equation, and evaluation of ergodicity coefficient, Physica A 390 (2011) 1009–1025. Q2 IN PHYSICS, MULTIDISCIPLINARY

37.      A.N. Gorban, L.I. Pokidysheva, E,V. Smirnova, T.A. Tyukina. Law of the Minimum Paradoxes, Bulletin of Mathematical Biology 73(9) (2011), 2013-2044. Q3 IN MATHEMATICAL & COMPUTATIONAL BIOLOGY

38.      A. Gorban and S. Petrovskii, Collective dynamics: when one plus one does not make two, Mathematical Medicine and Biology-A Journal of the IMA (2011) 28, 85−88. Q2 IN MATHEMATICAL & COMPUTATIONAL BIOLOGY

39.         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.

40.         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.

41.         E. Chiavazzo, I.V. Karlin, A.N. Gorban, K. Boulouchos, Coupling of the model reduction technique with the lattice Boltzmann method, Combustion and Flame, 2010 

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

43.         A. N. Gorban and V. M. Cheresiz, Slow Relaxations and Bifurcations of the Limit Sets of Dynamical Systems. I. Bifurcations of Limit Sets, Journal of Applied and Industrial Mathematics, 2010, Vol. 4, No. 1, pp. 54–64.

44.         A. N. Gorban and V. M. Cheresiz, Slow Relaxations and Bifurcations of the Limit Sets of Dynamical Systems. II. Slow Relaxations of a Family of Semiflows, Journal of Applied and Industrial Mathematics, 2010, Vol. 4, No. 2, pp. 182–190.

45.         E. Chiavazzo, I.V. Karlin, and A.N. Gorban, The Role of Thermodynamics in Model Reduction when Using Invariant Grids, Commun. Comput. Phys., Vol. 8, No. 4 (2010), pp. 701-734.

46.         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)

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

48.         A.N. Gorban, E.V. Smirnova, T.A. Tyukina, General Laws of Adaptation to Environmental Factors: from Ecological Stress to Financial Crisis. Math. Model. Nat. Phenom. Vol. 4, No. 6, 2009, pp. 1-53

49.         E. Chiavazzo, I. V. Karlin, A. N. Gorban and K Boulouchos, Combustion simulation via lattice Boltzmann and reduced chemical kinetics, J. Stat. Mech. (2009) P06013,

50.         Ovidiu Radulescu, Alexander N Gorban, Andrei Zinovyev, and Alain Lilienbaum, Robust simplifications of multiscale biochemical networks, BMC Systems Biology 2008, 2:86

51.         A.N. Gorban and O. Radulescu, Dynamic and Static Limitation in Multiscale Reaction Networks, Revisited, Advances in Chemical Engineering 34, 103-173.

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

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

54.         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.

55.         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)

56.         E. Chiavazzo, A.N. Gorban, and I.V. Karlin, Comparison of Invariant Manifolds for Model Reduction in Chemical Kinetics, Commun. Comput. Phys. Vol. 2, No. 5 (2007), pp. 964-992

57.         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

58.         A.N. Gorban, Order–disorder separation: Geometric revision, Physica A  374 (1), (2007), 85-102

59.         R.A. Brownlee, A.N. Gorban, and J. Levesley, Stabilization of the lattice Boltzmann method using the Ehrenfests' coarse-graining idea, Phys. Rev. E 74, 037703 (2006)

60.         A. Gorban, I. Karlin, A. Zinovyev, Invariant Grids: Method of Complexity Reduction in Reaction Networks, Complexus, V. 2, 110–127.

61.         A.N. Gorban, I.V. Karlin, Quasi-Equilibrium Closure Hierarchies for the Boltzmann Equation, Physica A 360 (2006) 325–364

62.         A. Gorban, A. Zinovyev, Elastic Principal Graphs and Manifolds and their Practical Applications, Computing 75, 359–379 (2005),

63.         A.N. Gorban, I.V. Karlin, Invariance correction to Grad's equations: Where to go beyond approximations? Continuum Mechanics and Thermodynamics, 17(4) (2005), 311–335,

64.         A.N. Gorban,  T.G.Popova, 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.

65.         A.N. Gorban,  T.G.Popova, A.Yu. Zinovyev, Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences, In Silico Biology, 5 (2005), 0039.

66.         A.N. Gorban, P.A.Gorban, and I. V. Karlin, Legendre Integrators, Post-Processing and Quasiequilibrium, J. Non-Newtonian Fluid Mech. 120 (2004) 149-167.

67.         A.N. Gorban, I.V. Karlin, A.Yu. Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Physics Reports, V. 396, N 4-6 (2004), p. 197-403.

68.         A.N. Gorban, I.V. Karlin, A.Yu. Zinovyev, Invariant grids for reaction kinetics, Physica A, 333 (2004), 106--154.

69.         A.N. Gorban, I.V. Karlin, Uniqueness of thermodynamic projector and kinetic basis of molecular individualism, Physica A, 336, 3-4 (2004), 391-432.

70.         A.N. Gorban, T. G. Popova, and A. Yu. Zinovyev: Self-organizing approach for automated gene identification. Open Sys. Information Dyn. 10 (2003) 1-13.

71.         A.N. Gorban and I. V. Karlin, Family of additive entropy functions out of thermodynamic limit, Phys. Rev. E. 2003, V.67, 016104, E-print: http:,

72.         A.N. Gorban, I. V. Karlin and H. C. Ottinger, The additive generalization of the Boltzmann entropy. Phys. Rev. E. (2003), V. 67. E-print: http:,

73.         A.N. Gorban, I. V. Karlin, Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 58 (2003) 4751-4768.

74.         I.V. Karlin, L. L. Tatarinova, A. N. Gorban, and H. C. Öttinger, Irreversibility in the short memory approximation, Physica A 327 (2003) 399-424.

75.         A. Gorban, A. Zinovyev, T. Popova. Seven clusters in genomic triplet distributions. In Silico Biology. V.3 (2003), 471-482.

76.         A.N. Gorban, T.G Popova, M.G Sadovsky, Classification of nucleotide sequences over their frequency dictionaries reveals a relation between the structure of sequences and taxonomy of their bearers, Zh Obshch Biol 64 (1), 65-77. 2003

77.         A. Gorban', Braverman M., Silantyev V. Modified Kirchhoff flow with a partially penetrable obstacle and its application to the efficiency of free flow  turbines. Math. Comput. Modelling 35 (2002), No. 13, 1371-1375.

78.         A. Gorban', Silantyev V. Riabouchinsky Flow with Partially Penetrable Obstacle. Math. Comput. Modelling 35 (2002), no. 13, 1365-1370.

79.         I.V. Karlin, M. Grmela, and A.N. Gorban: Duality in nonextensive statistical mechanics, Phys. Rev. E 65 (2002) 036128.

80.         A.N. Gorban and I. V. Karlin, Reconstruction lemma and fluctuation-dissipation theorem, Revista Mexicana de Fisica, 2002. V. 48 Suplemento 1,  PP. 238-242.

81.         A.N. Gorban and I. V. Karlin, Geometry of irreversibility, in: Recent Developments in Mathematical and Experimental Physics, Volume C:  Hydrodynamics and Dynamical Systems, Ed. F. Uribe (Kluwer, Dordrecht, 2002), pp. 19-43.

82.         A.N. Gorban and I. V. Karlin, Macroscopic dynamics through coarse-graining: A solvable example, Phys. Rev. E. V 65. 026116(1-5) (2002).

83.         I.V. Karlin and A.N. Gorban, Hydrodynamics from Grad's equations: What can we learn from exact solutions? Ann. Phys. (Leipzig) 10-11 (2002),  pp. 783-833. E-print: http:,

84.         A.N. Gorban, Zinov'ev A.Y., Pitenko A.A., Data vizualization. The method of elastic maps, Neirocompjutery, 2002, 4, 19-30.

85.         A.N. Gorban, A.A Rossiev, Iterative modeling of data with gaps via submanifolds of small dimension, Neirocompjutery, 2002, 4, 40-44.

86.         A. Gorban, Rossiev A., Makarenko N., Kuandykov Y., Dergachev V. Recovering data gaps through neural network methods. International Journal of  Geomagnetism and Aeronomy, 2002, Vol. 3, No. 2, December 2002.

87.         A.N. Gorban, V.T. Manchuk, A.V.Perfil’eva, E.V.Smirnova, E.P. Cheusova, The mechanism of increasing the correlation between physiological parameters for high adaptation tension, Siberian Ecological Journal, 2001, No 5, 651-655.

88.         A.N. Gorban, Gorlov A.M., Silantyev V.M. Limits of the turbin efficiency for free fluid flow, ASME Journal of Energy Resourses Technology, Dec.  2001, V. 123, Iss. 4, pp. 311-317.

89.         A.N. Gorban, Pitenko A.A., Zinov'ev A.Y., Wunsch D.C. Vizualization of any data uzing elastic map method ,  Smart Engineering System Design.  2001, V.11, p. 363-368.

90.         A.N. Gorban, Popova T.G., Sadovsky M.G., Wunsch D.C. Information content of the frequency dictionaries, reconstruction, transformation and  classification of dictionaries and genetic texts. Smart Engineering System Design, 2001, V.11, p. 657-663.

91.         A.N.Gorban, I.V.Karlin, P.Ilg and H.C.Ottinger Corrections and enhancements of quasi-equilibrium states, J. Non-Newtonian Fluid Mech., 2001,  V.96(1-2), PP. 203-219.

92.         A.N. Gorban, Karlin I.V., Ottinger H.C., Tatarinova L.L. Ehrenfest's argument extended to a formalism of nonequilibrium thermodynaics, Phys. Rev. E. 2001, V. 63. 066124.

93.         A.N. Gorban, Gorbunova K.O., Wunsch D.C. Liquid Brain: The Proof of Algorithmic Universality of Quasichemical Model of Fine-Grained Parallelism, Neural Network World, 2001, No. 4. P P. 391-412.

94.         A.N. Gorban, Zinovyev A. Yu. Method of Elastic Maps and its Applications in Data Visualization and Data Modeling. International Journal of Computing Anticipatory Systems, CHAOS. 2001. V. 12. PP. 353-369.

95.         V.A. Dergachev, Gorban A.N., Rossiev A.A., Karimova L.M., Kuandykov E., Makarenko N.G., Steier. The filling of gaps in geophysical time series by artificial neural networks, Radiocarbon, 2001, V. 43, No. 2, PP. 343-348.

96.         A.N.Gorban, V.P.Torchilin, M.V.Malyutov, M. Lu Modeling polymer brushes protective action ,  Simulation in Industry' 2000. Proceedings of 12-th  European Simulation Symposium ESS'2000. September 28-30, 2000, Hamburg, Germany. A publication of the Society of Computer Simulation  International. Printed in Delft, The Netherlands, 2000. PP. 651-655.

97.         A.N.Gorban, Neuroinformatics: What are us, where are we going, how to measure our way? Informacionnye technologii, 2000, 4. - С. 10-14.

98.         A.N. Gorban, K. O. Gorbunova, Liquid Brain: Kinetic Model of Structureless Parallelism, Internation Journal of Computing Anticipatory Systems, CHAOS, V. 6, 2000, P.117-126.

99.         A.N. Gorban, I.V. Karlin, V.B. Zmievskii and S.V. Dymova, Reduced description in reaction kinetics, Physica A, 2000. V. 275, No. 3-4, PP. 361-379.

100.     A.N Gorban, The generalized Stone approximation theorem for arbitrary algebras of continuous functions, Dokl Akad Nauk, 365 (5), 586-588, 1999

101.     A.N. Gorban, A.A Rossiev, Neural network iterative method of principal curves for data with gaps,  J Comput Sys Sc Int, 38 (5): 825-830, 1999.

102.     A.N. Gorban, I.V.Karlin and  V.B.Zmievskii, Two-step approximation of space-independent relaxation, Transp.Theory Stat.Phys., 1999. V. 28(3), PP. 271-296.

103.     A.N. Gorban, Approximation of Continuous Functions of Several Variables by an Arbitrary Nonlinear Continuous Function of One Variable, Linear Functions, and  Their Superpositions. Appl. Math. Lett., 1998. V. 11, No. 3, pp. 45-49.

104.     S.E. Gilev, A.N. Gorban, The completeness theorem for semigroups of continuous functions, Dokl Akad Nauk, 362 (6): 733-734, 1998

105.     N.N.Bugaenko, A. N. Gorban, M.G.Sadovskii, Maximum entropy method in analysis of genetic text and measurement of its information content ,  Open systems and information dynamics. No. 5, 1998. - pp.265-278. 

106.     A.N. Gorban, Neuroinformatics and applications, Otkrytye sistemy (Open Systems), 1998, No. 4-5. pp. 36-41.

107.     A.N. Gorban, I.V. Karlin, Sroedinger operator in a overfull set ,  Europhys. Lett., 1998, V. 42, No.2, pp. 113-117.

108.     I.V. Karlin, A. N. Gorban, S. Succi, V.  Boffi, Maximum Entropy Principle for Lattice Kinetic Equation ,  Physical Review Letters, 1998, V. 81, No. 1, pp. 6-9.

109.     A.N. Gorban, Yeugenii M. Mirkes and Donald Wunsch, High Order Orthogonal Tensor Networks: Information Capacity and Reliability, Proc. IEEE/INNS International Conference on Neural Networks, Houston, IEEE, 1997, pp. 1311-1314.

110.     A.N. Gorban, Masha Yu. Senashova and Donald Wunsch, Back-Propagation of Accuracy, Proc. IEEE/INNS International Conference on Neural Networks, Houston, IEEE, 1997, pp. 1998-2001.

111.     N.N. Bugaenko, A. N. Gorban, M.G.Sadovskii, Information content of nucleotid sequences and their fragments. Biofizika. 1997. V. 42, Iss. 5, pp. 1047-1053.

112.     V.I. Bykov, A.N. Gorban, S.V. Dymova, Method of invariant manifolds for the reduction of kinetic description, ACH-Models Chem 134 (1): 83-95 1997

113.     A.N. Gorban, I.V.Karlin, Scattering rates versus moments: Alternative Grad equations, Phys. Rev. E, 1996, 54(4), R3109.

114.     A.N. Gorban, I.V.Karlin, Short-Wave Limit of Hydrodynamics: A Soluble Example, Phys. Rev. Lett., 1996, V. 77, N. 2, P. 282-285.

115.     N.N. Bugaenko, A.N. Gorban, M.G. Sadovskii, Information content in nucleotide sequences, Mol Biol, 30 (3): 313-320, 1996.

116.     A.N. Gorban, T.G. Popova, M.G. Sadovskii, Human virus genes are less redundant than human genes, Genetika, 32 (2), 289-294, 1996.

117.     A.N. Gorban, I.V.Karlin, V.B.Zmievskii, T.F.Nonnenmacher, Relaxational trajectories: global approximations, Physica A, 1996, V.231, No.4, p.648-672.

118.     A.N. Gorban, D.N.Golub, Multi-Particle Networks for Associative Memory, Proc. of the World Congress on Neural Networks, Sept. 15-18, 1996, San Diego, CA, Lawrence  Erlbaum Associates, 1996, pp. 772-775.

119.     S.E. Gilev, A. N. Gorban, On Completeness of the Class of Functions Computable by Neural Networks, Proc. of the World Congress on Neural Networks, Sept. 15-18, 1996,  San Diego, CA, Lawrence Erlbaum Associates, 1996, pp. 984-991.

120.     A.N. Gorban, D.A. Rossiyev, E.V. Butakova, S.E. Gilev, S.E. Golovenkin, S.A. Dogadin, D.A. Kochenov, E.V. Maslennikova, G.V. Matyushin, Y.E. Mirkes, B.V. Nazarov, Medical and Physiological Applications of MultiNeuron Neural Simulator. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.

121.     M.G. Dorrer, A.N. Gorban, A.G. Kopytov, V.I. Zenkin, Psychological Intuition of Neural Networks. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.

122.     A.N. Gorban, C. Waxman, Neural Networks for Political Forecast. Proceedings of the 1995 World Congress On Neural Networks, A Volume in the INNS Series of Texts, Monographs, and Proceedings, Vol. 1, 1995.

123.     A.N. Gorban, T.G. Popova, M.G. Sadovskii, Redundancy of genetic texts, Mol Biol, 28 (2), 206-213, 1994.

124.     A.N. Gorban, T.G. Popova, M.G. Sadovskii, Correlation approach to comparing nucleotide-sequences, Zh Obshch Biol, 55 (4-5), 420-430, 1994.

125.     A.N. Gorban, I.V. Karlin, General approach to constructing models of the Boltzmann equation, Physica A, 206 (1994), 401-420.

126.     A.N. Gorban, I.V. Karlin, Method of invariant manifolds and regularization of acoustic spectra, Transport Theory and Stat. Phys., 23, 559-632, 1994.

127.     A.N. Gorban, E.M. Mirkes, T.G. Popova, M.G. Sadovskii, A new approach to the investigations of statistical properties of genetic texts, Biofizika 38 (5), 762-767, 1993.

128.     A.N. Gorban, E.M. Mirkes, T.G. Popova, M.G. Sadovskii, The comparative redundancy of genes of various organisms and viruses, Genetika 29 (9), 1413-1419, 1993.

129.     A.N. Gorban, I.V.Karlin, Structure and Approximations of the Chapman-Enskog Expansion for Linearized Grad Equations, Transport Theory and Stat.Phys, V.21, No 1&2,  P.101-117, 1992.

130.     V.I. Verbitskii, A.N. Gorban, Jointly dissipative operators and their applications, Siberian Math J, 33 (1), 19-23, 1992.

131.     A.N. Gorban, E.M. Mirkes, A.P. Svitin, Method of multiplet covering and its application for the prediction of atom and molecular-properties, Zh Fiz Khim, 66 (6): 1504-1510, 1992.

132.     V.I. Bykov, V.I. Verbitskii, A.N. Gorban, Evaluation of cauchy-problem solution with inaccurately given initial data and the right part, Izv Vuz Mat, (12), 5-8, 1991.

133.     A.N. Gorban, V.I.Verbitsky, Simultaneously Dissipative Operators and Quasi-Thermodynamicity of the Chemical Reactions Systems, Advances in Modelling and Simulation, 1992, V.26,  N1, p.13-21.

134.     N.N. Bugaenko, A. N. Gorban, I.V.Karlin  Universal Expansion of the Triplet Distribution Function, Teoreticheskaya i Matematicheskaya Fisica, V.88, No.3, P.430-441(1991).

135.     A.N. Gorban, I.V.Karlin, Approximations of the Chapman-Enskog Expansion, Zh.Exp.Teor.Fis., V.100, No.4(10), P.1153-1161(1991); Sov. Phys. JETP, V.73(4),  P.637-641.(1991).

136.     S.Ye. Gilev, A. N. Gorban and E.M. Mirkes, Small Experts and Internal Conflicts in Learnable Neural Networks, Doklady Acad. Nauk SSSR, V.320, No.1, (1991) P.220-223.

137.     A.N. Gorban, E.M. Mirkes, A.N. Bocharov, V.I. Bykov,  Thermodynamic consistency of kinetic data, Combust Explosion & Shock, 25 (5), 593-600, 1989.

138.     V.I. Verbitskii, A.N. Gorban, G.S. Utiubaev, Y.I. Shokin, Moores effect in interval spaces, Dokl Akad Nauk SSSR, 304 (1), 17-21 1989.

139.     A.N. Gorban, M.G. Sadovskii, Optimal strategies of spatial-distribution - Olli effect, Zh Obshch Biol 50 (1), 16-21, 1989.

140.     A.N. Gorban, K.R.Sedov and  E.V.Smirnova, Correlation Adaptometry as a Method for Measuring the Health, Vestnik Acad. Medic. Nauk SSSR, No.5, P.69-75(1989).

141.     V.I.Bykov, A. N. Gorban, A Model of Autooscillations in Association Reactions, Chem.Eng.Sci., V.42, No.5, P.1249-1251(1987).

142.     A.N. Gorban, M.G.Sadovskii, Evolutionary Mechanisms of Creation of Cellular Clusters in Flowrate Cultivators, Biotechnology and Biotechnics, No.5, P.34-36(1987).

143.     V.I.Bykov, A. N. Gorban, G.S.Yablonskii. Thermodynamic Function Analogue for Reactions Proceeding Without Interactions of Various Substances, Chem.Eng.Sci., V.41, No.11, P.2739-2745 (1986).

144.     V.I. Bykov, S.E. Gilev, A.N. Gorban, G.S. Yablonskii, Imitation modeling of the diffusion on the surface of a catalyst, Dokl Akad Nauk SSSR, 283 (5): 1217-1220 1985.

145.     V.I. Bykov, A.N. Gorban, Simplest model of self-oscillations in association reactions, React Kinet Catal Lett, 27 (1): 153-155 1985

146.     V.I. Bykov, A.N. Gorban, T.P. Pushkareva, Autooscillation model in reactions of the association, Zh Fiz Khim, 59 (2): 486-488, 1985.

147.     A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Description of non-isothermal reactions using equations of nonideal chemical-kinetics, Kinet Catal, 24 (5), 1055-1063, 1983.

148.     V.I. Bykov, A.N. Gorban, L.P. Kamenshchikov, G.S. Yablonskii, Inhomogeneous stationary states in reaction of carbon-monoxide oxidation on platinum, Kinet Catal, 24 (3), 520-524, 1983

149.     V.I. Bykov, A.N. Gorban, Quasithermodynamic characteristic of reactions without the reaction of different substances, Zh Fiz Khim, 57 (12), 2942-2948, 1983.

150.     V.I. Bykov, A.N. Gorban, G.S. Yablonskii, Description of non-isothermal reactions in terms of Marcelin-De-Donder kinetics and its generalizations, React Kinet Catal Lett, 20 (3-4), 261-265, 1982.

151.     S.E. Gilev, A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Simulative modeling of processes on a catalyst surface, Dokl Akad Nauk SSSR, 262 (6), 1413-1416, 1982.

152.     V.I. Elokhin, G.S. Yablonskii, A.N. Gorban, V.M. Ceresiz, Dynamics of chemical-reactions and non-physical steady-states, React Kinet Catal Lett, 15 (2), 245-250, 1980.

153.     A.N. Gorban, G.S. Yablonskii, On one unused possibility in the kinetic experiment design, Dokl Akad Nauk SSSR, 250 (5): 1171-1174, 1980.

154.     A.N. Gorban, V.I. Bykov, G.S. Yablonskii, The Path to Equilibrium, Intern. Chem. Eng. V.22, No.2, P.386-375(1982).

155.     A.N. Gorban, V.M.Ceresiz, Slow Relaxations of Dynamical Systems and Bifurcations of Omega-Limit Sets, Soviet Math. Dokl., V.24, P.645-649(1981).

156.     A.N. Gorban, V.I. Bykov, G.S. Yablonskii, Macroscopic Clusters Induced by Diffusion in Catalytic Oxidation Reactions, Chem. Eng. Sci., 1980. V. 35, N. 11. P. 2351-2352. .

157.     A.N. Gorban, V.I.Bykov, V.I.Dimitrov. Marcelin-De Donder Kinetics Near Equilibrium, React. Kinet. Catal. Lett., V.12, No.1, P.19-23(1979).

158.     A.N. Gorban, Priori evaluation of the region of linearity for kinetic-equations, React Kinet Catal Lett, 10 (2), 149-152, 1979

159.     A.N. Gorban, Invariant Sets for Kinetic Equations, React. Kinet. Catal. Lett., 1979, V.10, P.187-190.

160.     A.N. Gorban, Sets of Removable Singularities and Continuous Mappings, Siberian Math. Journ., V.19, P.1388-1391(1978).

161.     A.N. Gorban, V.B. Melamed, Certain properties of Fredholm analytic sets in Banach-spaces, Siberian Math J, 17 (3), 523-526, 1976.