Ivan Tyukin

Professor of Applied Mathematics

Head of the Visual Intelligence Lab

Tel: +44(0) 116 252 5106

Email: I.Tyukin@le.ac.uk

Personal details

• PhD, DrSc, Department of Mathematics
• My CV

Websites

• Google Scholar Profile
• Leicester Mathematics on Google Scholar

Teaching

• MA2021/MA2022 Differential equations and dynamics
• MA3077/MA7077 Operations Research

Research Highlights in Media

• Six degrees of separation: why it is a small world after all, October 2017 (EurekAlert!, Phys.org, Science Newsline, The Viral News)
• New theorems help Robots to correct errors on-the-fly and learn from each other, University in Science Daily, August 2017.
• Brain power breakthrough in mathematical modelling , University of Leicester Press Release, September 2007; Alpha Galileo, The world's leading resource for European research news, September 2007.
• Vision requires flexibility, Special Feature of RIKEN  (The Institute of Physical and Chemical Research), Brain Science Institute News, Quarterly Leaflet on the Research Highlights, Vol. 36, 2007

Patents

I. Romanenko, I. Tyukin, A.N. Gorban, K. Sofeikov. US Patent number US 10062013B2. Method of Image Processing

Current grants

Principal Investigator:

• £179,135. Innovate UK KTP009890 between Apical Ltd and the University of Leicester (Visual Intelligence), 2015-2017, Knowledge Base Academic Leader: Prof. A.N. Gorban, Company supervisor: Dr. Ilya Romanenko.
• £206,176. Innovate UK KTP010522 between Visual Management Systems Limited and the University of Leicester (Security and Visual Intelligence), 2017-2019, Knowledge Base Academic Leader: Prof. A.N. Gorban. Company Supervisor Mr. G. Campbell.

Academic Leader

• £245,824. Innovate UK KTP010819 between Photek Limited and University of Leicester (Data Analytics and Mathematical Modelling in High Energy Physics).

Selected Publications

Books

I. Tyukin. Adaptation in Dynamical Systems, Cambridge University Press, 2011

(ISBN-10: 0521198194 | ISBN-13: 9780521198196)

Journal

[1] A.N. Gorban, I.Y. Tyukin. Stochastic Separation Theorems. Neural Networks, 94, 255-259, 2017. doi:10.1016/j.neunet.2017.07.014 . Preprint available at https://arxiv.org/abs/1703.01203

[2] A.N. Gorban, I. Tyukin, D. Prokhorov, K. Sofeikov. Approximation with random bases: Pro et contra. Information Sciences, 324-325, 129-145, 2016.  Preprint available at http://arxiv.org/abs/1506.04631

[3] I.Yu. Tyukin, E. Steur, H. Nijmeijer, and Cees van Leeuwen. Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in Parameters.  Automatica, 49(8), 2409-2423, 2013, preprint available at  http://arxiv.org/abs/0903.2361

[4] A.N. Gorban, I.Yu. Tyukin,  E. Steur, H. Nijmeijer. Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems. SIAM Journal on Control and Optimization, 51(3): 2306-2334, 2013 (preprint available at http://arxiv.org/abs/0901.3577).

[5] E. Steur, I. Tyukin, and  H. Nijmeijer. Semipassivity and synchronization of diffusively coupled neural oscillators. Physica D: Nonlinear Phenomena, 2009. doi:10.1016/j.physd.2009.08.007. (preprint available at http://arxiv.org/abs/0903.3535)

Extended list of publications is available here

Research Areas and Interests

The area of my research interests contains the problems of analysis, modelling and synthesis of fragile, nonlinear, chaotic, meta-stable dynamics; control theory; adaptation in presence of unstable target dynamics, nonlinear parametrisation; state and parameter estimations for systems of ODEs with nonlinear in parameter right-had sides; synchronisation (stable and critical), biologically-inspired systems for processing of the visual information; specific networks with spiking neurons; analysis of dynamics of the spiking neuron models, their properties and possible functions. More recently I became interested in fundamentals of machine learning for problems with high-dimensional feature spaces, computer vision, and intelligent image processing.

They can be characterised by five major topics which are connected to each other by general idea of complex systems approach to understanding, analysis and synthesis of natural and artificial, intelligent systems.

• Processes and mechanisms of adaptation in complex nonlinear systems
  Systems with nonlinear parametrisation, unstable target dynamics, non-dominating (non-majorating, gentle, non-dominating) adaptation

• Artificial Intelligence and Machine learning
  Applications to data analytics and modelling, measure concentration effects for high-dimensional data, computer vision and security systems.

• Synchronisation in nonlinear dynamical systems
  Global, partial, intermittent  synchronisation in the ensembles of linearly and nonlinearly  coupled nonlinear oscillators. Study of connectivity-dependent synchronisation. Adaptive and unstable, multi-stable, alternating synchrony

• Optimisation algorithms for nonconvex and nonlinear problems
  Parameter estimation of superpositions of nonlinear parameterised functions (with applications to the problem of learning in multilayered pereceptrons)

• Neuroscience and physics of neuronal cells
  Principles of neuronal processing of  information. Study of properties of the biological cells, analysis of their functions. Structural organisation of the visual system, models system for robust  and adaptive processing (w.r.t modelled uncertainties) of visual information.

Other projects

• Mathematical Modelling of Adaptation and Decision-Making in Neural Systems
• Adaptation in Presence of Nonlinear Parameterization
• Non-uniform Small-gain Theorems and Convergence to Lyapunov-Unstable Invariant Sets

More detailed information about ongoing research projects