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Results Connected to Time Series Analysis and Machine Learning

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Research in Computer Science in the Bulgarian Academy of Sciences

Part of the book series: Studies in Computational Intelligence ((SCI,volume 934))

Abstract

Machine learning is connected to the scientific study of algorithms and statistical models used by computer systems to perform a specific task without using explicit instructions. In this chapter we describe results of our studies on the methods connected to machine learning and the practical application of these methods to various problems by our team in the last two decades. We discuss in more detail the research on concepts of the nonlinear time series analysis and extreme events theory and their applications to natural, economic and social systems, statistical analysis of flows in channels of networks and the methodology for solving nonlinear differential equations.

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References

  1. Andres, A.: Measuring Academic Research. How to Undertake a Bibliometric Study. Chandos, Oxford (2009)

    Google Scholar 

  2. Ashenfelter, K.T., Boker, S.M., Waddell, J.R., Vitanov, N.: Spatiotemporal symmetry and multifractal structure of head movements during dyadic conversation. J. Exp. Psychol. Hum. Percept. Perform. 35, 1072–1091 (2009)

    Article  Google Scholar 

  3. Ausloos, M., Cloots, R., Gadomski, A., Vitanov, N.K.: Ranking structures and rank-rank correlations of countries: the FIFA and UEFA cases. Int. J. Modern Phys. C 25, 1450060 (2014)

    Article  Google Scholar 

  4. Ausloos, M., Gadomski, A., Vitanov, N.K.: Primacy and ranking of UEFA soccer teams from biasing organization rules. Physica Scripta 89 (2014)

    Google Scholar 

  5. Basuchoudhary, A., Bang, J.T., Sen, T.: Machine-Learning Techniques in Economics. New Tools for Predicting Economic Growth. Springer, Cham (2017)

    Google Scholar 

  6. Boeck, T., Vitanov, N.K.: Low-dimensional chaos in zero-Prandtl-number Benard–Marangoni convection. Phys. Rev. E 65 (2002)

    Google Scholar 

  7. Borisov, R., Vitanov, N.K.: Human migration: model of a migration channel with a secondary and a tertiary arm. In: AIP Conference Proceedings, vol. 2075, pp. 150001. AIP Publishing (2019)

    Google Scholar 

  8. Dehmer, M., Basac, S.C.: Machine Learning Approaches for Network Analysis. Wiley, New York (2012)

    Book  Google Scholar 

  9. Ding, Y., Rousseau, R., Wolfram, D. (eds.): Measuring Scholarly Impact. Springer, Cham (2014)

    Google Scholar 

  10. Dimitrova, Z.: Fluctuations and dynamics of the chaotic attractor connected to an instability in heating from below fluid layer. Comptes Rendus de l’Academie bulgare des Sciences 60(10), 1065–1071 (2007)

    Google Scholar 

  11. Dimitrova, Z.: On traveling waves in lattices: the case of Riccati lattices. J. Theor. Appl. Mech. 42(3), 3–22 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Dimitrova, Z.I.: Relation between the G’/G-expansion method and modified method of simplest equation. Comptes Rendus de l’Academie bulgare des Sciences 65(11), 1513–1520 (2012)

    MathSciNet  Google Scholar 

  13. Dimitrova, Z.I., Vitanov, N.K.: Influence of adaptation on the nonlinear dynamics of a system of competing populations. Phys. Lett. A 272, 368–380 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  14. Dimitrova, Z.I., Vitanov, N.K.: Dynamical consequences of adaptation of the growth rates in a system of three competing populations. J. Phys. A Math. General 34, 7459–7473 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  15. Dimitrova, Z.I., Vitanov, N.K.: Adaptation and its impact on the dynamics of a system of three competing populations. Physica A 300, 91–115 (2001)

    Article  MATH  Google Scholar 

  16. Dimitrova, Z.I., Vitanov, N.K.: Chaotic pairwise competition. Theor. Popul. Biol. 66, 1–12 (2004)

    Article  MATH  Google Scholar 

  17. Dimitrova, Z.I., Vitanov, N.K.: Shilnikov chaos in a generalized system for modelling dynamics of competing populations. Comptes Rendus de l’Academie Bulgare des Sciences 58, 257–264 (2005)

    Google Scholar 

  18. Dimitrova, Z.I., Vitanov, K.N.: Integrability of differential equations with fluid mechanics application: from Painleve property to the method of simplest equation. J. Theor. Appl. Mech. 43(2), 31–42 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  19. Goyal, P., Pandey, S., Jain, K.: Deep Learning for Natural Language Processing. Creating Neural Networks with Python. Apress, Springer, New York (2018)

    Google Scholar 

  20. Hirota, R.: Exact solution of Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27, 1192–1194 (1971)

    Article  MATH  Google Scholar 

  21. Hegger, R., Kantz, H., Schreiber, T.: Practical implementation of nonlinear time series methods: the TISEAN package. CHAOS 9, 413–435 (1999)

    Article  MATH  Google Scholar 

  22. Jordanov, I.P., Vitanov N.K.: On the exact travelling wave solutions of a hyperbolic reaction-diffusion equation. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. BGSIAM 2017, pp. 199–201. Springer, Cham (2019)

    Google Scholar 

  23. Kantz, H., Schreiber, T.: Nonlinear Time Series Analysis. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  24. Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Markov chain model for turbulent wind speed data. Physica A 342, 315–321 (2004)

    Article  Google Scholar 

  25. Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Extreme events in surface wind: predicting turbulent gusts. In: AIP Conference Proceedings, vol. 742, pp. 315–324 (2004)

    Google Scholar 

  26. Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Predicting probability for stochastic processes with local Markov property. In: Peinke, J., Kittel, A., Brath, S., Oberlack, M. (eds.) Progress in Turbulence, pp. 95–98. Springer, Berlin (2005)

    Chapter  Google Scholar 

  27. Kantz, H., Holstein, D., Ragwitz, M., Vitanov, N.K.: Short time prediction of wind speeds from local measurements. In: Peinke, J., Schaumann, P., Barth, S. Wind Energy (eds.) Proceedings of the Euromech Colloqium, pp. 93–98. Springer, Berlin (2007)

    Google Scholar 

  28. Konar, A., Bhattacharaya, D.: Time-Series Predictiona and Applications. A Machine Intelligence Approach. Springer, Cham (2017)

    Google Scholar 

  29. Kudryashov, N.A.: Exact solutions of the generalized Kuramoto-Sivashinsky equation. Phys. Lett. A 147, 287–291 (1990)

    Article  MathSciNet  Google Scholar 

  30. Kudryashov, N.A.: On types of nonlinear nonitegrable equations with exact solutions. Phys. Lett. A 155, 269–275 (1991)

    Article  MathSciNet  Google Scholar 

  31. Kudryshov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos, Solitons Fractals 24, 1217–1231 (2005)

    Article  MathSciNet  Google Scholar 

  32. Kudryashov, N.A., Loguinova, N.B.: Extended simplest equation method for nonlinear differential equations. Appl. Math. Comput. 205, 361–365 (2008)

    MathSciNet  MATH  Google Scholar 

  33. Martinov, N., Vitanov, N.: On the correspondence between the self-consistent 2D Poisson-Boltzmann structures and the sine-Gordon waves. J. Phys. A Math. General 25, L51–L56 (1992)

    Article  MATH  Google Scholar 

  34. Martinov, N., Vitanov, N.: On some solutions of the two-dimensional sine-Gordon equation. J. Phys. A Math. General 25, L419–L426 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  35. Martinov, N., Vitanov, N.: Running wave solutions of the two-dimensional sine-Gordon equation. J. Phys. A Math. General 25, 3609–3613 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  36. Martinov, N.K., Vitanov, N.K.: New class of running-wave solutions of the (2+1)-dimensional sine-Gordon equation. J. Phys. A Math. General 27, 4611–4617 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  37. May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. SIAM J. Appl. Math. 29, 243–253 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  38. Moed, H.F., Glänzel, W., Schmoch, U. (eds.): Handbook of Quantitative Science and Technology Research. Springer, Netherlands (2005)

    Google Scholar 

  39. Moed, H.: Citation Analysis in Research Evaluation. Springer, Netherlands (2005)

    Google Scholar 

  40. Nikolova, E.V.: On nonlinear waves in a blood-filled artery with an aneurysm. In: AIP Conference Proceedings, vol. 1978 (2018)

    Google Scholar 

  41. Nikolova, E.V., Jordanov, I.P., Dimitrova, Z.I., Vitanov, N.K.: Evolution of nonlinear waves in a blood-filled artery with an aneurysm. In: AIP Conference Proceedings, vol. 1895 (2017)

    Google Scholar 

  42. Nikolova, E.V., Jordanov, I.P., Dimitrova, Z.I., Vitanov, N.K.: Nonlinear evolution equation for propagation of waves in an artery with an aneurysm: an exact solution obtained by the modified method of simplest equation. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. Studies in Computational Intelligence, vol. 728, pp. 131–144. Springer, Cham (2018)

    Chapter  Google Scholar 

  43. Nikolova, E.V., Serbezov, D.Z., Jordanov, I.P.: On the spatio-temporal dynamics of interacting economic agents: application of the modified method of simplest equation. In: AIP Conference Proceedings, vol. 2075 (2019)

    Google Scholar 

  44. Panchev, S., Spassova, T., Vitanov, N.K.: Analytical and numerical investigation of two families of Lorenz-like dynamical systems. Chaos, Solitons Fractals 33, 1658–1671 (2007)

    Article  MATH  Google Scholar 

  45. Ramasubramanian, K., Singh, A.: Machine Learning Using R. Springer, New York (2017)

    Book  MATH  Google Scholar 

  46. Sakai, K., Managi, S., Vitanov, N.K., Demura, K.: Transition of chaotic motion to a limit cycle by intervention of economic policy: an empirical analysis in agriculture. Nonlinear Dyn. Psychol. Life Sci. 11, 253–265 (2007)

    Google Scholar 

  47. Scharnhorst, A., Börner, K., Van den Besselaar, P. (eds.): Models for Science Dynamics. Springer, Berlin (2012)

    Google Scholar 

  48. Silva, T.C., Zhao, L.: Machine Learning in Complex Networks. Springer, Cham (2016)

    Book  MATH  Google Scholar 

  49. Vitanov, N.K.: On travelling waves and double-periodic structures in two-dimensional sine-Gordon systems. J. Phys. A Math. General 29, 5195–5207 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  50. Vitanov, N.K.: Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity. Commun. Nonlinear Sci. Numer. Simul. 15, 2050–2060 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  51. Vitanov, N.K.: Modified method of simplest equation: powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs. Commun. Nonlinear Sci. Numer. Simul. 16, 1176–1185 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  52. Vitanov, N.K.: On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs: the role of the simplest equation. Commun. Nonlinear Sci. Numer. Simul. 16, 4215–4231 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  53. Vitanov, N.K.: Science Dynamics and Research Production. Springer, Cham (2016)

    Book  Google Scholar 

  54. Vitanov, N.K.: Science and society. Assessment of research. In: Vitanov, N.K. (eds.) Science Dynamics and Research Production, pp. 3–52. Cham, Springer (2016)

    Google Scholar 

  55. Vitanov, N.K.: Commonly used indexes for assessment of research production. In: Vitanov, N.K. (ed.) Science Dynamics and Research Production, pp. 55–99. Springer, Cham (2016)

    Google Scholar 

  56. Vitanov, N.K: Additional indexes and indicators for assessment of research production. In: Vitanov, N.K. (eds.) Science Dynamics and Research Production, pp. 101–154. Cham, Springer (2016)

    Google Scholar 

  57. Vitanov, N.K: Frequency and rank approaches to research production. Classical statistical laws. In: Vitanov, N.K.: Science Dynamics and Research Production, pp. 157–193. Cham, Springer (2016)

    Google Scholar 

  58. Vitanov, N.K: Selected models for dynamics of research organizations and research production. In: Vitanov, N.K. (eds.) Science Dynamics and Research Production, pp. 195–268. Cham, Springer (2016)

    Google Scholar 

  59. Vitanov, N.K., Siefert, M., Peinke, J.: Topological analysis of the chaotic behaviour of Shinriki oscillator. Comptes Rendus de l’Academie Bulgare des Sciences 55, 31–36 (2002)

    Google Scholar 

  60. Vitanov, N., Yankulova, E.: On some properties of the point correlation dimension. Comptes Rendus de l’Academie Bulgare des Sciences 56, 25–30 (2003)

    Google Scholar 

  61. Vitanov, N.K., Sakai, K.: Upper bounds on the number of significant degrees of freedom of noise influenced oscillations of moving machines. Syst. Anal. Model. Simul. 43, 815–828 (2003)

    Article  Google Scholar 

  62. Vitanov, N.K., Dimitrova, Z.I., Kantz, H.: On the trap of extinction and its elimination. Phys. Lett. A 349, 350–355 (2006)

    Article  Google Scholar 

  63. Vitanov, N.K., Yankulova, E.D.: Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster. Chaos, Solitons Fractals 28, 768–775 (2006)

    Article  MATH  Google Scholar 

  64. Vitanov, N.K., Tarnev, K., Kantz, H.: 2006. Hölder-exponent-MFDFA-based test for long-range correlations in pseudorandom sequences. J. Theor. Appl. Mech. 36(2), 47–64 (2006)

    Google Scholar 

  65. Vitanov, N.K., Sakai, K., Jordanov, I.P., Managi, S., Demura, K.: Analysis of a Japan government intervention on the domestic agriculture market. Physica A 382, 330–335 (2007)

    Article  Google Scholar 

  66. Vitanov, N.K., Sakai, K., Dimitrova, Z.I.: SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series. Chaos, Solitons Fractals 37, 187–202 (2008)

    Article  Google Scholar 

  67. Vitanov, N.K., Hoffmann, N.: On probability for rogue waves in the North sea. Comptes Rendus de l’Academie Bulgare des Sciences 62, 187–194 (2009)

    Google Scholar 

  68. Vitanov, N.K., Jordanov, I.P., Dimitrova, Z.I.: On nonlinear dynamics of interacting populations: coupled kink waves in a system of two populations. Commun. Nonlinear Sci. Numer. Simul. 14, 2379–2388 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  69. Vitanov, N.K., Jordanov, I.P., Dimitrova, Z.I.: On nonlinear population waves. Appl. Math. Comput. 215, 2950–2964 (2009)

    MathSciNet  MATH  Google Scholar 

  70. Vitanov, N.K., Dimitrova, Z.I., Kantz, H.: Modified method of simplest equation and its application to nonlinear PDEs. Appl. Math. Comput. 216, 2587–2595 (2010)

    MathSciNet  MATH  Google Scholar 

  71. Vitanov, N.K., Dimitrova, Z.I.: Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics. Commun. Nonlinear Sci. Numer. Simul. 15, 2836–2845 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  72. Vitanov, N.K., Dimitrova, Z.I., Ausloos, M.: Verhulst-Lotka-Volterra (VLV) model of ideological struggle. Physica A 389, 4970–4980 (2010)

    Article  MATH  Google Scholar 

  73. Vitanov, N.K., Dimitrova, Z.I., Vitanov, K.N.: On the class of nonlinear PDEs that can be treated by the modified method of simplest equation. Application to generalized Degasperis–Processi equation and b–equation. Commun. Nonlinear Sci. Numer. Simul. 16, 3033–3044 (2011)

    Google Scholar 

  74. Vitanov, N.K., Ausloos, M.R.: 2012. Knowledge epidemics and population dynamics models for describing idea diffusion. In: Scharnhorst, A., Börner, K., van den Besselaar, P. (eds.) Models of Science Dynamics, pp. 69–125. Springer, Berlin (2012)

    Google Scholar 

  75. Vitanov, N.K., Ausloos, M., Rotundo, G.: Discrete model of ideological struggle accounting for migration. Adv. Complex Syst. 15(supp01), 1250049 (2012)

    Article  MathSciNet  Google Scholar 

  76. Vitanov, N.K., Dimitrova, Z.I., Kantz, H.: Application of the method of simplest equation for obtaining exact traveling-wave solutions for the extended Korteweg-de Vries equation and generalized Camassa-Holm equation. Appl. Math. Comput. 219, 7480–7492 (2013)

    MathSciNet  MATH  Google Scholar 

  77. Vitanov, N.K., Dimitrova, Z.I., Vitanov, K.N.: Traveling waves and statistical distributions connected to systems of interacting populations. Comput. Math. Appl. 66, 1666–1684 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  78. Vitanov, N.K., Vitanov, K.N.: Population dynamics in presence of state dependent fluctuations. Comput. Math. Appl. 68, 962–971 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  79. Vitanov, N.K., Dimitrova, Z.I.: 2014. Solitary wave solutions for nonlinear partial differential equations that contain monomials of odd and even grades with respect to participating derivatives. Appl. Math. Comput. 247, 213–217 (2014)

    Google Scholar 

  80. Vitanov, N.K., Hoffmann, N.P., Wernitz, B.: Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA. Chaos, Solitons Fractals 69, 90–99 (2014)

    Article  Google Scholar 

  81. Vitanov, N.K., Dimitrova, Z.I., Vitanov, K.N.: Modified method of simplest equation for obtaining exact analytical solutions of nonlinear partial differential equations: further development of the methodology with applications. Appl. Math. Comput. 269, 363–378 (2015)

    MathSciNet  MATH  Google Scholar 

  82. Vitanov, N.K., Ausloos, M.: Test of two hypotheses explaining the size of populations in a system of cities. J. Appl. Stat. 42, 2686–2693 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  83. Vitanov, N.K., Vitanov, K.N.: Box model of migration channels. Math. Soc. Sci. 80, 108–114 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  84. Vitanov, N.K., Dimitrova, Z.I., Ivanova, T.I.: On solitary wave solutions of a class of nonlinear partial differential equations based on the function \(1/cosh^n (x+ t)\). Appl. Math. Comput. 315, 372–380 (2017)

    MathSciNet  MATH  Google Scholar 

  85. Vitanov, N.K., Borisov, R.: Statistical characteristics of a flow of substance in a channel of network that contains three arms. In: Georgiev, K., Todorov, M., Georgiev, I. (eds.) Advanced Computing in Industrial Mathematics. BGSIAM 2017, Studies in Computational Intelligence, vol. 793, pp. 421–432. Springer, Cham (2019)

    Chapter  Google Scholar 

  86. Vitanov, N.K., Vitanov, K.N.: Discrete-time model for a motion of substance in a channel of a network with application to channels of human migration. Physica A 509, 635–650 (2018)

    Article  MathSciNet  Google Scholar 

  87. Vitanov, N.K., Vitanov, K.N.: On the motion of substance in a channel of a network and human migration. Physica A 490, 1277–1294 (2018)

    Article  MathSciNet  Google Scholar 

  88. Vitanov, N.K., Dimitrova, Z.I.: Modified method of simplest equation applied to the nonlinear Schrödinger equation. J. Theor. Appl. Mech. 48(1), 59–68 (2018)

    Article  Google Scholar 

  89. Vitanov, N.K., Borisov, R.: A model of a motion of substance in a channel of a network. J. Theor. Appl. Mech. 48(3), 74–84 (2018)

    MathSciNet  Google Scholar 

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Acknowledgements

We acknowledge the partial support by the project BG05M2OP001-1.001-0008 “National Center for Mechatronics and Clean Technologies”, funded by the Operating Program “Science and Education for Intelligent Growth” of Republic of Bulgaria.

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Correspondence to Nikolay K. Vitanov .

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Vitanov, N.K. (2021). Results Connected to Time Series Analysis and Machine Learning. In: Atanassov, K.T. (eds) Research in Computer Science in the Bulgarian Academy of Sciences. Studies in Computational Intelligence, vol 934. Springer, Cham. https://doi.org/10.1007/978-3-030-72284-5_17

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