Alexander Gorban
Director of the Mathematical Modelling Centre and Professor of Applied Mathematics
Tel: +44(0) 116 223 1433
Email: ag153@le.ac.uk
New: A honorary title: Pioneer of Russian Neuroinformatics (2 October 2017).
Nomination for the Research Impact Award
Pattern Recognition in Big Data
Researchers: Professor Alexander Gorban, Professor Jeremy Levesley, Dr Ivan Tyukin, Dr Evgeny Mirkes, Dr Andrey Mudrov, Department of Mathematics
Nomination
LtoR: I. Tyukin, J. Levesley, A. Gorban, E. Mirkes
Websites
 Google Scholar Profile
 Personal webpage
Teaching
Data mining
Online resources:
 PCA, SOM and GSOM applet
 Kmeans and Kmedoids applet
 kNN and Potential energy applet
 Data cartography: Political Atlas of the World (to be continued)
Highlights:
Workshop "Hilbert's Sixth Problem'', University of Leicester, May 0204, 2016. The original Hilbert's formulation (in English translation) was: "6. Mathematical Treatment of the Axioms of Physics. ...(continued here)
Preface to the special issue “Model reduction across disciplines” of Math. Model. Nat. Phenom. (Vol. 10, No. 3, 2015, pp. 1–5) dedicated to 60th birthday of A. Gorban, by Guest Editors: G. Fridman, J. Levesley, I. Tyukin, D. Wunsch
Lifetime Achievement Award
MaCKIE2015, Mathematics in (bio)Chemical Kinetics and Engineering.
Lifetime Achievement Award in recognition of outstanding contributions to the research field of (bio)chemical kinetics.
Media
 High praise for Leicester data mining team’s research into trauma patient deaths (11 May 2017) Our paper highlighted by the journal 'Computers in Biology and Medicine' as ‘honoured’ and ‘esteemed’
 Leicester students win international data analytics competition
 Reaction to the work about Hilbert Sixth Problem: QuantaMagazine, July 21, 2015: Famous Fluid Equations Are Incomplete
A 115year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.
Press release in AlphaGalileo
 Visualisation of the invisible: University of Leicester mathematicians working with geoscientists from Weatherford give the possibility to see structures deeply in the Earth (November 29, 2017)
 Unsolved after 116 years: International academics to discuss Hilbert's sixth problem (April 11,2016)
Press releases in ScienceDaily:

Helping robots correct errors onthefly and learn from each other (August 21, 2017)
 New capillarity effects in ideal gases solve an old mathematical mystery(November 24, 2016)
 New approach for screening toxic chemicals mimics mammal senses (10 October 2016).
 Trauma patient deaths peak at two weeks (September 2, 2016)
 'Adaptation energy' in animals: Mathematicians provide solution to 78 year old mystery (March 22, 2016)
 Breakthrough study discovers six changing faces of 'global killer' bacteria(September 30, 2014)
 New hope for beloved family pets: New blood test for canine cancer(September 23, 2014)
 Mathematicians solve decadeold 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)
Publications
Selected books
 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.
 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 9783540737490)
 A.N. Gorban, N. Kazantzis, I.G. Kevrekidis, H.C. Öttinger, C. Theodoropoulos (eds), Model Reduction and CoarseGraining Approaches for Multiscale Phenomena, Springer, BerlinHeidelbergNew 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, BerlinHeidelbergNew 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)] [PrefaceContentsIntroduction(pdf)] [Editorial Reviews (htm)][Authors(gif)] Russian website with this book
 A.N. Gorban, Singularities of transition processes in dynamical systems: Qualitative theory of critical delays, Electron. J. Diff. Eqns. Monograph 5, 2004, 55 p.
 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), 54845485; (2) G. Wedler in Chem.Ing.Tech. 64 (1992) (8), 767768)
Selected papers

I. Tyukin, A.N. Gorban, C. Calvo, J. Makarova, V.A. Makarov. HighDimensional Brain: A Tool for Encoding and Rapid Learning of Memories by Single Neurons, Bull Math Biol, 2018, https://doi.org/10.1007/s1153801804155

A.N. Gorban. Hilbert's Sixth Problem: the endless road to rigour. Philosophical Transactions of The Royal Society A 376(2118), 20170238, 2018. Introduction to the special issue of Phil. Trans. R. Soc. A 376, 2018, `Hilbert's Sixth Problem'

A.N. Gorban, I.Y. Tyukin. Blessing of dimensionality: mathematical foundations of the statistical physics of data. Philosophical Transactions of The Royal Society A 376(2118), 20170237, 2018.

A.N. Gorban, N. Çabukoǧlu, Basic model of purposeful kinesis , Ecological Complexity, 33, 2018, 7583.

E.M. Mirkes, A.N. Gorban, J. Levesley, P.A.S. Elkington, J.A. Whetton, Pseudooutcrop Visualization of Borehole Images and Core Scans , Mathematical Geosciences, November 2017, 49 (8), 947–964.

Fehrman E., Muhammad A.K., Mirkes E.M., Egan V., Gorban A.N.
The Five Factor Model of Personality and Evaluation of Drug Consumption Risk. In: Palumbo F., Montanari A., Vichi M. (eds) Data Science. Studies in Classification, Data Analysis, and Knowledge Organization. Springer (2017), pp 231242. 
Gorban A.N., Tyukin I.Y. Stochastic Separation Theorems, Neural Networks, 94, October 2017, 255259

A.N. Gorban, I.V. Karlin, Beyond Navier–Stokes equations: capillarity of ideal gas, Contemporary Physics 58(1) (2017), 7090, DOI:10.1080/00107514.2016.1256123. arXiv eprint

E. Moczko, E.M. Mirkes, C. Ceceres, A.N. Gorban, S. Piletsky, Fluorescencebased assay as a new screening tool for toxic chemicals, Scientific Reports 6, Article number: 33922 (2016)

A.N. Gorban, E.M. Mirkes, A. Zinovyev, Piecewise quadratic approximations of arbitrary error functions for fast and robust machine learning, Neural Networks 84 (2016), 2838

E.M. Mirkes, T.J. Coats, J. Levesley, A.N. Gorban, Handling missing data in large healthcare dataset: a case study of unknown trauma outcomes, Computers in Biology and Medicine 75 (2016), 203216.

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 405 (2016), 127139.

A.N. Gorban, I.Yu. Tyukin, D.V. Prokhorov, K.I. Sofeikov, Approximation with random bases: Pro et Contra, Information Sciences 364365, (2016), 129145.

A. N. Gorban,·A. Zinovyev, Fast and userfriendly nonlinear principal manifold learning by method of elastic maps, in Proceedings DSAA 2015  IEEE International Conference on Data Science and Advanced Analytics, Paris; 10/2015.

A.N. Gorban, V.N. Kolokoltsov, Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes, Math. Model. Nat. Phenom. Vol. 10, No. 5, 2015, pp. 16–46.

A.N. Gorban, I.Yu. Tyukin, H. Nijmeijer, Further Results on LyapunovLike Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems, Proceedings of 53rd IEEE Conference on Decision and Control, December 1517, 2014. Los Angeles, California, USA, IEEE, 2014, pp. 15571562.

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 sixphase switch regulates pneumococcal virulence via global epigenetic changes, Nature Communications 5 (2014), Article number: 5055. Supplementary Information

A.N. Gorban, I. Karlin, Hilbert's 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations, Bulletin of the American Mathematical Society, Vol. 51, Issue 2, 2014, 186246. arXiv:1310.0406 [mathph]

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, 279290. arXiv:1305.4942 [qbio.QM].

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

A.N. Gorban, I. Tyukin, E. Steur, and H. Nijmeijer, Lyapunovlike conditions of forward invariance and boundedness for a class of unstable systems, SIAM J. Control Optim., Vol. 51, No. 3, 2013, pp. 23062334.

A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 14381456.

A.N. Gorban, G.S. Yablonsky, Grasping Complexity, Computers & Mathematics with Applications, Volume 65, Issue 10, May 2013, 14211426.

R.A. Brownlee, J. Levesley, D. Packwood, A.N. Gorban, Addons for Lattice Boltzmann Methods: Regularization, Filtering and Limiters, Progress in Computational Physics, 2013, vol. 3, 3152.

A.N. Gorban, Thermodynamic Tree: The Space of Admissible Paths, SIAM J. Applied Dynamical Systems, Vol. 12, No. 1 (2013), pp. 246278. DOI: 10.1137/120866919 arXiv eprint

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

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

Zinovyev, N. Morozova, A.N. Gorban, and A. HarelBelan, Mathematical Modeling of microRNAMediated 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. 189224.

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

N. Morozova, A. Zinovyev, N. Nonne, L.L. Pritchard, A.N. Gorban, and A. HarelBellan, Kinetic signatures of microRNA modes of action, RNA, Vol. 18, No. 9 (2012), 16351655.

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

A.N. Gorban, L.I. Pokidysheva,·E,V. Smirnova, T.A. Tyukina, Law of the Minimum Paradoxes, Bull Math Biol 73(9) (2011), 20132044.

A.N. Gorban, E.V. Smirnova, T.A. Tyukina, Correlations, risk and crisis: From physiology to finance, Physica A, Vol. 389, Issue 16, 2010, 31933217.

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

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. 2859.

R.A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, (23) (2008), 385406.

A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 145.

A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological grammars for data approximation, Applied Mathematics Letters, 20 (4) (2007), 382386.

A.N. Gorban, T.G.Popova, A.Yu. Zinovyev, Codon usage trajectories and 7cluster structure of 143 complete bacterial genomic sequences Physica A 353C (2005), 365387.

A.N. Gorban, I.V. Karlin, A.Y Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Phys. Rep., 396, 2004, 197403.

A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58, 2003, 47514768.
Recent preprints
 I.Y. Tyukin, A.N. Gorban, C. Calvo, J. Makarova, V.A. Makarov, Highdimensional brain. A tool for encoding and rapid learning of memories by single neurons, arXiv:1710.11227 [qbio.NC]
 I.Y. Tyukin, A.N. Gorban, K. Sofeikov, I. Romanenko, Knowledge Transfer Between Artificial Intelligence Systems, arXiv:1709.01547 [cs.AI]
 D.L. Crane, R.L. Davidchack, A.N. Gorban, Minimal cover of highdimensional chaotic attractors by embedded coherent structures, arXiv:1607.02180 [nlin.CD]
Scientific achievements
Kinetics
I developed a family of methods for model reduction and coarsegraining: method of invariant manifold, method of natural projector, relaxation methods. I have solved problems in gas kinetics, polymer dynamics, chemical reaction kinetics and biological kinetics. For this series of work I received the I. Prigogine prize and medal. I have been Clay Scholar (Cambridge, USA, 2000).
Solution of Hilbert problem
My student Karlin and I recently received the recognition of the scientific community for solving an important part of the Hilbert Sixth 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 7cluster 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 knowledgebased 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 visualisation 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. I, with with coauthors, 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
I 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 me in my 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.
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
Current grants
I'm the Lead Academic in three Knowledge Transfer Partnership (KTP) grants funded by Innovate UK foundation:
 KTP009890 between Apical Ltd and the University of Leicester (Visual Intelligence), 20152017, Knowledge Base Supervisor Dr I.Y. Tyukin
 KTP010522 between Visual Management Systems Limited and the University of Leicester (Visual Intelligence), 20172019, Knowledge Base Supervisor Dr I.Y. Tyukin
 KTP010604 between Dataffirm Limited and the University of Leicester (Mining of Big Text Data), 20172019, Knowledge Base Supervisor Dr E.M. Mirkes
Other grants and awards
 International Research Workshop: Hilbert's Sixth Problem, LMS, 2016;
 International Research Workshop: Hilbert's Sixth Problem, EPSRC, 2016;
 Weatherford Contract Research, 07.201306.2015
 Data Mining for Geological Information, NERC (Natural Environment Research Council), 07.201310.2013
 Development Fund, 2012; Mathematical Modelling of Adaptation and DecisionMaking in Neural Systems, The Royal Society, UK: International Joint UKJapan Project
 Modularity, Abstraction and Robustness of Network Models in Molecular Biology, Alliance : FrancoBritish Research Partnership Programme
 EPSRC and LMS grants for the International Workshop: Model Reduction and CoarseGraining Approaches for Multiscale Phenomena, Leicester, UK August 2426 2005
 Prigogine Award and Medal (2003)
 Clay Scholar, (Clay Mathematics Institute, Cambridge, USA, 2000)
 Russian Federal Grant of the 'Integration' program, 4 times (19982003)
 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 (19961998)
 19941996 American Mathematical Society Fellowship.
Personal details
Appointments history
2004present, University of Leicester
 2006present, Director of the Centre for Mathematical Modelling
 2004present, Chair in Applied Mathematics
20032004, Swiss Federal Institute of technology (ETH), Zurich, Switzerland)
 Senior Researcher
19832005, Institute of Computational Modelling, Russian Academy of Sciences, Siberian Branch, Krasnoyarsk, Russia (last year was on leave)
 19952005: Deputy Director and Head of the Computer Sciences Department
 19892006 Head of the Nonequilibrium Systems Laboratory
 19831989: Senior researcher
 19781983: Junior researcher
19771978, Institute of Catalysis, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia
 Engineer
1978, Institute of Theoretical & Applied Mechanics, USSR Academy of Sciences, Siberian Branch, Novosibirsk, Russia
 Engineer
1977, Tomsk Polytechnic University, Laboratory of Kinetics, Tomsk, Russia
 Junior researcher
1976, Omsk State University, Laboratory of Kinetics, Omsk, Russia
 Junior researcher
19731976, Omsk Railway Engineering Institute, Research Division, Omsk, Russia
 Engineer
Parttime teaching
19932006, Krasnoyarsk State Technical University, Krasnoyarsk, Russia: (last years was on leave)
 Head of Neurocomputers Department and Professor
19932003, Krasnoyask State Technological University, Krasnoyarsk, Russia
 Professor, Department of Automatization and Robots, 19932003;
19812001, Krasnoyarsk State University, Krasnoyarsk, Russia
 Professor, Psychological Faculty, 19982001
 Associate Professor, Higher Mathematics Chair, 19811989
Visiting positions
 Isaac Newton Institute for Mathematical Sciences (Cambridge, UK), 2010
 Institut des Hautes Etudes Scientiques (IHES, BuressurYvette, 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
 ViceChairman of Scientific Council at Krasnoyarsk State Technical University (direction: Software and tools for mathematical modelling) (19992006)
 Head of Workgroup on Neurocomputing, Ministry of Science and Technology Russian Federation (19982000)
 ViceChairman of Expert Council Krasnoyarsk Regional Science Foundation (19931996)
 Chairman of the Analytic Games Committee, Krasnoyarsk (19891994)
 Member of Jury of USSR National competition in mathematics for students of technical universities (19861990)
Membership of associations
 SIAM
 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)
Organiser of:
 International Research Workshop: Hilbert's Sixth Problem, University of Leicester, Leicester, UK, May 2May 4, 2016
 International Research Workshop: Coping with Complexity: Model Reduction and Data Analysis, Ambleside, Lake District, UK August 31September 4, 2009
 International Research workshop: Mathematics of Model Reduction, University of Leicester, Leicester, UK August 28August 30, 2007
 International Research Workshop: Lattice Boltzmann at allscales: 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 2426, 2006, Leicester University, Leicester, UK
 International Research Workshop: Geometry of Genome: Unravelling of Structures Hidden in Genomic Sequences,Leicester University, Leicester, UK, 22/09/200524/09/2005
 International Research Workshop: Model Reduction and CoarseGraining Approaches for Multiscale Phenomena, Leicester University, Leicester, UK August 2426 2005
 International Research Workshop: "Invariance and Model Reduction for Multiscale Phenomena," Zurich, August, 2003
 USANIS Neurocomputing Opportunities Workshop, Washington, DC, July 1999, (Sponsored by the National Science Foundation of the USA and Applied Computational Intelligence Lab, TTU) (CoChair)
 Russian annual National Conference: Neurionformatics (1998present)
 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, 19982003
 Soviet Union National competition in Neuroinformatics and Neurocomputers for students and young scientists, 1991
Supervision
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, NonEquilibrium 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, Universit 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
 '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, RussiaFrance, 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)