# Alexander Gorban

Director of the Mathematical Modelling Centre

phone: +44 (0) 116 223 1433

email: ag153(at)le.ac.uk

Google Scholar Profile

**Teaching**

**Data mining**

**Online resources:**PCA, SOM and GSOM applet, K-means and K-medoids applet

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**kNN and Potential energy applet and**

**Data cartography: Political Atlas of the World**(to be continued)

Leicester students win international data analytics competition

**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.

**Highlights:**

Workshop "Hilbert's Sixth Problem''**, University of Leicester, May 02-04, 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

MaCKIE-2015, Mathematics in (bio)Chemical Kinetics and Engineering.

Lifetime Achievement Award in recognition of outstanding contributions to the research field of (bio)chemical kinetics.

**Current grants**

Prof A.N. Gorban is 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), 2015-2017, Knowledge Base Supervisor Dr I.Y. Tyukin.
- KTP010522 between Visual Management Systems Limited and the University of Leicester (Visual Intelligence), 2017-2019, Knowledge Base Supervisor Dr I.Y. Tyukin.
- KTP010604 between Dataffirm Limited and the University of Leicester (Mining of Big Text Data), 2017-2019, Knowledge Base Supervisor Dr E.M. Mirkes.

**Media reaction on the** work about Hilbert Sixth Problem

QuantaMagazine, July 21, 2015

Famous Fluid Equations Are Incomplete

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer.

**Press Release** in EurecAlert

**Press Releases** in ScienceDaily:

- 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 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

**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 978-3-540-73749-0)****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.****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**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), 5484-5485;**(2) G. Wedler in Chem.-Ing.-Tech**. 64 (1992) (8), 767-768)**

**Selected Papers **

- A.N. Gorban, I.V. Karlin, Beyond Navier–Stokes equations: capillarity of ideal gas,
*Contemporary Physics*58(1) (2017), 70-90, DOI:10.1080/00107514.2016.1256123.**arXiv e-print** - E. Moczko, E.M. Mirkes, C. Ceceres, A.N. Gorban, S. Piletsky,
**Fluorescence-based assay as a new screening tool for toxic chemicals**,*Scientific Reports*6, Article number: 33922 (2016) - A.N. Gorban, E.M. Mirkes, A. Zinovyev,
**Piece-wise quadratic approximations of arbitrary error functions for fast and robust machine learning****,***Neural Networks*84 (2016), 28-38 - 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), 203-216. - 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), 127-139. - A.N. Gorban, I.Yu. Tyukin, D.V. Prokhorov, K.I. Sofeikov,
**Approximation with random bases: Pro et Contra**,*Information Sciences*364-365, (2016), 129-145. - A. N. Gorban,·A. Zinovyev,
**Fast and user-friendly non-linear 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 Lyapunov-Like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems,
*Proceedings of 53rd IEEE Conference on Decision and Control*, December 15-17, 2014. Los Angeles, California, USA, IEEE, 2014, pp. 1557-1562. - 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. 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, 186-246. arXiv:1310.0406 [math-ph] - 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. arXiv:1305.4942 [q-bio.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, Lyapunov-like conditions of forward invariance and boundedness for a class of unstable systems,
*SIAM J. Control Optim*., Vol. 51, No. 3, 2013, pp. 2306-2334. - A.N. Gorban, Maxallent: Maximizers of all entropies and uncertainty of uncertainty,
*Computers & Mathematics with Applications*, Volume 65, Issue 10, May 2013, 1438-1456. - A.N. Gorban, G.S. Yablonsky, Grasping Complexity
*, Computers & Mathematics with Applications*, Volume 65, Issue 10, May 2013, 1421-1426. - 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. - 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
- 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. 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.
- 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. Harel-Bellan, Kinetic signatures of microRNA modes of action, RNA, Vol. 18, No. 9 (2012), 1635-1655.
- 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), 2013-2044.
- 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.
- 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. 28-59.
- R.A. Brownlee, A. N. Gorban, and J. Levesley, Nonequilibrium entropy limiters in lattice Boltzmann methods, Physica A, 387, (2-3) (2008), 385-406.
- A.N. Gorban, Selection Theorem for Systems with Inheritance, Math. Model. Nat. Phenom., Vol. 2, No. 4, 2007, pp. 1-45.
- A.N. Gorban, N.R. Sumner, and A.Y. Zinovyev, Topological grammars for data approximation, Applied Mathematics Letters, 20 (4) (2007), 382-386.
- 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.
- A.N. Gorban, I.V. Karlin, A.Y Zinovyev, Constructive methods of invariant manifolds for kinetic problems, Phys. Rep., 396, 2004, 197-403.
- A.N. Gorban, I.V. Karlin, Method of invariant manifold for chemical kinetics, Chem. Eng. Sci. 58, 2003, 4751-4768.

Recent preprints

- A.N. Gorban, I.Y. Tyukin, Stochastic Separation Theorems, arXiv:1703.01203 [cs.LG]
- E.M. Mirkes, A.N. Gorban, J. Levesley, P.A.S. Elkington, J.A. Whetton, Pseudo-Outcrop Visualization of Borehole Images and Core Scans, arXiv:1702.02633 [physics.geo-ph]
- A.N. Gorban, I. Romanenko, R. Burton, I.Y. Tyukin, One-Trial Correction of Legacy AI Systems and Stochastic Separation Theorems, arXiv:1610.00494 [stat.ML]
- D.L. Crane, R.L. Davidchack, A.N. Gorban, Minimal cover of high-dimensional chaotic attractors by embedded coherent structures, arXiv:1607.02180 [nlin.CD]
- E. Fehrman, A.K. Muhammad, E.M. Mirkes, V. Egan, A.N. Gorban , The Five Factor Model of personality and evaluation of drug consumption risk, arXiv:1506.06297 [stat.AP].
- E. M. Mirkes, T. Walsh, E. J. Louis, A. N. Gorban, Long and short range multi-locus QTL interactions in a complex trait of yeast, arXiv:1503.05869 [q-bio.GN]