Minvydas Ragulskis

Professor (Applied Mathematics) at Kaunas University of Technology

Studentu 50-147, Kaunas LT-51368 Lithuania
minvydas.ragulskis@ktu.lt

Biography

Education

1989
Graduated Kaunas University of Technology, Faculty of Applied Mathematics
1992
Ph.D. (Doctor of Sciences) degree, Kaunas University of Technology
2002
Habilitation, Kaunas University of Technology

Positions and titles

1992 - 1997
Research fellow at Scientific Center “Vibrotechnika”, Kaunas
1997 - 1999
Assistant professor at Department of Mathematical Research in Systems, Faculty of Fundamental Sciences, Kaunas University of Technology
1999 - 2002
Associate professor at the Department of Mathematical Research in Systems and the Department of Informatics, Kaunas University of Technology
2000
Pedagogical degree of Docent
Since 2002
Full professor at Department of Mathematical Modeling
Since 2004
Founder and head of the Research Group for Mathematical and Numerical Analysis of Dynamical Systems
2008
Pedagogical degree of Professor, Kaunas University of Technology
2012
Member Elect Lithuanian Academy of Science
2015
Invited Expert at European Commission
2017
Honorary Invited Professor, Jinan University, Zhuhai, China

Awards and nominations

1998
Award for the best result in a section, in all ex-USSR Applied Mathematics Students Olympiad of Technical Universities
1989
Cum Laude Diploma, Kaunas University of Technology
2001
Lithuanian State stipend for young scientists
2005
Elsevier Grant
2005
Gold Medal at Lithuanian Annual Competition in the area of Machines and Instruments (with co-authors)
2005
Lithuanian State Science Award presented by Lithuanian Government
2008
Official Expert at Research Council of Lithuania
2010
Kazickas Foundation grant
2011
Spotlighting Exceptional Research Nomination - FOCUS: http://physics.aps.org/articles/v4/96
2012
Member Elect, Lithuanian National Academy of Sciences
2013
Official Expert at the Committee of National Science Awards
2015
Invited Expert, Research Executive Agency, European Commission, Brussels
2016
Zigmas Zemaitis Medal - awarded by Lithuanian Mathematical Society
2016
High-end Foreign Expert - Program administered by the State Administration of Foreign Experts Affairs (SAFEA), China
2016
Invited Rapporteur, Research Executive Agency, European Commission, Brussels
2017
Sentinels of Science Award (Computer Science) - Top overall contributors to peer review in science and research (http://publons.com/)

Grants

2011
MIP-041/2011 (Head of the Project) Project Title: H-rank for investigation of nonlinear systems – the concept and applications (2011-2012) Research Council of Lithuania
2012
MIP-100/2012 (Head of the Project) Project Title: Dynamic visual cryptography for the assessment of human visual system (2012-2014) Research Council of Lithuania
2013
VP1-3.1-SMM-10-V-02-005 (Senior Research Fellow) Project Title: Development, implementation and commercialization of training rocket equipment (2013-2015) European Social Fund
2015
GEOMAG (Head of the Project) Project Title: The impact of local and global magnetic fields to human heath (2015) KTU-LSMU
2015
MIP-078/2015 (Head of the Project) Project Title: Algebraic techniques and algorithms for time series analysis (2015-2018) Research Council of Lithuania
2016
CA15140 (Member of the Executive Committee) Project Title: Improving applicability of nature-inspired optimization by joining theory and practice (2016-2018) COST Program, European Commission

Editorial work

Official reviewer

Publons

Conference Committees

2010
M.Ragulskis (Member of the Scientific Committee) 3ICCSMS - The 3rd International Congress COMPLEX SYSTEMS IN MEDICINE AND SPORT, Kaunas, Lithuania. September 15-18, 2010.
2011
M.Ragulskis (International Program Committee Member; Invited Session Chair) KES'2011. Invited Session: Time Series Prediction Based on Fuzzy and Neural Networks. - 15th Internatioanl Conference on Knowledge based Engineering Systems, Kaiserslautern, Germany. 12-14 September 2011.
2011
M.Ragulskis (Member of the Scientific Committee) RA'11 - 2-rd International Symposium Rare Attractors and Rare Phenomena in Nonlinear Dynamics, Riga-Jurmala, Latvia. 16-20 May, 2011
2012
M.Ragulskis (Program Committee Member) AMATH'12 - 17th International Conference on Applied Mathematics, Montreux, Switzerland. December 29-31, 2012.
2012
M.Ragulskis (International Scientific Committee) ICEM 15 - 15th International Conference on Experimental Mechanics, Faculty of Engineering, University of Porto, Potugal. 22-27 July 2012.
2013
M.Ragulskis (Member of the Program Committee) SAM 13 - The 2013 International Conference on Security and Management, Las Vegas, USA. July 22-25, 2013.
2013
M.Ragulskis (Program Committee Member) SCSI 2013 - The 2013 International Conference on Systems, Control, Signal Processing and Informatics, Rhodes (Rodos) Island, Greece. July 16-19, 2013.
2013
M.Ragulskis (Program Committee Member) AMCM 2013 - The 2013 International Conference on Applied Mathematics and Computational Methods, Venice, Italy. September 28-30, 2013.
2014
M.Ragulskis (Program Committee Member) EICTA 2014 - International Conference on Emerging Information and Communication Technologies and Applications 2014, Hangzhou, China. Nov 15-16, 2014.
2014
M.Ragulskis (Program Committee Member) CC 2014 - The 2014 International Conference on Communications and Computers, Saint Petersburg State Politechnical University, Saint Petersburg, Russia. September 23-25, 2014.
2014
M.Ragulskis (Program Committee Member) ETE 2014 - The 2014 International Conference on Educational Technologies and Education, Interlaken, Switzerland. February 22-24, 2014.
2014
M.Ragulskis (Program Committee Member) SCSI 2014 - The 2014 International Conference on Systems, Control, Signal Processing and Informatics, Prague, Czech Republic. April 2-4, 2014.
2014
M.Ragulskis (International Scientific Committee) CSCC 2014 - 18th International Conference on Circuits, Systems, Communications and Computers, Santorini Island, Greece. July 17-21, 2014.
2014
M.Ragulskis (Member of the Program Committee) ITISE 2014 - International Work-Conference on Time Series Analysis, Granada, Spain. June 25-27, 2014.
2014
M.Ragulskis (International Scientific Committee) MSM 2014 - 10-th International Conference Mechatronic Systems and Materials, Opole, Poland. 7-10 July, 2014.
2014
M.Ragulskis (Head of the Organization Committee) International Conference VIBROENGINEERING, Katowice, Poland. 13-15 October, 2014.
2014
M.Ragulskis (Head of the Organization Committee) International Conference VIBROENGINEERING, Guiyang, China. 7-10 November, 2014.
2014
M.Ragulskis (Program Committee Member) ICICC 2014 - International Conference on IoT and Cloud Computing, Shanghai, China. 21-23 November, 2014.
2015
M.Ragulskis (International Scientific Committee) CSCC 2015 - 19th Int. Conf. on Circuits, Systems, Communications and Computers, Zakynthos, Greece. 16-20 July, 2015.
2015
M.Ragulskis (International Scientific Committee) IMETI 2015 - International Multi-Conference on Engineering and Technology Innovation 2015. Kaohsiung, Taiwan, October 30 - November 03, 2015.
2016
M.Ragulskis (Scientific Advisory Board) ICEM 17 - 17-th International Conference on Experimental Mechanics, Rhodes, Greece. 3-7 July, 2016.
2016
M.Ragulskis (International Scientific Committee) OPTICS2016 - 5th International Conference and Exhibition on Lasers, Optics & Photonics, Atlanta, Georgia , USA, November 28-30, 2016
2016
M.Ragulskis (Program Committee Member) ICATI 2016 - International Conference on Advanced Technology Innovation, Bali, Indonesia, June 30 - July 3, 2016
2016
M.Ragulskis (Conference Chairman) 21-st International Conference on VIBROENGINEERING, Brno, Czech Republic, August 31-September 1, 2016
2016
M.Ragulskis (Conference Chairman) 22-nd International Conference on VIBROENGINEERING, Moscow, Russia, October 4-7, 2016
2016
M.Ragulskis (Conference Chairman) 23-rd International Conference on VIBROENGINEERING, Istanbul, Turkey, October 7-9, 2016
2016
M.Ragulskis (Conference Chairman) 24-rd International Conference on VIBROENGINEERING, Shanghai, China, December 7-8, 2016
2016
M.Ragulskis (International Scientific Committee) CSCC 2016 - 20-th International Conference on Circuits, Systems, Communications and Computers, Corfu Island, Greece, July 14-17, 2016
2016
M.Ragulskis (International Scientific Committee) APSAC 2016 - 1-st International Conference on: Applied Physics, System Science and Computers, Dubrovnik, Croatia, September 28-30, 2016
2016
M.Ragulskis (Program Advisory Committee) 21-st International Scientific Conference MECHANIKA 2016, Kaunas, Lithuania, May 12-13, 2016
2016
M.Ragulskis (Program Committee) ITISE-2016 International Work-Conference on Time Series Analysis, Granada, Spain, June 27-29, 2016
2016
M.Ragulskis (Program Committee) IMETI-2016 International Multi-Conference on Engineering and Technology Innovation, Taichung, Taiwan, October 28 - November 01, 2016

Invited, Keynote or Plenary Speaker

2010
M.Ragulskis (Invited Keynote Speaker) 3ICCSMS - The 3rd International Congress COMPLEX SYSTEMS IN MEDICINE AND SPORT, Kaunas, Lithuania. September 15-18, 2010.
2011
M.Ragulskis (Invited Session Chair) KES'2011. Invited Session: Time Series Prediction Based on Fuzzy and Neural Networks. - 15th Internatioanl Conference on Knowledge based Engineering Systems, Kaiserslautern, Germany. 12-14 September 2011.
2012
M.Ragulskis (Invited Plenary Speaker) AMATH'12 - 17th International Conference on Applied Mathematics, Montreux, Switzerland. December 29-31, 2012.
2013
M.Ragulskis (Keynote Speaker) MSM-2013 - The 9th International Conference Mechatronic Systems and Materials, Vilnius, Lithuania. 1–3 July, 2013.
2014
M.Ragulskis (Invited Keynote Speaker) "Dynamic visual cryptography - theory and applications" ICETI 2014 - The 3-rd International Conference on Engineering and Technology Innovation, Kenting, Taiwan. October 31 - November 04, 2014.
2015
M.Ragulskis (Invited Keynote Speaker) "Dynamic Visual Cryptography for Fault Identification in Vibrating Micromechanical Structures" - International Conference on Reliability Systems Engineering & 2015 Prognostics and System Health Management Conference. Beijing, China, October 21-23, 2015.
2016
M.Ragulskis (Invited Keynote Speaker) "Identification on clusters in a trial group of persons based on their cardiac intervals and magnetic field data" - 8th international workshop Data Analysis Methods for Software Systems. Druskininkai, Lithuania, December 1-3, 2016.

Editorial Boards

Journal of Vibroengineering ISSN 1392-8716 (since 1999)
Journal of Measurements in Engineering ISSN 2335-2124 (since 2012)
Mathematical Models in Engineering ISSN 2351-5279 (since 2015)
Mathematical Modelling and Analysis ISSN 1392-6292 (since 2014)
The Open Numerical Methods Journal ISSN 1876-3898 (2009 - 2012) Discontinued
Vibroengineering Procedia ISSN 2345-0533 (since 2013)
International Journal of Engineering and Technology Innovation ISSN 2223-5329 (since 2013)
Journal of Computational Engineering ISSN 2356-7260 (since 2015)
Dyagnostyka ISSN 1641-6414 (since 2014)

Graduate students

Official Supervisor for graduate students

Since 2013
Martynas Vaidelys (09P - Informatics, Physical Sciences)
Since 2014
Sandra Aleksiene (09P - Informatics, Physical Sciences)
Since 2015
Tadas Telksnys (09P - Informatics, Physical Sciences)
Since 2017
Vaiva Siauciunaite (09P - Informatics, Physical Sciences)

Graduate students that successfully defended their Ph.D. thesis

2016
Mantas Landauskas. Title of Thesis: H-ranks for investigation of nonlinear and chaotic systems. ( 09P Informatics, Physical Sciences)
2015
Rita Palivonaite. Title of Thesis: Chaotic visual cryptography. ( 09P Informatics, Physical Sciences)
2015
Paulius Palevicius. Title of Thesis: Interferometric techniques for investigation of dynamical processes in microsystems. ( 09T Mechanical Engineering, Technological Sciences)
2014
Vilma Petrauskiene. Title of Thesis: Dynamic visual cryptography based on non-linear oscillations. ( 09T Mechanical Engineering, Technological Sciences)
2012
Kristina Lukoseviciute. Title of Thesis: Chaotic embedding and algebraic models for time series forecasting. ( 09P Informatics, Physical Sciences)
2010
Algiment Aleksa. Title of Thesis: Dynamic visual cryptography – the method and algorithmic realization. ( 09P Informatics, Physical Sciences)
2008
Violeta Kravcenkiene. Title of Thesis: Adaptive conjugate smoothing in hybrid numerical-experimental environments. ( 09P Informatics, Physical Sciences)
2007
Loreta Saunoriene. Title of Thesis: Time-averaged moiré techniques for nonlinear dynamical systems. ( 09P Informatics, Physical Sciences)

Doctoral Defense Committees

2002
M.Ragulskis (Opponent). Author: Vytautas Bucinskas. Title of Thesis: Investigation of characteristics of rolling ring drive with changable pitch. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2002.
2003
M.Ragulskis (Opponent). Author: Rima Kregzdyte. Title of Thesis: Statistical models of environmental pollution by heavy metals on health indices. Discipline: Biomedicine (10B). Degree Level: Doctoral. University: Kaunas University of Medicine. Defence Date: 2003.
2006
M.Ragulskis (Opponent). Author: Vitas Lendraitis. Title of Thesis: Development and investigation of membranous nanopositioning microactuator. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2006.
2009
M.Ragulskis (Doctoral dissertation committee member). Author: Gintare Leonaite. Title of Thesis: Analytical investigation of delay systems. Discipline: Informatics (09P). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2009.
2009
M.Ragulskis (Doctoral dissertation committee member). Author: Asta Kabelkaite. Title of Thesis: Investigation of influence of the running direction of paper and cardboard and defects of material to the eigenmodes of vibrations. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2009.
2010
M.Ragulskis (Doctoral dissertation committee member). Author: Inga Dulkiniene. Title of Thesis: The evaluation of the complexity of cardiovascular system parameters when performing physical tasks. Discipline: Biology (01B). Degree Level: Doctoral. University: Kaunas University of Medicine. Defense Date: 2010.
2010
M.Ragulskis (Opponent). Author: Martynas Patasius. Title of Thesis: Automated analysis of eye fundus images. Discipline: Informatics Engineering (07T). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2010
2010
M.Ragulskis (Scientific Consultant). Author: Ruta Rimasauskiene. Title of Thesis: Research and Development of the flow control devices with piezo actuators. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2010.
2011
M.Ragulskis (Opponent). Author: Darius Rudinskas. Title of Thesis: Design of an unmanned aerial vehicle flight parameter data transmission safety method. Discipline: Measurement Engineering (10T). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2011.
2012
M.Ragulskis (Doctoral dissertation committee member). Author: Natalija Tumanova. Title of Thesis: The numerical analysis of nonlinear mathematical models on graphs. Discipline: Mathematics (01P). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2012.
2012
M.Ragulskis (Doctoral dissertation committee member). Author: Sandra Bardauskiene. Title of Thesis: Short-term fasting on functional parameters of the cardiovascular system. Discipline: Nursing (10B). Degree Level: Doctoral. University: Lithuanian University of Health Sciences. Defense Date: 2012.
2013
M.Ragulskis (Doctoral dissertation committee member). Author: Ivan Suzdalev. Title of Thesis: Artificial neural networks to updrafts localization and forecasting. Discipline: Measurement Engineering. Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2013.
2013
M.Ragulskis (Doctoral dissertation committee member). Author: Vytautas Aseris. Title of Thesis: Computational modelling of biosensors utilizing intermediate substances. Discipline: Physical Sciences, Informatics (09P). Degree Level: Doctoral. University: Vilnius University. Defense Date: 2013.
2014
M.Ragulskis (Doctoral dissertation committee member). Author: Vytautas Rimsa. Title of Thesis: Discrete model of the particulate composite. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2014.
2014
M.Ragulskis (Doctoral dissertation committee member). Author: Mindaugas Skujus. Title of Thesis: Asymptotic conditions at infinity for the time-periodic Stokes problem set in domains with cylindrical outlets to infinity. Discipline: Mathematics (01P). Degree Level: Doctoral. University: Vilnius University. Defense Date: 2014.
2014
M.Ragulskis (Opponent). Author: Giedre Talateviciene. Title of Thesis: Changes of electrocardiographic parameters and their dynamic concatenations during whole-body cryotherapy and peliodotherapy procedures. Discipline: Nursing (10B). Degree Level: Doctoral. University: Lithuanian University of Health Sciences. Defense Date: 2014.
2014
M.Ragulskis (Doctoral dissertation committee member). Author: Saulius Pilkavicius. Title of Thesis: Modelling study of mechanical behavior of concrete-to-rebar bond under tension. Discipline: Mechanical Engineering (09T). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2014.
2014
M.Ragulskis (Doctoral dissertation committee member). Author: Olga Lavcel-Budko. Title of Thesis: The investigation of resonant interaction of some mathematical model of nonlinear waves. Discipline: Mathematics (01P). Degree Level: Doctoral. University: Vilnius Gediminas Technical University. Defense Date: 2014.
2015
M.Ragulskis (Dissertation Defense Board member). Author: Aleksejus Michalkovic. Title of Dissertation: Asymetric encryption system based on non-commuting algebraic systems creation and investigation. Discipline: Informatics (07T). Degree Level: Doctoral. University: Kaunas University of Technology. Defense Date: 2015.
2016
M.Ragulskis (Foreign Evaluator). Author: Alvar Daza Estaban. Title of Dissertation: Unpredictability and fractality in nonlinear dynamics. Discipline: Physics. Degree Level: Ph.D. University: University Rey Juan Carlos, Spain. Defense Date: 2016.
2017
M.Ragulskis (Dissertation Defense Board member). Author: Gintare Vaideliene. Title of Dissertation: Wavelet-based approach to the detection of defects in texture images: theoretical and practical aspects. Discipline: Physical Sciences, Informatics (09P). Degree Level: Doctoral. University: Kaunas University of Technology and Vytautas Magnus University. Defense Date: 2017.
2017
M.Ragulskis (Chairman of the Dissertation Defense Board). Author: Andrius Krisciunas. Title of Dissertation: Development of highly convergent numerical algorithms for short elastic wave simulation. Discipline: Physical Sciences, Informatics (09P). Degree Level: Doctoral. University: Kaunas University of Technology and Vytautas Magnus University. Defense Date: 2017.
2017
M.Ragulskis (Chairman of the Dissertation Defense Board). Author: Dalia Calneryte. Title of Dissertation: Development of multi-scale models for dynamic analysis of unidirectional composite textiles. Discipline: Physical Sciences, Informatics (09P). Degree Level: Doctoral. University: Kaunas University of Technology and Vytautas Magnus University. Defense Date: 2017.

Research interests

Introduction

Phase control of dendrytic neural networks, evolutionary algorithms for time series forecasting, dynamic visual cryptography, adaptive quadratures for realtime applications, non-uniform embeddings in multi-dimensional phase spaces, chaotic time-averaged moire fringes – is there anything in common among these diverse fields? The answer is a definite Yes. It all perfectly fits into the interests of the Research Group for Mathematical and Numerical Analysis of Dynamical Systems Nonlinear dynamical systems and chaos play an important role in many areas of science and engineering. Thus it is quite natural that our research interests are quite wide. Moreover, a healthy balance between rigorous theoretical analysis and practical applications produces fruitful results. In general, research directions in our Group can be conditionally classified into four subject areas: optics, numerical methods, cryptography and nonlinear dynamics. Though some aspects of different subject areas are highly intertwined, separate classification can help to crystallize the essential qualifiers of the each subject area.

Modelling of Optical Effects

Optics has traditionally been an important research area for our Group. Our field in optics could be shortly described as modelling of optical effects in virtual computational environments. The utilization of three basic components – numerical models of elastic dynamically interacting bodies, a physical model describing interference effects occurring whenever optical whole field fringe based experimental techniques are used to investigate these bodies, and the construction of digital graphical representations helps to mimic realistic optical processes taking place in those systems. And not only – such tools help to interpret complex optical phenomena and help to develop new measurement techniques.
We managed to propose several new measurement techniques and improvements of existing measurement techniques – time average photoelasticity; time average stochastic moire; time average geometric super moire; the generalization of Abel transform for vibrating tubes; corrections of classical formulas describing time average projection moire and time average geometric moire. The range of investigated systems is quite wide: from MEMS up to fluids, membranes, or bodies with fractal surface geometry. Investigations of optical phenomena originated new numerical cryptographic methods and initiated the development of specialized numerical techniques.

Development of Numerical Methods

We have been always heavily dependent on the development of novel numerical methods for the visualization of optical effects. One of the important results in this area worth noting is a new method based on conjugate smoothing used to represent a discontinuous field on a finite element mesh. Since our main interest lies in dynamical systems, time-averaging operators play an important role in our research (these operators also lead to applications in cryptography). We have proposed new quadrature rules which are especially effective in real time computational experiments.
A new numerical technique for time series forecasting based on fuzzy inference systems produced by symbolic multiplicative operator techniques. The employment of this criterion also gives an answer on the structure of the solution – contrary to the exp-function method where the structure of the solution is initially guessed and only then symbolic computations are used to identify the necessary parameters. Our technique provides a deeper insight into the structure of the original differential equation.

Visual Cryptography

Visual Cryptography (VC) is a cryptographic technique which allows visual information (pictures, text, etc.) to be encrypted in such way that the decryption can be performed by the human visual system, without the aid of computers. Classical VC is developed in the nineties and is based on a visual secret sharing scheme, where an image was broken up into n shares so that only someone with all n shares could decrypt the image, while any n−1 share revealed no information about the original image. Numerous modifications and advancements of the method have been proposed so far: halftone VC, colored VC, secret sharing schemes without pixel expansion, polynomial style sharing, multiple secrets schemes, circular VC, progressive image sharing, etc.
We have proposed a new concept of Dynamic VC. It is a one share method; the secret is encoded into a single image. The secret can be leaked only when this image is oscillated into a predefined direction at predefined amplitude. We exploit the inability of human visual system to follow rapid oscillatory motion and exploit the optical moiré phenomenon to form the secret in the time-averaged image. The security of the encryption can be increased if a non-harmonic moiré grating is used to form the image.
Another important development in the area of cryptography is a new class of hash functions based on time-averaging moiré operators. Special properties of algebras of moiré grating functions and time-averaging operators enabled to construct efficient one-way collision-free hash functions. The functional principle of these hash functions is based on the inherent ill-posed inverse problem which is in its turn based on optical moiré phenomena.

Nonlinear Dynamical Systems and Chaos

Since the title of our research group is Mathematical and Numerical Analysis of Dynamical Systems, dynamical systems traditionally occupy an important part of our research. Attractor control strategies based on small external impulses have been developed for adaptive control of particles in a field of propagating waves; for particles and films conveyed by an undulating membrane; for the parametric identification of complex systems. The bouncing ball model was generalized for Rayleigh surface waves; for electrophoresis and control of biomedical particles. The principles of the developed attractor control techniques are used to control chaotic networks of neurons with dendrytic dynamics.

Results and Future Trends

Our Group has originated a number of interesting solutions, methods and applications. We have developed the concept of dynamic visual cryptography which is a new branch in the science of digital image security. Our fuzzy time series forecasting methods based on the optimal attractor embedding outperform state-of-the-art predictors for such benchmark tests as Mackey-Glass series. We have developed an analytical criterion which determines if solution of nonlinear differential equation can be expressed in a form comprising finite number of standard functions; moreover, this criterion generates the structure of the solution automatically and outperforms homotopy perturbation methods. As mentioned previously, all these developments are closely related and originated by the theory of nonlinear dynamical systems and chaos.
Modelling of optical effects in virtual computational environments, novel numerical techniques and applications, dynamic visual cryptography, control and characterization of chaotic nonlinear systems build the ground for new challenging possibilities in mathematical and numerical analysis of dynamical systems.