Papers in the Web of Science

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• M.Ragulskis, R.Maskeliunas, L.Ragulskis. Plotting moire fringes for circular structures from FEM results. Experimental Techniques. ISSN 0732-8818, Wiley. 2002, vol.26(1), p.31-35.

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Papers in the Web of Science

• M.Ragulskis, A.Palevicius, L.Ragulskis. Plotting holographic interferograms for visualisation of dynamic results from finite element calculations. International Journal for Numerical Methods in Engineering. ISSN 0029-5981, John Wiley & Sons. 2003, vol.56, p.1647-1659.

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Papers in the Web of Science

• M.Ragulskis, L.Ragulskis. Plotting isoclinics for hybrid photoelasticity and finite element analysis. Experimental Mechanics. ISSN 0014-4851, Sage Science Press. 2004, vol.44(3), p.235-240.

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• M.Ragulskis, K.Koizumi. Applicability of attractor control techniques for a particle conveyed by a propagating wave. Journal of Vibration and Control. ISSN 1077-5463, Sage Publications. 2004, vol.10(7), p.1057-1071.

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• M.Ragulskis, L.Ragulskis, R.Maskeliunas. Applicability of time average geometric moire for vibrating elastic structures. Experimental Techniques. ISSN 0732-8818, Wiley. 2004, vol.28(4), p.27-30.

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• R.Bansevicius, A.Fedaravicius, V.Ostasevicius, M.Ragulskis. Development of laser rifle trainer with full shot Imitation. Shock and Vibration. ISSN 1070-9622, IOS Press. 2004, vol.11(2), p.81-88.

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• M.Ragulskis, L.Ragulskis. Conjugate approximation with smoothing for hybrid photoelastic and FEM analysis. Communications in Numerical Methods in Engineering. ISSN 1069-8299. John Wiley & Sons. 2004, vol. 20(8), p.647-653.

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• M.Ragulskis. Coexisting attractors and their control in rotary motion transfer mechanism. Journal of Vibration and Control. ISSN 1077-5463. Sage Publications, 2004, vol. 10, p. 101-113. DOI: 10.1177/107754604031475

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Papers in the Web of Science

• M.Ragulskis, L.Ragulskis. On interpretation of fringe patterns produced by time average photoelasticity. Experimental Techniques. ISSN 0732-8818, Wiley. 2005, vol.29(3), p.48-51.

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• M.Ragulskis, R.Maskeliunas, L.Saunoriene. Identification of in-plane vibrations using time average stochastic moiré. Experimental Techniques. ISSN 0732-8818, Wiley. 2005, vol.29(6), p.41-45.

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• M.Ragulskis, R.Maskeliunas, L.Ragulskis, V.Turla. Investigation of dynamic displacements of lithographic press rubber roller by time average geometric moire. Optics and Lasers in Engineering. ISSN 0143-8166, Elsevier. 2005, vol.43(4), p.951-962.

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• V.Ostasevicius, S.Tamulevicius, A.Palevicius, M.Ragulskis, R.Palevicius, V.Grigaliunas. Hybrid numerical—experimental approach for investigation of dynamics of microcantilever relay system. Optics and Lasers in Engineering. ISSN 0143-8166, Elsevier. 2005, vol.43(1), p.63-73.

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• .Ostasevicius, S.Tamulevicius, A. Palevicius, M.Ragulskis, V.Grigaliunas, V.Minialga. Synergy of Contact and Non-Contact Techniques for Design and Characterization of Vibrating MOEMS Elements. Journal of Microlithography, Microfabrication, and Microsystems. ISSN 1932-5150, SPIE. 2005, vol. 4(4), article no. 041602.

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• M.Ragulskis, A.Palevicius, L.Ragulskis, A.Fedaravicius. Applicability of time average fluid holography for analysis of propagating waves. Optical Engineering. ISSN 0091-3286, SPIE. 2005, vol. 44(10), article no. 105801.

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Presentations at Conferences

• M.Ragulskis, V.Kravcenkiene. Adaptive conjugate smoothing of discontinuous fields. Lecture Notes in Computer Science. Numerical Analysis and Its Applications: Third International Conference. Springer Verlag. 2005, vol.3401-0463, p.463-470.

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• A.Fedaravicius, M.Ragulskis, Z.Klimavicius. Computational support of the development of a mortar simulator with re-usable shells. 2nd International Conference on Computational Ballistics, MAY 18-20, 2005. WIT Transactions on Modelling and Simulation, vol.40, p.381-389, WIT Press, ISSN 1743-355X.

• L.Ragulskis, M.Ragulskis, A.Palevicius, et al. Shearographic technique for NDE analysis of high frequency bending vibrations of microstructures. 3rd Conference on Testing, Reliability, and Application of Micro and Nano-Material Systems, Proc. SPIE. MAR 08-10, 2005, p.118-125, 2005.

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Papers in the Web of Science

• M.Ragulskis, A.Fedaravicius, K.Ragulskis. Harmonic balance method for FEM analysis of fluid flow in a vibrating pipe. Communications in Numerical Methods in Engineering. ISSN 1069-8299, Wiley. 2006, vol.22(4), p.347-356.

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• M.Ragulskis, L.Saunoriene, J.Ragulskiene. Interpretation of fringes produced by time average reflection moire on a circular disk. Optics and Lasers in Engineering. ISSN 0143-8166, Elsevier. 2006, vol.44(11), p.1209-1218.

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• M.Ragulskis, L.Saunoriene. Applicability of optical geometric differentiation for time-average geometric moiré. Strain. ISSN 0039-2103.- 2006, Vol. 42(3), p. 173-179.

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• M.Ragulskis, R.Maskeliunas. Measurement of transverse vibrations of piezoelectric ceramics by atomic force microscopy. Experimental Techniques. ISSN 0732-8818, Wiley. 2006, vol.30(2), p.37-41.

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• M.Ragulskis, L.Ragulskis. Order adaptive integration rule with equivalently weighted internal nodes. Engineering Computations. ISSN 0264-4401, Emerald Publishing. 2006, vol.23(4), p.368-381.

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• V.Kravcenkiene, A.Aleksa, M.Ragulskis, R.Maskeliunas. Choice of smoothing parameter using photo-elastic coatings. Journal of Mechanical Engineering. ISSN 0039-2480, Universitas Labacensis. 2006, vol.52(4), p.237-241.

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Presentations at Conferences

• V.Ostasevicius, N.Gitis, A.Palevicius, M.Ragulskis, S.Tamulevicius. Hybrid experimental-numerical full-field displacement evaluation for characterization of micro-scale components of mechatronic systems. Solid State Phenomena. ISSN 1662-9779, Scientific Net. 2006, vol.113, p.73-78.

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• L.Saunoriene, M.Ragulskis, A.Palevicius, V.Ostasevicius, G.Janusas. Hybrid numerical-experimental moire technique for analysis of microstructures. Proc. SPIE 6345, Seventh International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, 2006, article no. 634511.

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Papers in the Web of Science

• M.Ragulskis, K.Ragulskis. The effect of dynamical self-orientation and its applicability for identification of natural frequencies. Nonlinear Dynamics. ISSN 0924-090X, Springer. 2007, vol.50(1-2), p.61-71.

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• M.Ragulskis, A.Bubulis, K.Ragulskis. Numerical procedure for fluid flow in a pipe performing transverse oscillations. Communications in Numerical Methods in Engineering. ISSN 1069-8299, John Wiley & Sons. 2007, vol.23, p.335-343.

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• A.Fedaravicius, V.Jonevicius, M.Ragulskis. Development of mortar simulator with shell-in-shell system – problem of external ballistics. Shock and Vibration. ISSN 1070-9622, IOS Press. 2007, vol.14(5), p.371-376.

• M.Ragulskis, A.Palevicius, L.Ragulskis, A.Bubulis. Generalised Abel transform for the analysis of fluid vibration in a tube. Optical Engineering. ISSN 0091-3286, SPIE. 2007, vol.46(6), 065801.

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• M.Ragulskis, A.Aleksa, L.Saunoriene. Improved algorithm for image encryption based on stochastic geometric moire and its application. Optics Communications. ISSN 0030-4018, Elsevier. 2007, vol.273(2), p.370-378.

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• M.Ragulskis, Z.Navickas. Hash function construction based on time average moiré. Discrete and Continuous Dynamical Systems-Series B. ISSN 1531-3492, American Institute of Mathematical Sciences. 2007, vol.8(4), p.1007-1020.

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• M.Ragulskis, M.Sanjuan, L.Saunoriene. Applicability of time average moire techniques for chaotic oscillations. Physical Review E. ISSN 1539-3755, American Physical Soc. 2007, vol. 76, article no. 036208.

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Book Chapters

• M.Ragulskis. Applicability of time average stochastic moire for cryptographic applications. Experimental Analysis of Nano and Engineering Materials and Structures. ISBN 978-1-4020-6238-4. Amsterdam: Springer, 2007, p.335-336.

Presentations at Conferences

• M.Ragulskis, L.Saunoriene. Order adaptive quadrature rule for real time holography applications. In: Boyanov T., Dimova S., Georgiev K., Nikolov G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. ISSN 0302-9743, Springer. 2007, vol.4310, p.685-692.

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• M.Ragulskis, V.Ostasevicius, A.Aleksa, A.Palevicius. Hybrid numerical-experimental technique of transverse vibration of fluid in tube. Proceedings of FEDSM2007: 5th Joint ASME/JSME Fluids Engineering Conference, July 30 - August 2, 2007, San Diego, California, USA. - ISBN 0-7918-3805-6. - New York, 2007, p.[1-4].

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• R.Bansevicius, A.Busilas, M.Ragulskis, A.Palevicius, V.Ostasevicius. Development and experimental analysis of piezoelectric optical scanner based on FEM and laser holography. IMAC-XXV: a conference & exposition on structural dynamics, February 19-22, 2007, Orlando, Florida, USA - ISBN 0-912053-96-8. 2007, p.1-8.

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Papers in the Web of Science

• M.Ragulskis, M.A.F.Sanjuan. Chaotic pattern of unsmoothed isochromatics around the regions of concentrated stresses. Computers and Graphics. ISSN 0097-8493, Elsevier. 2008, vol.31(1), p.116-119.

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• M.Ragulskis, L.Saunoriene. Generalisations of compound trapeziodal rule. Applied Numerical Mathematics. ISSN 0168-9274, Elsevier. 2008, vol.58(1), p.40-58.

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• M.Ragulskis, M.A.F.Sanjuan. Transport of particles by surface waves: a modification of the classical bouncer model. New Journal of Physics. ISSN 1367-2630, Institute of Physics. 2008, issue 10, article No.083017.

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• M.Ragulskis, K.Ragulskis. Algorithm for analysis of periodic oscillations of structural systems with geometric nonlinearity. Communications in Numerical Methods in Engineering. ISSN 1069-8299, John Wiley & Sons. 2008, vol.24(12), p.1863-1871.

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Presentations at Conferences

• J.Ragulskiene, E.Sakyte, M.Ragulskis. Traveling wave electrophoresis - construction of numerical model. International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics Proceedings, vol.1048, p.450-453.

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Papers in the Web of Science

• M.Ragulskis, A.Aleksa, R.Maskeliunas. Contrast enhancement of time averaged fringes based on moving average mapping functions. Optics and Lasers in Engineering. ISSN 0143-8166, Elsevier. 2009, vol. 47(7-8), p.768-773.

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• M.Ragulskis, L.Saunoriene, R.Maskeliunas. The structure of moire grating lines and influence to time averaged fringes. Experimental Techniques. ISSN 0732-8818, Wiley-Blackwell Publishing. 2009, vol. march/april, p.60-64.

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• M.Ragulskis, Z.Navickas. Time average moire - back to the basics. Experimental Mechanics. ISSN 0014-4851, Springer. 2009, vol.49(8), p.439-450.

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• Z.Navickas, M.Ragulskis. How far one can go with the Exp function method? Applied Mathematics and Computations. ISSN 0096-3003, Elsevier. 2009, vol.211(2), p.522-530.

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• M.Ragulskis, K.Lukoseviciute. Non-uniform attractor embedding for time series forecasting by fuzzy inference systems. Neurocomputing. ISSN 0925-2312, Elsevier. 2009, vol.72(10-12), p.2618-2626.

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• M.Ragulskis. Time-averaged patterns produced by stochastic moiré gratings. Computers and Graphics. ISSN 0097-8493, Elsevier. 2009, vol.33(2), p.147-150.

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• M.Ragulskis, A.Aleksa. Image hiding based on time-averaging moire. Optics Communications. ISSN 0030-4018, Elsevier,.2009, vol.282, p.2752-2759.

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• M.Ragulskis, A.Aleksa, Z.Navickas. Image hiding based on time-averaged fringes produced by non-harmonic oscillations. Journal of Optics A: Pure and Applied Optics. ISSN 1464-4258, Institute of Physics Publishing. 2009, vol.11(12), article no. 125411.

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• M.Ragulskis, E.Sakyte, J.Seaone, M.A.F. Sanjuan. A new mechanical model for particle transport by surface waves and applications. Mathematical Problems in Engineering. ISSN 1024-123X, Hindawi Publishing Corporation. 2009, vol.2009, article ID 731358, 17 pages.

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• M.Ragulskis, E.Sakyte. An explicit equation for the dynamics of a particle conveyed by a propagating wave. Mathematical and Computer Modelling of Dynamical Systems. ISSN 1387-3954, Taylor & Francis. 2009, vol.15(4), p.395-405.

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Presentations at Conferences

• R.P.Bansevičius, A.Lipnickas, M.Ragulskis. New type of multi-degree-of-freedom piezoelectric actuators, based on active kinematic pairs. ICINCO 2009: Proceedings of the 6th International Conference on Informatics in Control, Automation and Robotics, July 2-5, 2009, Milan, Italy. Vol. 2. Robotics and Automation. Setsbal : INSTICC, 2009, p.159-164.

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• J.Ragulskienė, K.Lukoseviciūte, M.Ragulskis. Near-optimal embedding by genetic algorithms for time series prediction. International Conference on Numerical Analysis and Applied Mathematics 2009, Vol. 1, September 18-22, 2009, Rethymno, Crete, Greece. Melville, New York : American Institute of Physics, 2009, p. 148-151.

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• M.Ragulskis, E.Sakytė, A.Palevičius, R.Bendikienė. Thermo photo elasticity: hybrid numerical experimental approach for investigation smart structures. Proceedings of SPIE: Modeling, Signal Processing, and Control for Smart Structures 2009. Bellingham, vol. 7286, article no. 728608.

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• A.Algiment, M.Ragulskis, A.Palevičius, J.Ragulskienė. Adaptive conjugate smoothing of digital images using photo-elastic coatings. Proceedings of SPIE: Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2009. Bellingham, vol.7292, article no. 72924B

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Other Publications

• A.Aleksa, M.Ragulskis. Time-Averaged Moiré Fringes. Wolfram demonstration. http://demonstrations.wolfram.com/TimeAveragedMoireFringes/

• M.Ragulskis, Z.Navickas, L.Saunorienė, K.Lukoseviciute. Construction of cryptographic hash functions based on time average chaotic map. Journal of Applied Functional Analysis. ISSN 1559-1948, Eudoxus Press LLC. 2009, vol.4(4), p.611-622.

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Papers in the Web of Science

• K.Lukoseviciute, M.Ragulskis. Evolutionary algorithms for the selection of time lags for time series forecasting by fuzzy inference systems. Neurocomputing. ISSN 0925-2312, Elsevier. 2010, vol.73, p.2077-2088.

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• Z.Navickas, M.Ragulskis, L.Bikulciene. Be careful with the Exp-function method - additional remarks. Communications in Nonlinear Science and Numerical Simulation. ISSN 1007-5704, Elsevier. 2010, vol.15, p.3874-3886.

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• Z.Navickas, L.Bikulciene, M.Ragulskis. Generalization of Exp-function and other standard function based methods. Applied Mathematics and Computations. ISSN 0096-3003, Elsevier. 2010, vol.216(8), p.2380-2393.

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Book Chapters

• Loreta Saunoriene, Minvydas Ragulskis. Algorithms and Techniques for Time-Averaged Moiré Fringes. LAP Lambert Academic Publishing. 2010, Saarbrücken. ISBN 978-3-8383-5700-3, paperback, 148 Pages.

Other Publications

• M.Ragulskis, A.Aleksa, J.Ragulskiene. Image hiding based on circular moire fringes. WSEAS Transactions on Mathematics. ISSN 1109-2769, WSEAS. 2010, vol.9(2), p.90-99.

• M.Ragulskis. Book Review solicited by the Publisher. CHAOS IN STRUCTURAL MECHANICS by Awrejcewicz J. and Krysko V.A.. 1st Edition., 2008, XIII, 424 p. 195 illus., Hardcover, ISBN: 978-3-540-77675-8. Springer. Series: Understanding Complex Systems. http://www.springer.com/engineering/book/978-3-540-77675-8?detailsPage=reviews

• M.Ragulskis. Book Review solicited by the Publisher. RECENT PROGRESS IN CONTROLLING CHAOS edited by Miguel A.F. Sanjuan and Celso Grebogi. 2010, 431 pp., ISBN-13 978-981-4291-69-9; ISBN-10 981-4291-69-2. World Scientific Publishing. Series on Stability Vibration and Control of Systems, Series B - Vol. 16. http://www.worldscibooks.com/chaos/7563.html

Papers in the Web of Science

• E.Sakyte, R.Palivonaite, A.Aleksa, M.Ragulskis. Image hiding based on near-optimal moire gratings. Optics Communications. ISSN 0030-4018, Elsevier. 2011, vol.284, p.3954-3964.

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• M.Ragulskis, Z.Navickas. Interpretation of fringes produced by time-averaged projection moire. Strain. ISSN 0039-2103, Blackwell Publishing. 2011, vol.47, p.e357-e370.

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• Z.Navickas, R.Smidtaite, A.Vainoras, M.Ragulskis. The logistic map of matrices. Discrete and Continuous Dynamical Systems-Series B. ISSN 1531-3492, American Institute of Mathematical Sciences. 2011, vol.16(3), p.927-944.

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• E.Sakyte, M.Ragulskis. Self-calming of a random network of dendritic neurons. Neurocomputing. ISSN 0925-2312, Elsevier. 2011, vol.74(11), p.3912-3920.

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• M.Ragulskis, Z.Navickas, L.Bikulciene. The solitary solution of the Liouville equation produced by the Exp-function method holds not for all initial conditions. Computers and Mathematics with Applications. ISSN 0898-1221, Elsevier. 2011, vol.62, p367-382.

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• Z.Navickas, M.Ragulskis, L.Bikulciene. Special solutions of Huxley differential equation. Mathematical Modelling and Analysis. ISSN 1392-6292, Taylor & Francis. 2011, vol.16(2), p.248-259.

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• M.Ragulskis, K.Lukoseviciute, Z.Navickas, R.Palivonaite. Short-term time series forecasting based on the identification of skeleton algebraic sequences. Neurocomputing. ISSN 0925-2312, Elsevier. 2011, vol. 64(10), p.1735-1747.

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• M.Ragulskis, Z.Navickas. The rank of a sequence as an indicator of chaos in discrete nonlinear dynamical systems. Communications in Nonlinear Science and Numerical Simulation. ISSN 1007-5704, Elsevier. 2011, vol.16, p.2894-2906.

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• L.Saunoriene, M.Ragulskis. A secure steganographic communication algorithm based on self-organizing patterns. Physical Review E. ISSN 1539-3755, American Physical Soc. 2011, vol. 84(5), article no. 056213.

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Book Chapters

• Editor Dr. Elhadj Zeraoulia. Book title: Models and Applications of Chaos Theory in Modern Sciences. Science Publishers (USA) ISBN 978-1-57808-722-8. May 2011; 770 pages. A New Mechanical Model for Particle Transport by Surface Waves and Applications: M. Ragulskis, E. Sakyte, J.M. Seoane and M.A.F. Sanjuan in Section VII: Models and Applications of Chaos Theory in Mechanical Sciences. http://www.scipub.net/mathematics-and-statistics/models-and-applications-of-chaos-theory.html

• M.Ragulskis, A.Palevicius, L.Saunoriene. Chapter Title: Hybrid Numerical-Experimental Holographic Interferometry for Investigation of Nonlinearities in MEMS Dynamics, pp. 303-324. Book Title: Holography, Research and Technologies. Editor: Joseph Rosen. ISBN 978-953-307-227-2, Hard cover, 454 pages, Publisher: InTech, February 2011. http://www.intechweb.org/books/show/title/holography-research-and-technologies

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Presentations at Conferences

• V.Petrauskiene, J.Ragulskiene, E.Sakyte, M.Ragulskis. Near-optimal time function for secure dynamic visual cryptography. G. Bebis et al. (Eds.): International Symposium on Visual Computing 2011, Part II, Lecture Notes in Computer Science, Vol. 6939, pp.300–309.

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Other Publications

• PHYSICS - Spotlighting Exceptional Research. FOCUS: Hiding Secrets in Spontaneous Patterns. Published November 18, 2011. Physics 4, 96 (2011).  http://physics.aps.org/articles/v4/96

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• A.Aleksa, V.Petrauskiene, M.Ragulskis. Stochastic Time-Averaged Moiré Fringes. WOLFRAM Demonstration Project. The permanent URL for the Demonstration: http://demonstrations.wolfram.com/StochasticTimeAveragedMoireFringes/

Papers in the Web of Science

• M.Landauskas, M.Ragulskis. Clocking convergence to a stable limit cycle of a periodically driven nonlinear pendulum. Chaos: An Interdisciplinary Journal of Nonlinear Science. SSN 1089-7682, American Institute of Physics. 2012, vol.22, article no. 033138.

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• Z.Navickas, R.Smidtaite, A.Vainoras, M.Ragulskis. The explosive divergence in iterative maps of matrices. Communications in Nonlinear Science and Numerical Simulation. ISSN 1007-5704, Elsevier. 2012, vol.17(11), p.4430-4438.

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• M.Ragulskis, Z.Navickas, R.Palivonaite, M.Landauskas. Algebraic approach for the exploration of the onset of chaos in discrete nonlinear dynamical systems. Communications in Nonlinear Science and Numerical Simulation. ISSN 1007-5704, Elsevier. 2012, vol.17(11), p.4304-4315.

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• V.Petrauskiene, A.Aleksa, A.Fedaravicius, M.Ragulskis. Dynamic visual cryptography for optical control of vibration generation equipment. Optics and Lasers in Engineering. ISSN 0143-8166, Elsevier. 2012, vol.50(6), p.869-876.

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Presentations at Conferences

• M.Landauskas, J.Ragulskiene, M.Ragulskis. H-rank as a control tool for discrete dynamical systems. International Conference of Numerical Analysis and Applied MAathematics (ICNAAM 2012), Kos, Greece, Sep. 19-25, 2012, Book Series: AIP Conference Proceedings, vol.: 1479, p.2098-2101.

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• P.Palevicius, L.Saunoriene, M.Ragulskis. A secure communication system based on self-organizing patterns. Proceedings of the 2012 International Conference on Security & Management SAM 2012. Editors K.Daimi, H.R.Arabnia, CSREA Press, p.421-426.

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Papers in the Web of Science

• A.Palevicius, M.Ragulskis, G.Janusas. High frequency excitation for thermal imprint of microstructures into a polymer. Experimental techniques. ISSN 0732-8818, Wiley-Blackwell Publishing. 2013, vol.37(5), p.41-47.

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• Z.Navickas, M.Ragulskis. Comments on "Two exact solutions to the general relativistic Binet's equation". Astrophysics Space Sciences. ISSN: 0004-640X, Springer. 2013, vol.334(2), p.281-285.

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• Z.Navickas, L.Bikulciene, M.Rahula, M.Ragulskis. Algebraic operator method for the construction of solitary solutions to nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation. ISSN 1007-5704, Elsevier. 2013, vol.18(6), p.1374-1389.

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• R.Palivonaite, K.Lukoseviciute, M.Ragulskis. Algebraic segmentation of short nonstationary time series based on evolutionary prediction algorithms. Neurocomputing. ISSN 0925-2312, Elsevier. 2013, vol.121, p.354-364.

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• K.Malinauskas, P.Palevicius, M.Ragulskis, V.Ostasevicius. Validation of noninvasive MOEMS-assisted measurement system based on CCD sensor for radial pulse analysis. Sensors. ISSN 1424-8220, MPDI. 2013, vol.13, p.5368-5380.

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Presentations at Conferences

• M.Landauskas, M.Ragulskis. Clocking convergence to Arnold tongues - the H-rank approach. International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2013), Rhodes, Greece, Sep. 21-27, 2013, Book Series: AIP Conference Proceedings vol.1558, p.2457.

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• R.Palivonaite, A.Fedaravicius, A.Aleksa, M.Ragulskis. Near-optimal moire grating for chaotic dynamic visual cryptography. Lecture Notes in Computer Science, vol. 8237 "Advances in Visual Informatics", Proceedings of the Third International Visual Informatics Conference, 2013, p.48-58.

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• R.Palivonaite, A.Aleksa, M.Ragulskis. Visual Cryptography based on optical image projection. Lecture Notes in Electrical Engineering, vol.152: Innovations and Advances in Computer, Infomation, Systems Sciences, and Engineering. Editors K.Elleithy, T.Sobh. Springer, 2013, part 1, p.431-442.

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Papers in the Web of Science

• M.Landauskas, M.Ragulskis. A pseudo-stable structure in a completely invertible bouncer system. Nonlinear Dynamics. ISSN 0924-090X, Springer. 2014, vol.78(3), p.1629-1643.

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• R.Palivonaite, M.Ragulskis. Short-term time series algebraic forecasting with internal smoothing. Neurocomputing. ISSN 0925-2312, Elsevier. 2014, vol.127, p161-171.

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• V.Petrauskiene, R.Palivonaite, A.Aleksa, M.Ragulskis. Dynamic visual cryptography based on chaotic oscillations. Communications in Nonlinear Science and Numerical Simulation. ISSN:1007-5704, Elsevier. 2014, vol.19(1), p.112-120.

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• P.Ziaukas, T.Ragulskis, M.Ragulskis. Communication scheme based on evolutionary spatial 2x2 games. Physica A: Statistical Mechanics and its Applications. ISSN 0378-4371, Elsevier. 2014, vol.403, p.177-188.

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• Z.Navickas, M.Ragulskis. Comments on "A new algorithm for automatic computation of solitary wave solutions to nonlinear partial differential equations based on the Exp-function method". Applied Mathematics and Computations. ISSN 0096-3003, Elsevier. 2014, vol.243, p.419-425.

  [DOI] [PDF]

• V.Petrauskiene, A.Survila, A.Fedaravicius, M.Ragulskis. Dynamic visual cryptography for optical control of chaotic oscillations. Optics & Laser Technology. ISSN: 0030-3992, Elsevier. 2014, vol.57, p.129-135.

  [DOI] [PDF]

• R.Palivonaite, A.Aleksa, A.Paunksnis, A.Gelzinis and M.Ragulskis. Image hiding in time-averaged deformable moire gratings. Journal of Optics. ISSN 2040-8978, IOPScience. 2014, vol.16, article no. 025401.

  [DOI] [PDF]

• P.Palevicius, M.Ragulskis, A.Palevicius, V.Ostasevicius. Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations. Sensors. ISSN 1424-8220, MPDI. 2014, vol.14(1), p.1805-1821.

  [DOI] [PDF]

• M.Ragulskis, Hongyuan Jiang, Quan Quan, A.Fedaravicius, Gongnan Xie. Mechatronics and mechanical engineering in cyber-physical systems. Advances in Mechanical Engineering. ISSN 1687-8132, SAGE Publications. 2014, vol.2014, article no:591629.

  [DOI] [PDF]

Presentations at Conferences

• R.Palivonaite, K.Lukoseviciute, M.Ragulskis. Algebraic level-set approach for the segmentation of financial time series. A.I. Esparcia-Alcazar et al. (Eds.): EvoApplications 2014, Lecture Notes in Computer Sciences. vol.8602, pp. 239–250, 2014.

  [DOI] [PDF]

• T.Ragulskis, V.Ostasevicius, V.Pilkauskas, M.Ragulskis. Communication scheme based on evolutionary spatial games in the cloud computing environment. Transaction on IoT and Cloud Computing. ICAS Publishing. ISSN 2331-4753. 2014, vol.2(3), p.1-10.

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• P.Palevicius, M.Ragulskis, G.Janusas, A.Palevicius. A technique for the reconstruction of a map of continuous curves from interference fringes. Proc. of SPIE Vol. 9286, 92861G, p.1-8. Second International Conference on Applications of Optics and Photonics, edited by Manuel Filipe P. C. Martins Costa, Rogério Nunes Nogueira, 2014 SPIE. CCC code: 0277-786X/14/$18.

  [DOI] [PDF]

Papers in the Web of Science

• M.Vaidelys, J.Ragulskiene, S.Aleksiene, M.Ragulskis. Image hiding in time-averaged moiré gratings on finite element grids. Applied Mathematical Modelling. ISSN 0307-904X, Elsevier. 2015, vol.39, p.5783-5790.

  [DOI] [PDF]

• P.Palevicius, M.Ragulskis. Image communication scheme based on dynamic visual cryptography and computer generated holography. Optics Communications. ISSN 0030-4018, Elsevier. 2015, vol.335, p.161-167.

  [DOI] [PDF]

• D.Karaliene, Z.Navickas, R.Ciegis, M.Ragulskis. An extended Prony’s interpolation scheme on an equispaced grid. Open Mathematics. ISSN 2391-5455, De Gruyter. 2015, vol.13, p.333-347.

  [DOI] [PDF]

• Z.Navickas, T.Telksnys, M.Ragulskis. Comments on "The exp-function method and generalized solitary solutions". Computers and Mathematics With Applications. ISSN 0898-1221, Elsevier. 2015, vol.69, p.798-803.

  [DOI] [PDF]

• M.Vaidelys, J.Ragulskiene, P.Ziaukas, M.Ragulskis. Image hiding scheme based on the atrial fibrillation model. Applied Sciences. ISSN 2076-3417, MDPI. 2015, vol.5, p.1980-1991.

  [DOI] [PDF]

Book Chapters

• P.Palevicius, M.Ragulskis, A.Palevicius. Applicability of Time-Averaged Holography for Reliability Assessment of Chemical Sensors. Chapter 17 (pages 193-203). Book Title: "Nanotechnology in the Security Systems" - NATO Science for Peace and Security - Series C - Environmental Security. Edited by J.Bonza and S.Kruchinin. ISBN 978-94-017-9004-8. Springer Science+Business Media, Dordrecht, 2015.

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Presentations at Conferences

• Z.Navickas, T.Telksnys, M.Ragulskis. Special multiplicative operators for the solution of ODE - invariants and representations. International Journal of Engineering and Technology Innovation. ISSN 2223-5329, TAETI. 2015, vol.5(1), p.01-18.

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Papers in the Web of Science

• Z.Navickas, M.Ragulskis, R.Marcinkevicius, T.Telksnys. Generalized solitary waves in nonintegrable KdV equations. Journal of Vibroengineering. ISSN 1392-8716, JVE International, 2016, vol.18(2), p.1270‑1279.

  [DOI] [PDF]

• Z.Navickas, R.Marcinkevicius, T.Telksnys, M.Ragulskis. Existence of second order solitary solutions to Riccati differential equations coupled with a multiplicative term. IMA Journal of Applied Mathematics. ISSN 0272-4960, Oxford University Press. 2016, vol. 81, p.1163–1190.

  [DOI] [PDF]

• T. Telksnys, Z. Navickas, M. Ragulskis, M. Vaidelys. The order of a 2-sequence and the complexity of digital images. Advances in Complex Systems. World Scientific. ISSN: 0219-5259, 2016, vol.19, issue:04n05, article no.1650010 (25 pages).

  [DOI] [PDF]

• R.Ciegis, V.Starikovicius, N.Tumanova, M.Ragulskis. Application of distributed parallel computing for dynamic visual cryptography. The Journal of Supercomputing. ISSN 0920-8542. 2016, vol.72, p.4204-4220.

  [DOI] [PDF]

• Z.Navickas, R.Vilkas, T.Telksnys, M.Ragulskis. Direct and inverse relationships between Riccati systems coupled with multiplicative terms. Journal of Biological Dynamics. ISSN 1751-3758 , Taylor and Francis. 2016, vol.10, p 297-313.

  [DOI] [PDF]

• Z.Navickas, M.Ragulskis, T.Telksnys. Existence of solitary solutions in a class of nonlinear differential equations with polynomial nonlinearity. Applied Mathematics and Computation. ISSN 0096-3003, Elsevier, 2016, vol.283, p.333-338.

  [DOI] [PDF]

• A.P.Fedaravicius, Maosen Cao, M.Ragulskis. Control of a dendritic neuron driven by a phase-independent stimulation. Chaos, Solitons & Fractals, ISSN 0960-0779. Elsevier, 2016, vol. 85, p.77-83.

  [DOI] [PDF]

• M.Vaidelys, P.Ziaukas, M.Ragulskis. Competitively coupled maps for hiding secret visual information. Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, Elsevier. 2016, vol.443, p.91-97.

  [DOI] [PDF]

• R.Palivonaite, K.Lukoseviciute, M.Ragulskis. Short-term time series algebraic forecasting with mixed smoothing. Neurocomputing. ISSN 0925-2312, Elsevier, 2016, vol. 171, p. 854-865.

  [DOI] [PDF]

• R.Marcinkevicius, Z.Navickas, M.Ragulskis, T.Telksnys. Solitary solutions to a relativistic two-body problem. Astrophysics and Space Science. ISSN:0004-640X, Springer. 2016, vol. 361:201.

  [DOI] [PDF]

• Lu C., Wang Y., Ragulskis M., Cheng Y. Fault diagnosis for rotating machinery: A method based on image processing. PLOS ONE. ISSN 1932-6203, Public Library Science. 2016, vol.11(10), article ID: e0164111.

  [DOI] [PDF]

• M.Ragulskis, L.E.Munoz, R.Burdzik, J.I.Real, W.H.Hsieh, R.Zimroz. Shock and vibration in transportation engineering. Shock and Vibration. ISSN:1875-9203, Hindawi. 2016, vol.2016, article ID:8457605.

  [DOI] [PDF]

Papers in the Web of Science

• M.Vaidelys, Chen Lu, Yujie Cheng, M.Ragulskis. Digital image communication scheme based on the breakup of spiral waves. Physica A: Statistical Mechanics and its Applications. ISSN 0378-4371, Elsevier. 2017, vol.467, p.1-10.

  [DOI] [PDF]

• Z.Navickas, M.Ragulskis, R.Marcinkevicius, T.Telksnys. Kink solitary solutions to generalized Riccati equations with polynomial coefficients. Journal of Mathematical Analysis and Applications. ISSN 0022-247X, Elsevier. 2017, vol.448(1), p.156-170.

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• P.Ziaukas, A.Alabdulgader, A.Vainoras, Z.Navickas, M.Ragulskis. New approach for visualization of relationships between RR and JT intervals. PLoS ONE. ISSN 1932-6203, Public Library Science. 2017, vol.12(4). article ID e0174279.

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• P.Ziaukas, M.Ragulskis. Fractal dimension and Wada measure revisited: no straightforward relationships in NDDS. Nonlinear Dynamics. ISSN 0924-090X, Springer. 2017, vol.88, p.871-882.

  [DOI] [PDF]

• P.Palevicius, A.Aleksa, R.Maskeliunas, M.Ragulskis. Circular geometric moire for degradation prediction of mechanical components performing angular oscillations. Mechanical Systems and Signal Processing. ISSN 0888-3270, Elsevier. 2017, vol.86(A), p.278-285.

  [DOI] [PDF]

• Z. Navickas, M. Ragulskis, N. Listopadskis, T. Telksnys. Comments on "Soliton solutions to fractional-order nonlinear differential equations based on the exp-function method". Optik - International Journal for Light and Electron Optics. ISSN: 0030-4026, Elsevier. 2017, vol.132, p.223-231.

  [DOI] [PDF]

• M.Ragulskis, Lu Chen, G.Song, A.El Sinawi. Intelligent fault diagnosis based on vibration signal analysis. Shock and Vibration. ISSN:1875-9203, Hindawi. 2017, vol.2017, article ID 9186989.

  [DOI] [PDF]

• Z.Navickas, T.Telksnys, R.Marcinkevicius, M.Ragulskis. Operator-based approach for the construction of analytical soliton solutions to nonlinear fractional-order differential equations. Chaos Solitons and Fractals. ISSN 0960-0779, Elsevier. 2017, vol.104, p.625-634.

  [DOI] [PDF]

• M.Landauskas, Z.Navickas, A.Vainoras and M.Ragulskis. Weighted moving averaging revisited - an algebraic approach. Computational and Applied Mathematics. ISSN 0101-8205, Springer. 2017, vol.36(4), p.1545-1558.

  [DOI] [PDF]

• I.Timofejeva, R.McCraty, M.Atkinson, R.Joffe, A.Vainoras, A.Alabdulgader, M.Ragulskis. Identification of a group's physiological synchronization with Earth's magnetic field. International Journal of Environmental Research and Public Health. ISSN 1660-4601, MDPI. 2017, vol.14(9), article ID: 998.

  [DOI] [PDF]

• R.McCraty, M.Atkinson, V.Stolc, A.Alabdulgader, A.Vainoras, M.Ragulskis. Synchronization of human autonomic nervous system rhythms with geomagnetic activity in human subjects. International Journal of Environmental Research and Public Health. ISSN 1660-4601, MDPI. 2017, vol.14(7), article ID: 770.

  [DOI] [PDF]

• L.Saunoriene, S.Aleksiene, R.Maskeliunas, M.Ragulskis. Image hiding scheme based on time-averaged elliptic oscillations. Optics and Lasers in Engineering, ISSN 0143-8166, Elsevier. 2017, vol.98, p.83-88.

  [DOI] [PDF]

• Mao-Sen Cao, Yu-Juan Ding, Wei-Xin Ren, Quan Wang, M.Ragulskis, Zhi-Chun Ding. Hierarchical wavelet-aided neural intelligent identification of structural damage in noisy conditions. Applied Sciences. MDPI, ISSN 2076-3417. 2017, vol. 7(4), article ID: 391 (20 pages).

  [DOI] [PDF]

Presentations at Conferences

• M.Ragulskis, K.Lokoseviciute, Z.Navickas, M.Ragulskis. Short-term time series forecasting based on internal smoothing of Pade interpolants. Proceedings ITISE 2017. International Work-Conference on Time Series. Granada, 18-20, September, 2017. ISBN: 978-84-17293-01-7, vol.2, p. 974-984.

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Papers in the Web of Science

• Z.Navickas, M.Ragulskis, D.Karaliene, T.Telksnys. Weak and strong orders of linear recurring sequences. Computational and Applied Mathematics. ISSN 0101-8205, Springer. 2018, vol.37(3) p. 3539-3561.

  [DOI] [PDF]

• K.Lukoseviciute, R.Baubliene, D.Howard, M.Ragulskis. Bernstein polynomials for adaptive evolutionary prediction of short-term time series. Applied Soft Computing. ISSN 1568-4946, Elsevier. 2018, vol. 65, p. 47-57.

  [DOI] [PDF]

• T.Telksnys, Z.Navickas, R.Marcinkevicius, M.Ragulskis. Existence of solitary solutions in systems of PDEs with multiplicative polynomial coupling. Applied Mathematics and Computation. ISSN 0096-3003. Elsevier. 2018, vol.320, p.380-388.

  [DOI] [PDF]

• A.Alabdulgader, R.McCraty, M.Atkinson, Y.Dobyns, A.Vainoras, M.Ragulskis, V. Stolc. Long-term study of heart rate variability responses to changes in the solar and geomagnetic environment. Scientific Reports. ISSN 2045-2322. Nature Publishing Group. 2018, article no. 2663. 

  [DOI] [PDF]

• Z.Navickas, T.Telksnys, I.Timofejeva, R.Marcinkevicius, M.Ragulskis. An operator-based approach for the construction of closed-form solutions to fractional differential equations. Mathematical Modelling and Analysis. ISSN 1392-6292, Taylor and Francis. 2018, vol.23(4), p.665-685.

  [DOI] [PDF]

• M.Ragulskis, Chen Lu, Maosen Cao, Gangbing Song, R.Burdzik. Fault identification, diagnosis, and prognostics based on complex signal analysis. Complexity. ISSN 1099-0526, Wiley - Hindawi. 2018, article ID: 4020729.

  [DOI] [PDF]

• Guangqing Lu, L.Saunoriene, S.Aleksiene, M.Ragulskis. Optical image hiding based on chaotic vibration of deformable moire grating. Optics Communications. ISSN 0030-4018, Elsevier, 2018, vol.410, p.457-467.

  [DOI] [PDF]

• Laifa Tao, Chao Yang, Yujie Cheng, Chen Lu, M.Ragulskis. Machine component health prognostics with only truncated histories using geometrical metric approach. Mechanical Systems and Signal Processing. ISSN 0888-3270, Elsevier. 2018, vo.113, p.168-179.

  [DOI] [PDF]

• N.F.Alkayem, Maosen Cao, M.Ragulskis. Damage diagnosis in 3D structures using a novel hybrid multi-objective optimization and FE model updating framework. Complexity. ISSN 1099-0526, Wiley - Hindawi. 2018, article ID 3541676.

  [DOI] [PDF]

• Guangqing Lu, M.Landauskas, M.Ragulskis. Control of divergence in an extended invertible logistic map. International Journal of Bifurcation and Chaos. ISSN 0218-1274, World Scientific, 2018, vol.28(10), article no.1850129.

  [DOI] [PDF]

• Guangqing Lu, R.Smidtaite, Z.Navickas, M.Ragulskis. The effect of explosive divergence in a coupled map lattice of matrices. Chaos Solitons and Fractals. ISSN 0960-0779, Elsevier, 2018, vol.113, p.308-313.

  [DOI]

• Mei Tao, K.Poskuviene, N.F.Alkayem, Maosen Cao, M.Ragulskis. Permutation entropy based on non-uniform embedding. Entropy. ISSN 1099-4300, MDPI. 2018, vol. 20(8), article ID: 612.

  [DOI] [PDF]

• I.Timofejeva, K.Poskuviene, Maosen Cao, M.Ragulskis. Synchronization measure based on a geometric approach to attractor embedding using finite observation windows. Complexity. ISSN 1099-0526, Wiley - Hindawi. 2018, article ID: 8259496.

  [DOI] [PDF]

• Guangqing Lu, L.Saunoriene, A.Gelzinis, V.Petrauskiene, M.Ragulskis. Visual integration of vibrating images in time. Optical Engineering. ISSN 0091-3286, SPIE. 2018, vol.57(9), article no.093107.

  [DOI] [PDF]

Book Chapters

• A.Palevicius, G.Janusas, M.Ragulskis, G.Amer. Design, Analysis and Application of Dynamic Visual Cryptography for Visual Inspection of Biomedical Systems. Chapter 17, p.223-232, 2018. NATO Science for Peace and Security Series A: Chemistry and Biology. DOI: 10.1007/978-94-024-1304-5_17. In book: Nanostructured Materials for the Detection of CBRN. (352 pages) Book edited by Janez Bonca, Sergei Kruchinin. Springer Science+Business Media B.V.

Papers in the Web of Science

• R.Smidtaite, Guangqing Lu, M.Ragulskis. Image entropy for the identification of chimera states of spatiotemporal divergence in complex coupled maps of matrices. Entropy. ISSN 1099-4300, MDPI. 2019, vol.21(5), article no.523.

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• Maosen Cao, N.F.Alkayem, M.Ragulskis. Damage localization in irregular shape structures using intelligent FE model updating approach with a new objective function and social swarm algorithm. Applied Soft Computing. ISSN 1568-4946, Elsevier. 2019, vol.83, art.no.105604.

  [DOI] [PDF]

• Xiao-Jun Yang, M.Ragulskis, Thiab Taha. A new general fractional-order derivative with Rabotnov fractional-exponential kernel. Thermal Science. Society of Thermal Engineers of Serbia. ISSN 0354-9836. 2019, vol.23 (6 part B), p.3711-3718.

  [DOI] [PDF]

• Wen-Hsiang Hsieh, J.Rozenblit, M.Ragulskis. Guest editorial: Special section on recent advances in data driven modeling. Intelligent Automation and Soft Computing. ISSN:1079-8587, TSI Press-USA. 2019, vol.25(2), p.315-317.

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• L.Saunoriene, V.Siauciunaite, A.Vainoras, V.Bertasiute, Z.Navickas, M.Ragulskis. The characterization of the transit through the anaerobic threshold based on relationships between RR and QRS cardiac intervals. PLOS ONE. ISSN 1932-6203, Public Library Science. 2019, 14(5): e0216938.

  [DOI] [PDF]

• T.Telksnys, Z.Navickas, I.Timofejeva, R.Marcinkevicius, M.Ragulskis. Symmetry breaking in solitary solutions to the Hodgkin-Huxley model. Nonlinear Dynamics. ISSN 0924-090X, Springer, 2019, vol.97(1), p.571-582.

  [DOI] [PDF]

• Guangqing Lu, A.Cereska, G.Augustinavicius, R.Maskeliunas, M.Ragulskis. Intelligent control and performance evaluation of a novel precise positioning stage. Journal of Intelligent and Fuzzy Systems. ISSN 1064-1246, IOS Press. 2019, vol.36(2), p.1205-1214.

  [DOI] [PDF]

• T.Telksnys, Z.Navickas, R.Marcinkevicius, Maosen Cao, M.Ragulskis. Homoclinic and heteroclinic solutions to a hepatitis C evolution model. Open Mathematics. ISSN 2391-5455, De Gruyter. 2019, vol.16(1), p.1537-1555.

  [DOI] [PDF]

• Z.Navickas, T.Telksnys, I.Timofejeva, M.Ragulskis. An analytical scheme for the analysis of multi-hump solitons. Advances in Complex Systems. ISSN: 0219-5259, World Scientific, 2019, vol.22(01), article no.1850027.

  [DOI] [PDF]

• P.Palevicius, L.Saunoriene, Maosen Cao, M.Ragulskis. Time-averaged computer generated holography for the estimation of torsional amplitudes of oscillating microdevices. Optics Communications. ISSN 0030-4018, Elsevier, 2019, vol.439, p.260-269.

  [DOI] [PDF]

• Wei Xu, Keqin Ding, M.Ragulskis, Xiang Zhu, Maosen Cao. A segmenting scheme for evaluating exact high-order modes of uniform Timoshenko beams. Applied Acoustics. ISSN: 0003-682X, Elsevier, 2019, vol.150, p.76-80.

  [DOI] [PDF]

• Guangqing Lu, R.Smidtaite, D.Howard, M.Ragulskis. An image hiding scheme in a 2-dimensional coupled map lattice of matrices. Chaos Solitons and Fractals. ISSN 0960-0779, Elsevier, 2019, vol.124, p.78-85.

  [DOI] [PDF]

Presentations at Conferences

• Z.Rinkevicius, P.Palevicius, M.Kaminskas, K.Bockute, M.Ragulskis, G.Laukaitis. Polarizable coarse grain force field for metallic systems: A discrete interacting multipole model. National Meeting of the American-Chemical-Society (ACS), Mar 31-Apr 04, 2019. Abstracts of Papers of The American Chemical Society. ISSN:0065-7727, American Chemical Society, vol.257, abstract no.36.

• M.Landauskas, M.Ragulskis. Clustering of ECG segments for patients before sudden cardiac death based on Lagrange descriptors. Vibroengineering Procedia. ISSN 2538-8479, JVE International. 2019, vol.26, p.78-83.

  [DOI] [PDF]

• I.Timofejeva, R.McCraty, M.Ragulskis. Estimation of geometrical synchronization between human heart rate variability and local magnetic field via attractor reconstruction techniques. AIP Conference Proceedings. Conference: CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST) July 2019, 2116(1):450024

  [DOI]

Other Publications

• M.Landauskas, M.Ragulskis. Clocking convergence to Arnold tongues - the H-rank approach. Applied Mathematics & Information Sciences. ISSN 1935-0090, Natural Sciences Publishing. 2019, vol.13(5), p.799-806.

Papers in the Web of Science

• T.Telksnys, I.Timofejeva, Z.Navickas, R.Marcinkevicius, R.Mickevicius, M.Ragulskis. Solitary solutions to an androgen-deprivation prostate cancer treatment model. Mathematical Methods in the Applied Sciences. ISSN1099-1476, John Wiley & Sons Ltd. 2019, accepted article in press.

  [DOI]

• Tongwei Liu, Hao Xu, M.Ragulskis, Maosen Cao , W.Ostachowicz. A data-driven damage identification framework based on transmissibility function datasets and one-dimensional convolutional neural networks: verification on a structural health monitoring benchmark structure. Sensors. ISSN 1424-8220, MPDI. 2020, vol.20(4), art.no.1059.

  [DOI] [PDF]

• T.Telksnys, Z.Navickas, M.A.F.Sanjuan, R.Marcinkevicius, M.Ragulskis. Kink solitary solutions to a hepatitis C evolution model. Discrete and Continuous Dynamical Systems-Series B. ISSN 1531-3492, American Institute of Mathematical Sciences. 2020, accepted article in press.