Complex Systems Modeling in Python: a Manual for Self-Study of the Discipline (in Ukrainian)

Соловйов, Володимир Миколайович; Бєлінський, Андрій Олександрович

URI: http://elibrary.kdpu.edu.ua/xmlui/handle/123456789/10508
https://github.com/Butman2099/Complex-systems-book
https://butman2099.github.io/Complex-systems-book/

Date: 2024

Abstract:

У навчальному посібнику висвітлюються основні теоретичні та інструментальні аспекти моделювання складних систем різної природи з використанням інтерактивного веб-додатку Jupyter Notebook. Для дискретних даних у вигляді часових рядів розроблено та адаптовано сучасні міждисциплінарні методи кількісної оцінки складності: (мульти-)фрактальний, рекурентний, інформаційний, ентропійний та ін. види аналізу. Запропоновано відповідні міри складності. Показано, що більшість із них можна використовувати у якості індикаторів чи передвісників критичних або кризових явищ у складних системах. Посібником зможуть скористатися як здобувачі другого (магістр) рівня вищої освіти спеціальності 014 Середня освіта (Фізика та астрономія; Інформатика; Математика; Природничі науки), так і інших спеціальностей закладів вищої освіти, наукові працівники й особи, які цікавляться методами моделювання складних систем. The handbook covers the main theoretical and instrumental aspects of modeling complex systems of different nature using the interactive web application Jupyter Notebook. For discrete data in the form of time series, modern interdisciplinary methods for quantifying complexity are developed and adapted: (multi-)fractal, recurrence, informational, entropy, and other types of analysis. The corresponding measures of complexity are proposed. It is shown that most of them can be used as indicators or precursors of critical or crisis phenomena in complex systems. The handbook can be used by applicants for the second (master's) level of higher education in the specialty 014 Secondary Education (Physics and Astronomy; Computer Science; Mathematics; Natural Sciences) and other specialties of higher education institutions, researchers and people interested in methods of complex systems modeling. Ця книга є частиною прикладного дослідження "Моніторинг, прогнозування та запобігання кризовим явищам у складних соціально-економічних системах", яке фінансується Міністерством освіти і науки України (проєкт № 0122U001694). Автори також висловлюють подяку Збройним Силам України за забезпечення безпеки при виконанні цієї роботи. Публікація та подальший розвиток цієї книги став можливим лише завдяки стійкості та мужності української армії.

Description:

[1] N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Geometry from a Time Series, Phys. Rev. Lett. 45, 712 (1980). [2] F. Takens, Detecting Strange Attractors in Turbulence, in Dynamical Systems and Turbulence, Warwick 1980, edited by D. Rand and L.-S. Young (Springer Berlin Heidelberg, Berlin, Heidelberg, 1981), pp. 366–381. [3] J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, Recurrence Plots of Dynamical Systems, Europhysics Letters 4, 973 (1987). [4] V. N. Soloviev and A. Belinskyi, Methods of Nonlinear Dynamics and the Construction of Cryptocurrency Crisis Phenomena Precursors, in Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14-17, 2018, edited by V. Ermolayev, M. C. SuárezFigueroa, V. Yakovyna, V. S. Kharchenko, V. Kobets, H. Kravtsov, V. S. Peschanenko, Y. Prytula, M. S. Nikitchenko, and A. Spivakovsky, Vol. 2104 (CEURWS.org, 2018), pp. 116–127. [5] V. N. Soloviev and A. Belinskiy, Complex Systems Theory and Crashes of Cryptocurrency Market, in Information and Communication Technologies in Education, Research, and Industrial Applications, edited by V. Ermolayev, M. C. Suárez-Figueroa, V. Yakovyna, H. C. Mayr, M. Nikitchenko, and A. Spivakovsky (Springer International Publishing, Cham, 2019), pp. 276–297. [6] K. Shockley and M. Riley, In Recurrence Quantification Analysis: Theory and Best Practices, 1st ed. (Springer, New York, 2015). [7] T. Rawald, Scalable and Efficient Analysis of Large High-Dimensional Data Sets in the Context of Recurrence Analysis, PhD thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät, 2018. [8] A. M. Fraser and H. L. Swinney, Independent Coordinates for Strange Attractors from Mutual Information, Phys. Rev. A 33, 1134 (1986). [9] J. Theiler, Statistical Precision of Dimension Estimators, Phys. Rev. A 41, 3038 (1990). [10] M. Casdagli, S. Eubank, J. D. Farmer, and J. Gibson, State Space Reconstruction in the Presence of Noise, Physica D: Nonlinear Phenomena 51, 52 (1991). [11] M. T. Rosenstein, J. J. Collins, and C. J. De Luca, A Practical Method for Calculating Largest Lyapunov Exponents from Small Data Sets, Physica D: Nonlinear Phenomena 65, 117 (1993). [12] M. T. Rosenstein, J. J. Collins, and C. J. De Luca, Reconstruction Expansion as a Geometry-Based Framework for Choosing Proper Delay Times, Physica D: Nonlinear Phenomena 73, 82 (1994). [13] H. S. Kim, R. Eykholt, and J. D. Salas, Nonlinear Dynamics, Delay Times, and Embedding Windows, Physica D: Nonlinear Phenomena 127, 48 (1999). [14] J. V. Lyle, M. Nandi, and P. J. Aston, Symmetric Projection Attractor Reconstruction: Sex Differences in the ECG, Frontiers in Cardiovascular Medicine 8, (2021). [15] T. Gautama, D. Mandic, and M. Van Hulle, A Differential Entropy Based Method for Determining the Optimal Embedding Parameters of a Signal, Proceedings 6, 29 (2003). [16] P. Grassberger and I. Procaccia, Measuring the Strangeness of Strange Attractors, Physica D: Nonlinear Phenomena 9, 189 (1983). [17] P. Grassberger and I. Procaccia, Characterization of Strange Attractors, Phys. Rev. Lett. 50, 346 (1983). [18] P. Grassberger, Generalized Dimensions of Strange Attractors, Physics Letters A 97, 227 (1983). [19] M. B. Kennel, R. Brown, and H. D. I. Abarbanel, Determining Embedding Dimension for Phase-Space Reconstruction Using a Geometrical Construction, Phys. Rev. A 45, 3403 (1992). [20] A. Krakovská, K. Mezeiová, and H. Budáčová, Use of False Nearest Neighbours for Selecting Variables and Embedding Parameters for State Space Reconstruction, Journal of Complex Systems 2015, (2015). [21] C. Rhodes and M. Morari, The False Nearest Neighbors Algorithm: An Overview, Computers & Chemical Engineering 21, S1149 (1997). [22] S. G. Stavrinides et al., On the Chaotic Nature of Random Telegraph Noise in Unipolar RRAM Memristor Devices, Chaos, Solitons & Fractals 160, 112224 (2022). [23] L. Cao, Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series, Physica D: Nonlinear Phenomena 110, 43 (1997). [24] C. L. Webber and J. P. Zbilut, Dynamical Assessment of Physiological Systems and States Using Recurrence Plot Strategies, Journal of Applied Physiology 76, 965 (1994). [25] J. P. Zbilut and C. L. Webber, Embeddings and Delays as Derived from Quantification of Recurrence Plots, Physics Letters A 171, 199 (1992). [26] N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, and J. Kurths, Recurrence-Plot-Based Measures of Complexity and Their Application to Heart-RateVariability Data, Phys. Rev. E 66, 026702 (2002). [27] A. O. Bielinskyi, V. N. Soloviev, V. Solovieva, S. O. Semerikov, and M. A. Radin, Recurrence Quantification Analysis of Energy Market Crises: A Nonlinear Approach to Risk Management, in Proceedings of the Selected and Revised Papers of 10th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2022), Virtual Event, Kryvyi Rih, Ukraine, November 17- 18, 2022, edited by H. B. Danylchuk and S. O. Semerikov, Vol. 3465 (CEUR-WS.org, 2022), pp. 110–131. [28] A. Tomashin, G. Leonardi, and S. Wallot, Four Methods to Distinguish Between Fractal Dimensions in Time Series Through Recurrence Quantification Analysis, Entropy 24, (2022). [29] M. S. Kanwal, J. A. Grochow, and N. Ay, Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines, Entropy 19, (2017). [30] A. N. Kolmogorov, Three Approaches to the Quantitative Definition of Information, International Journal of Computer Mathematics 2, 157 (1968). [31] D. G. Bonchev, Information Theoretic Complexity Measures, in Encyclopedia of Complexity and Systems Science, edited by R. A. Meyers (Springer New York, New York, NY, 2009), pp. 4820–4839. [32] L. T. Lui, G. Terrazas, H. Zenil, C. Alexander, and N. Krasnogor, Complexity Measurement Based on Information Theory and Kolmogorov Complexity, Artificial Life 21, 205 (2015). [33] M. Li and P. Vitányi, Preliminaries, in An Introduction to Kolmogorov Complexity and Its Applications (Springer New York, New York, NY, 2008), pp. 1– 99. [34] C. E. Shannon, A Mathematical Theory of Communication, Bell System Technical Journal 27, 379 (1948). [35] A. Lempel and J. Ziv, On the Complexity of Finite Sequences, IEEE Transactions on Information Theory 22, 75 (1976). [36] J.-L. Blanc, L. Pezard, and A. Lesne, Delay Independence of MutualInformation Rate of Two Symbolic Sequences, Phys. Rev. E 84, 036214 (2011). [37] S. Zozor, P. Ravier, and O. Buttelli, On Lempel–Ziv Complexity for Multidimensional Data Analysis, Physica A: Statistical Mechanics and Its Applications 345, 285 (2005). [38] E. Estevez-Rams, R. Lora Serrano, B. Aragón Fernández, and I. Brito Reyes, On the non-randomness of maximum Lempel Ziv complexity sequences of finite size, Chaos: An Interdisciplinary Journal of Nonlinear Science 23, 023118 (2013). [39] R. Giglio, R. Matsushita, A. Figueiredo, I. Gleria, and S. D. Silva, Algorithmic Complexity Theory and the Relative Efficiency of Financial Markets, Europhysics Letters 84, 48005 (2008). [40] C. Taufemback, R. Giglio, and S. D. Silva, Algorithmic complexity theory detects decreases in the relative efficiency of stock markets in the aftermath of the 2008 financial crisis, Economics Bulletin 31, 1631 (2011). [41] R. Giglio and S. Da Silva, Ranking the Stocks Listed on Bovespa According to Their Relative Efficiency, MPRA Paper, University Library of Munich, Germany, 2009. [42] Y. Bai, Z. Liang, and X. Li, A Permutation Lempel-Ziv Complexity Measure for EEG Analysis, Biomedical Signal Processing and Control 19, 102 (2015). [43] M. Borowska, Multiscale Permutation Lempel–Ziv Complexity Measure for Biomedical Signal Analysis: Interpretation and Application to Focal EEG Signals, Entropy 23, (2021). [44] B. K. Hillen, G. T. Yamaguchi, J. J. Abbas, and R. Jung, Joint-Specific Changes in Locomotor Complexity in the Absence of Muscle Atrophy Following Incomplete Spinal Cord Injury, Journal of NeuroEngineering and Rehabilitation 10, 1 (2013). [45] M. D. Costa, C.-K. Peng, and A. L. Goldberger, Multiscale Analysis of Heart Rate Dynamics: Entropy and Time Irreversibility Measures, Cardiovascular Engineering 8, 88 (2008). [46] R. A. Fisher and E. J. Russell, On the Mathematical Foundations of Theoretical Statistics, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character 222, 309 (1922). [47] B. Hjorth, EEG Analysis Based on Time Domain Properties, Electroencephalography and Clinical Neurophysiology 29, 306 (1970). [48] F. Mormann, T. Kreuz, C. Rieke, R. G. Andrzejak, A. Kraskov, P. David, C. E. Elger, and K. Lehnertz, On the Predictability of Epileptic Seizures, Clinical Neurophysiology 116, 569 (2005). [49] V. Marmelat, K. Torre, and D. Delignieres, Relative Roughness: An Index for Testing the Suitability of the Monofractal Model, Frontiers in Physiology 3, (2012). [50] T. M. Cover, Elements of Information Theory (John Wiley & Sons, 1999). [51] A. Hacine-Gharbi and P. Ravier, A Binning Formula of Bi-Histogram for Joint Entropy Estimation Using Mean Square Error Minimization, Pattern Recognition Letters 101, 21 (2018). [52] R. Clausius, T. A. Hirst, and J. Tyndall, The Mechanical Theory of Heat: With Its Applications to the Steam-Engine and to the Physical Properties of Bodies (J. Van Voorst, 1867). [53] L. Boltzmann, Weitere Studien über Das wärmegleichgewicht Unter Gasmolekülen, in Kinetische Theorie II: Irreversible Prozesse Einführung Und Originaltexte (Vieweg+Teubner Verlag, Wiesbaden, 1970), pp. 115–225. [54] S. M. Pincus, I. M. Gladstone, and R. A. Ehrenkranz, A Regularity Statistic for Medical Data Analysis, Journal of Clinical Monitoring 7, 335 (1991). [55] S. M. Pincus, Approximate Entropy as a Measure of System Complexity, Proceedings of the National Academy of Sciences 88, 2297 (1991). [56] V. N. Soloviev, A. O. Bielinskyi, and N. A. Kharadzjan, Coverage of the Coronavirus Pandemic Through Entropy Measures, in 3rd Workshop for Young Scientists in Computer Science and Software Engineering (CS and SE and SW 2020), Kryvyi Rih, Ukraine, November 27, 2020, edited by A. E. Kiv, S. O. Semerikov, V. N. Soloviev, and A. M. Striuk, Vol. 2832 (CEUR-WS.org, 2021), pp. 24–42. [57] W. Chen, Z. Wang, H. Xie, and W. Yu, Characterization of Surface EMG Signal Based on Fuzzy Entropy, IEEE Transactions on Neural Systems and Rehabilitation Engineering 15, 266 (2007). [58] H.-B. Xie, W.-X. He, and H. Liu, Measuring Time Series Regularity Using Nonlinear Similarity-Based Sample Entropy, Physics Letters A 372, 7140 (2008). [59] A. O. Bielinskyi, V. N. Soloviev, S. O. Semerikov, and V. V. Solovieva, IDENTIFYING STOCK MARKET CRASHES BY FUZZY MEASURES OF COMPLEXITY, Neuro-Fuzzy Modeling Techniques in Economics 10, 3 (2021). [60] J. S. Richman and J. R. Moorman, Physiological Time-Series Analysis Using Approximate Entropy and Sample Entropy, American Journal of Physiology-Heart and Circulatory Physiology 278, H2039 (2000). [61] C. Bandt and B. Pompe, Permutation Entropy: A Natural Complexity Measure for Time Series, Phys. Rev. Lett. 88, 174102 (2002). [62] H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, 2004). [63] V. N. Soloviev, A. Bielinskyi, and V. Solovieva, Entropy Analysis of Crisis Phenomena for DJIA Index, in Proceedings of the 15th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kherson, Ukraine, June 12-15, 2019, edited by V. Ermolayev, F. Mallet, V. Yakovyna, V. S. Kharchenko, V. Kobets, A. Kornilowicz, H. Kravtsov, M. S. Nikitchenko, S. Semerikov, and A. Spivakovsky, Vol. 2393 (CEUR-WS.org, 2019), pp. 434–449. [64] S. J. Roberts, W. Penny, and I. Rezek, Temporal and Spatial Complexity Measures for Electroencephalogram Based Brain-Computer Interfacing, Medical & Biological Engineering & Computing 37, 93 (1999). [65] M. Rostaghi and H. Azami, Dispersion Entropy: A Measure for Time-Series Analysis, IEEE Signal Processing Letters 23, 610 (2016). [66] J. C. Crepeau and L. K. Isaacson, Journal of Non-Equilibrium Thermodynamics 16, 137 (1991). [67] B. B. Mandelbrot and B. B. Mandelbrot, The Fractal Geometry of Nature, Vol. 1 (WH freeman New York, 1982). [68] B. B. Mandelbrot, C. J. G. Evertsz, and Y. Hayakawa, Exactly Self-Similar LeftSided Multifractal Measures, Phys. Rev. A 42, 4528 (1990). [69] H. F. Jelinek, N. Elston, and B. Zietsch, Fractal Analysis: Pitfalls and Revelations in Neuroscience, in Fractals in Biology and Medicine, edited by G. A. Losa, D. Merlini, T. F. Nonnenmacher, and E. R. Weibel (Birkhäuser Basel, Basel, 2005), pp. 85–94. [70] H. Steinhaus, Length, Shape and Area, in Colloquium Mathematicum, Vol. 3 (Polska Akademia Nauk. Instytut Matematyczny PAN, 1954), pp. 1–13. [71] A. Vulpiani, Lewis Fry Richardson: Scientist, Visionary and Pacifist, Lettera Matematica 2, 121 (2014). [72] B. Hayes, Computing Science: Statistics of Deadly Quarrels, American Scientist 90, 10 (2002). [73] B. Mandelbrot, How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, Science 156, 636 (1967). [74] S. V. Bozhokin and D. A. Parshin, Fractals and Multifractals: Textbook (Scientific; Publishing Center "Regular; Chaotic Dynamics", 2001). [75] T. Gneiting, H. Ševčíková, and D. B. Percival, Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data, Statistical Science 27, 247 (2012). [76] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications (John Wiley & Sons, 2003). [77] B. B. Mandelbrot and J. A. Wheeler, The Fractal Geometry of Nature, American Journal of Physics 51, 286 (1983). [78] H. E. Hurst, Long-Term Storage Capacity of Reservoirs, Transactions of the American Society of Civil Engineers 116, 770 (1951). [79] H. E. Hurst, A Suggested Statistical Model of Some Time Series Which Occur in Nature, Nature 180, 494 (1957). [80] C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, Mosaic Organization of DNA Nucleotides, Phys. Rev. E 49, 1685 (1994). [81] Z.-Q. Jiang, W.-J. Xie, and W.-X. Zhou, Testing the Weak-Form Efficiency of the WTI Crude Oil Futures Market, Physica A: Statistical Mechanics and Its Applications 405, 235 (2014). [82] T. Higuchi, Approach to an Irregular Time Series on the Basis of the Fractal Theory, Physica D: Nonlinear Phenomena 31, 277 (1988). [83] C. F. Vega and J. Noel, Parameters Analyzed of Higuchi’s Fractal Dimension for EEG Brain Signals, in 2015 Signal Processing Symposium (SPSympo) (2015), pp. 1–5. [84] A. Petrosian, Kolmogorov Complexity of Finite Sequences and Recognition of Different Preictal EEG Patterns, in Proceedings Eighth IEEE Symposium on Computer-Based Medical Systems (1995), pp. 212–217. [85] R. Esteller, G. Vachtsevanos, J. Echauz, and B. Litt, A Comparison of Waveform Fractal Dimension Algorithms, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48, 177 (2001). [86] C. Goh, B. Hamadicharef, G. T. Henderson, and E. C. Ifeachor, Comparison of Fractal Dimension Algorithms for the Computation of EEG Biomarkers for Dementia, in 2nd International Conference on Computational Intelligence in Medicine and Healthcare (CIMED2005) (Professor José Manuel Fonseca, UNINOVA, Portugal, Lisbon, Portugal, 2005). [87] M. J. Katz, Fractals and the Analysis of Waveforms, Computers in Biology and Medicine 18, 145 (1988). [88] C. Sevcik, A Procedure to Estimate the Fractal Dimension of Waveforms, (2010). [89] A. Kalauzi, T. Bojić, and L. Rakić, Extracting Complexity Waveforms from One-Dimensional Signals, Nonlinear Biomedical Physics 3, 1 (2009). [90] A. Kalauzi, T. Bojić, and L. Rakić, Extracting Complexity Waveforms from One-Dimensional Signals, Nonlinear Biomedical Physics 3, (2009). [91] F. Hasselman, When the Blind Curve Is Finite: Dimension Estimation and Model Inference Based on Empirical Waveforms, Frontiers in Physiology 4, (2013). [92] R. F. Voss, Fractals in Nature: From Characterization to Simulation, in The Science of Fractal Images, edited by H.-O. Peitgen and D. Saupe (Springer New York, New York, NY, 1988), pp. 21–70. [93] A. A. Anis and E. H. Lloyd, The Expected Value of the Adjusted Rescaled Hurst Range of Independent Normal Summands, Biometrika 63, 111 (1976). [94] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal Measures and Their Singularities: The Characterization of Strange Sets, Phys. Rev. A 33, 1141 (1986). [95] U. Frisch and G. Parisi, Turbulence and Predictability of Geophysical Flows and Climate Dynamics, in Proceedings of the International School of Physics“enrico Fermi," Course LXXXVIII, Varenna, 1983 (North-Holland, New York, 1985). [96] T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, Fractal Measures and Their Singularities: The Characterization of Strange Sets, Nuclear Physics B - Proceedings Supplements 2, 501 (1987). [97] J. W. Kantelhardt, E. Koscielny-Bunde, H. H. A. Rego, S. Havlin, and A. Bunde, Detecting Long-Range Correlations with Detrended Fluctuation Analysis, Physica A: Statistical Mechanics and Its Applications 295, 441 (2001). [98] J. W. Kantelhardt, Fractal and Multifractal Time Series, in Mathematics of Complexity and Dynamical Systems, edited by R. A. Meyers (Springer New York, New York, NY, 2011), pp. 463–487. [99] J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series, Physica A: Statistical Mechanics and Its Applications 316, 87 (2002). [100] S. Dutta, Multifractal Properties of ECG Patterns of Patients Suffering from Congestive Heart Failure, Journal of Statistical Mechanics: Theory and Experiment 2010, P12021 (2010). [101] E. Maiorino, L. Livi, A. Giuliani, A. Sadeghian, and A. Rizzi, Multifractal Characterization of Protein Contact Networks, Physica A: Statistical Mechanics and Its Applications 428, 302 (2015). [102] P. H. Figueirêdo, E. Nogueira, M. A. Moret, and S. Coutinho, Multifractal Analysis of Polyalanines Time Series, Physica A: Statistical Mechanics and Its Applications 389, 2090 (2010). [103] G. R. Jafari, P. Pedram, and L. Hedayatifar, Erratum: Long-Range Correlation and Multifractality in Bach’s Inventions Pitches, Journal of Statistical Mechanics: Theory and Experiment 2012, E03001 (2012). [104] Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, and D. Sornette, Multifractal Analysis of Financial Markets: A Review, Reports on Progress in Physics 82, 125901 (2019). [105] L. Telesca, V. Lapenna, and M. Macchiato, Multifractal Fluctuations in Earthquake-Related Geoelectrical Signals, New Journal of Physics 7, 214 (2005). [106] E. G. Yee Leung and Z. Yu, Temporal Scaling Behavior of Avian Influenza a (H5N1): The Multifractal Detrended Fluctuation Analysis, Annals of the Association of American Geographers 101, 1221 (2011). [107] F. Liao and Y.-K. Jan, Using Multifractal Detrended Fluctuation Analysis to Assess Sacral Skin Blood Flow Oscillations in People with Spinal Cord Injury, The Journal of Rehabilitation Research and Development 48, 787 (2011). [108] L. Telesca, V. Lapenna, and M. Macchiato, Multifractal Fluctuations in Seismic Interspike Series, Physica A: Statistical Mechanics and Its Applications 354, 629 (2005). [109] M. S. Movahed, F. Ghasemi, S. Rahvar, and M. R. R. Tabar, Long-Range Correlation in Cosmic Microwave Background Radiation, Phys. Rev. E 84, 021103 (2011). [110] P. Mali, S. Sarkar, S. Ghosh, A. Mukhopadhyay, and G. Singh, Multifractal Detrended Fluctuation Analysis of Particle Density Fluctuations in High-Energy Nuclear Collisions, Physica A: Statistical Mechanics and Its Applications 424, 25 (2015). [111] I. T. Pedron, Correlation and Multifractality in Climatological Time Series, Journal of Physics: Conference Series 246, 012034 (2010). [112] R. Rak, S. Drożdż, J. Kwapień, and P. Oświȩcimka, Detrended CrossCorrelations Between Returns, Volatility, Trading Activity, and Volume Traded for the Stock Market Companies, Europhysics Letters 112, 48001 (2015). [113] M. Wątorek, S. Drożdż, J. Kwapień, L. Minati, P. Oświęcimka, and M. Stanuszek, Multiscale Characteristics of the Emerging Global Cryptocurrency Market, Physics Reports 901, 1 (2021). [114] C.-K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series, Chaos: An Interdisciplinary Journal of Nonlinear Science 5, 82 (1995). [115] E. Canessa, Multifractality in Time Series, Journal of Physics A: Mathematical and General 33, 3637 (2000). [116] A. Kasprzak, R. Kutner, J. Perelló, and J. Masoliver, Higher-Order Phase Transitions on Financial Markets, The European Physical Journal B: Condensed Matter and Complex Systems 76, 513 (2010). [117] M. Dai, C. Zhang, and D. Zhang, Multifractal and Singularity Analysis of Highway Volume Data, Physica A: Statistical Mechanics and Its Applications 407, 332 (2014). [118] M. Dai, J. Hou, and D. Ye, Multifractal Detrended Fluctuation Analysis Based on Fractal Fitting: The Long-Range Correlation Detection Method for Highway Volume Data, Physica A: Statistical Mechanics and Its Applications 444, 722 (2016). [119] X. Sun, H. Chen, Z. Wu, and Y. Yuan, Multifractal Analysis of Hang Seng Index in Hong Kong Stock Market, Physica A: Statistical Mechanics and Its Applications 291, 553 (2001). [120] E. A. Ihlen, Introduction to Multifractal Detrended Fluctuation Analysis in Matlab, Frontiers in Physiology 3, (2012). [121] P. Oświȩcimka, L. Livi, and S. Drożdż, Right-Side-Stretched Multifractal Spectra Indicate Small-Worldness in Networks, Communications in Nonlinear Science and Numerical Simulation 57, 231 (2018). [122] S. Drożdż and P. Oświȩcimka, Detecting and Interpreting Distortions in Hierarchical Organization of Complex Time Series, Phys. Rev. E 91, 030902 (2015). [123] S. Drożdż, R. Kowalski, P. Oświȩcimka, R. Rak, and R. Gȩbarowski, Dynamical Variety of Shapes in Financial Multifractality, Complexity 2018, 1 (2018). [124] A. Orozco-Duque, D. Novak, V. Kremen, and J. Bustamante, Multifractal Analysis for Grading Complex Fractionated Electrograms in Atrial Fibrillation, Physiological Measurement 36, 2269 (2015). [125] A. Faini, G. Parati, and P. Castiglioni, Multiscale Assessment of the Degree of Multifractality for Physiological Time Series, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, 20200254 (2021). [126] A. Bielinskyi, V. Soloviev, V. Solovieva, A. Matviychuk, and S. Semerikov, The Analysis of Multifractal Cross-Correlation Connectedness Between Bitcoin and the Stock Market, in Information Technology for Education, Science, and Technics, edited by E. Faure, O. Danchenko, M. Bondarenko, Y. Tryus, C. Bazilo, and G. Zaspa (Springer Nature Switzerland, Cham, 2023), pp. 323–345. [127] E. P. Wigner, On the Statistical Distribution of the Widths and Spacings of Nuclear Resonance Levels, Mathematical Proceedings of the Cambridge Philosophical Society 47, 790 (1951). [128] E. P. Wigner, On a Class of Analytic Functions from the Quantum Theory of Collisions, Annals of Mathematics 53, 36 (1951). [129] F. J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. I, Journal of Mathematical Physics 3, 140 (2004). [130] F. J. Dyson and M. L. Mehta, Statistical Theory of the Energy Levels of Complex Systems. IV, Journal of Mathematical Physics 4, 701 (2004). [131] M. L. Mehta and F. J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. V, Journal of Mathematical Physics 4, 713 (2004). [132] M. L. Mehta, Random Matrices (Academic Press, 1991). [133] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Random-Matrix Physics: Spectrum and Strength Fluctuations, Rev. Mod. Phys. 53, 385 (1981). [134] L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Noise Dressing of Financial Correlation Matrices, Phys. Rev. Lett. 83, 1467 (1999). [135] Aspects of Multivariate Statistical Theory (Wiley, New York, 1982). [136] F. J. Dyson, Distribution of Eigenvalues for a Class of Real Symmetric Matrices, Revista Mexicana de Fisica 20, 231 (1971). [137] A. M. Sengupta and P. P. Mitra, Distributions of Singular Values for Some Random Matrices, Phys. Rev. E 60, 3389 (1999). [138] V. Plerou, P. Gopikrishnan, B. Rosenow, L. A. Nunes Amaral, and H. E. Stanley, Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series, Phys. Rev. Lett. 83, 1471 (1999). [139] T. Guhr, A. Müller–Groeling, and H. A. Weidenmüller, Random-Matrix Theories in Quantum Physics: Common Concepts, Physics Reports 299, 189 (1998). [140] Y. V. Fyodorov and A. D. Mirlin, Analytical Derivation of the Scaling Law for the Inverse Participation Ratio in Quasi-One-Dimensional Disordered Systems, Phys. Rev. Lett. 69, 1093 (1992). [141] C. J. Gavilán-Moreno and G. Espinosa-Paredes, Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors, Nuclear Engineering and Technology 48, 434 (2016). [142] A. Prieto-Guerrero and G. Espinosa-Paredes, Dynamics of BWRs and Mathematical Models, in Linear and Non-Linear Stability Analysis in Boiling Water Reactors, edited by A. Prieto-Guerrero and G. Espinosa-Paredes (Woodhead Publishing, 2019), pp. 193–268. [143] V. N. Soloviev, A. Bielinskyi, O. Serdyuk, V. Solovieva, and S. Semerikov, Lyapunov Exponents as Indicators of the Stock Market Crashes, in Proceedings of the 16th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kharkiv, Ukraine, October 06-10, 2020, edited by O. Sokolov, G. Zholtkevych, V. Yakovyna, Y. Tarasich, V. Kharchenko, V. Kobets, O. Burov, S. Semerikov, and H. Kravtsov, Vol. 2732 (CEUR-WS.org, 2020), pp. 455–470. [144] D. Nychka, S. Ellner, A. R. Gallant, and D. McCaffrey, Finding Chaos in Noisy Systems, Journal of the Royal Statistical Society. Series B (Methodological) 54, 399 (1992). [145] A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, Determining Lyapunov Exponents from a Time Series, Physica D: Nonlinear Phenomena 16, 285 (1985). [146] M. Sano and Y. Sawada, Measurement of the Lyapunov Spectrum from a Chaotic Time Series, Phys. Rev. Lett. 55, 1082 (1985). [147] J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Liapunov Exponents from Time Series, Phys. Rev. A 34, 4971 (1986). [148] U. Parlitz, Identification of True and Spurious Lyapunov Exponents from Time Series, International Journal of Bifurcation and Chaos 02, 155 (1992). [149] M. Balcerzak, D. Pikunov, and A. Dabrowski, The Fastest, Simplified Method of Lyapunov Exponents Spectrum Estimation for Continuous-Time Dynamical Systems, Nonlinear Dynamics 94, 3053 (2018). [150] H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, and L. Sh. Tsimring, The Analysis of Observed Chaotic Data in Physical Systems, Rev. Mod. Phys. 65, 1331 (1993). [151] J.-P. Eckmann and D. Ruelle, Ergodic Theory of Chaos and Strange Attractors, Rev. Mod. Phys. 57, 617 (1985). [152] A. Bielinskyi, S. Semerikov, O. Serdyuk, V. Solovieva, V. N. Soloviev, and L. Pichl, Econophysics of Sustainability Indices, in Proceedings of the Selected Papers of the Special Edition of International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2020), Odessa, Ukraine, July 13-18, 2020, edited by A. Kiv, Vol. 2713 (CEUR-WS.org, 2020), pp. 372–392. [153] G. Nicolis, I. Prigogine, W. H. Freeman, and Company, Exploring Complexity: An Introduction (W.H. Freeman, 1989). [154] C. Tsallis, Possible Generalization of Boltzmann-Gibbs Statistics, Journal of Statistical Physics 52, 479 (1988). [155] C. Tsallis, Dynamical Scenario for Nonextensive Statistical Mechanics, Physica A: Statistical Mechanics and Its Applications 340, 1 (2004). [156] C. Tsallis, M. Gell-Mann, and Y. Sato, Asymptotically Scale-Invariant Occupancy of Phase Space Makes the Entropy 𝑆𝑞 Extensive, Proceedings of the National Academy of Sciences 102, 15377 (2005). [157] C. Tsallis, Economics and Finance: Q-Statistical Stylized Features Galore, Entropy 19, (2017). [158] C. Tsallis, Beyond Boltzmann–Gibbs–Shannon in Physics and Elsewhere, Entropy 21, (2019). [159] E. G. Pavlos, O. E. Malandraki, O. V. Khabarova, L. P. Karakatsanis, G. P. Pavlos, and G. Livadiotis, Non-Extensive Statistical Analysis of Energetic Particle Flux Enhancements Caused by the Interplanetary Coronal Mass EjectionHeliospheric Current Sheet Interaction, Entropy 21, (2019). [160] R. de Oliveira, S. Brito, L. da Silva, and C. Tsallis, Connecting Complex Networks to Nonadditive Entropies, Scientific Reports 11, 1130 (2021). [161] G. Pavlos, A. Iliopoulos, L. Karakatsanis, M. Xenakis, and E. Pavlos, Complexity of Economical Systems., Journal of Engineering Science & Technology Review 8, (2015). [162] G. L. Ferri, M. F. Reynoso Savio, and A. Plastino, Tsallis’ q-Triplet and the Ozone Layer, Physica A: Statistical Mechanics and Its Applications 389, 1829 (2010). [163] S. Umarov, C. Tsallis, and S. Steinberg, On Aq-Central Limit Theorem Consistent with Nonextensive Statistical Mechanics, Milan Journal of Mathematics 76, 307 (2008). [164] C. Anteneodo and C. Tsallis, Breakdown of Exponential Sensitivity to Initial Conditions: Role of the Range of Interactions, Phys. Rev. Lett. 80, 5313 (1998). [165] C. TSALLIS, Some Open Problems in Nonextensive Statistical Mechanics, International Journal of Bifurcation and Chaos 22, 1230030 (2012). [166] D. Stosic, D. Stosic, T. B. Ludermir, and T. Stosic, Nonextensive Triplets in Cryptocurrency Exchanges, Physica A: Statistical Mechanics and Its Applications 505, 1069 (2018). [167] A. O. Bielinskyi, A. V. Matviychuk, O. A. Serdyuk, S. O. Semerikov, V. V. Solovieva, and V. N. Soloviev, Correlational and Non-Extensive Nature of Carbon Dioxide Pricing Market, in ICTERI 2021 Workshops, edited by O. Ignatenko, V. Kharchenko, V. Kobets, H. Kravtsov, Y. Tarasich, V. Ermolayev, D. Esteban, V. Yakovyna, and A. Spivakovsky, Vol. 1635 (Springer International Publishing, Cham, 2022), pp. 183–199. [168] I. Prigogine and E. N. Hiebert, From Being to Becoming: Time and Complexity in the Physical Sciences, Physics Today 35, 69 (1982). [169] M. Costa, A. L. Goldberger, and C.-K. Peng, Multiscale Entropy Analysis of Biological Signals, Phys. Rev. E 71, 021906 (2005). [170] J. F.Donges, R. V. Donner, and J. Kurths, Testing Time Series Irreversibility Using Complex Network Methods, Europhysics Letters 102, 10004 (2013). [171] M. Zanin, A. Rodríguez-González, E. Menasalvas Ruiz, and D. Papo, Assessing Time Series Reversibility Through Permutation Patterns, Entropy 20, (2018). [172] R. Flanagan and L. Lacasa, Irreversibility of Financial Time Series: A GraphTheoretical Approach, Physics Letters A 380, 1689 (2016). [173] A. Puglisi and D. Villamaina, Irreversible Effects of Memory, Europhysics Letters 88, 30004 (2009). [174] C. Diks, J. C. van Houwelingen, F. Takens, and J. DeGoede, Reversibility as a Criterion for Discriminating Time Series, Physics Letters A 201, 221 (1995). [175] C. S. Daw, C. E. A. Finney, and M. B. Kennel, Symbolic Approach for Measuring Temporal “Irreversibility”, Phys. Rev. E 62, 1912 (2000). [176] P. Guzik, J. Piskorski, T. Krauze, A. Wykretowicz, and H. Wysocki, Heart Rate Asymmetry by Poincaré Plots of RR Intervals, Biomedical Engineering / Biomedizinische Technik 51, 272 (2006). [177] A. Porta, S. Guzzetti, N. Montano, T. Gnecchi-Ruscone, R. Furlan, and A. Malliani, Time Reversibility in Short-Term Heart Period Variability, in 2006 Computers in Cardiology (2006), pp. 77–80. [178] L. Lacasa, A. Nuñez, É. Roldán, J. M. R. Parrondo, and B. Luque, Time Series Irreversibility: A Visibility Graph Approach, The European Physical Journal B 85, (2012). [179] A. O. Bielinskyi, S. V. Hushko, A. V. Matviychuk, O. A. Serdyuk, S. O. Semerikov, and V. N. Soloviev, Irreversibility of Financial Time Series: A Case of Crisis, in Proceedings of the Selected and Revised Papers of 9th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2- MLPEED 2021), Odessa, Ukraine, May 26-28, 2021, edited by A. E. Kiv, V. N. Soloviev, and S. O. Semerikov, Vol. 3048 (CEUR-WS.org, 2021), pp. 134–150. [180] A. Kiv, A. Bryukhanov, A. Bielinskyi, V. Soloviev, T. Kavetskyy, D. Dyachok, I. Donchev, and V. Lukashin, Irreversibility of Plastic Deformation Processes in Metals, in Information Technology for Education, Science, and Technics, edited by E. Faure, O. Danchenko, M. Bondarenko, Y. Tryus, C. Bazilo, and G. Zaspa (Springer Nature Switzerland, Cham, 2023), pp. 425–445. [181] M. Costa, A. L. Goldberger, and C.-K. Peng, Broken Asymmetry of the Human Heartbeat: Loss of Time Irreversibility in Aging and Disease, Phys. Rev. Lett. 95, 198102 (2005). [182] C. L. Ehlers, J. Havstad, D. Prichard, and J. Theiler, Low Doses of Ethanol Reduce Evidence for Nonlinear Structure in Brain Activity, The Journal of Neuroscience 18, 7474 (1998). [183] C. Yan, P. Li, L. Ji, L. Yao, C. Karmakar, and C. Liu, Area Asymmetry of Heart Rate Variability Signal, BioMedical Engineering OnLine 16, (2017). [184] C. K. Karmakar, A. Khandoker, and M. Palaniswami, Phase Asymmetry of Heart Rate Variability Signal, Physiological Measurement 36, 303 (2015). [185] B. Luque, L. Lacasa, F. Ballesteros, and J. Luque, Horizontal Visibility Graphs: Exact Results for Random Time Series, Phys. Rev. E 80, 046103 (2009). [186] L. Lacasa and R. Flanagan, Time Reversibility from Visibility Graphs of Nonstationary Processes, Phys. Rev. E 92, 022817 (2015). [187] I. Grosse, P. Bernaola-Galván, P. Carpena, R. Román-Roldán, J. Oliver, and H. E. Stanley, Analysis of Symbolic Sequences Using the Jensen-Shannon Divergence, Physical Review E 65, (2002). [188] A. O. Bielinskyi, A. E. Kiv, Y. O. Prikhozha, M. A. Slusarenko, and V. N. Soloviev, Complex Systems and Physics Education, in Proceedings of the 9th Workshop on Cloud Technologies in Education, CTE 2021, Kryvyi Rih, Ukraine, December 17, 2021, edited by A. E. Kiv, S. O. Semerikov, and M. P. Shyshkina, Vol. 3085 (CEUR-WS.org, 2021), pp. 56–80. [189] A. A. B. Pessa and H. V. Ribeiro, ordpy: A Python package for data analysis with permutation entropy and ordinal network methods, Chaos: An Interdisciplinary Journal of Nonlinear Science 31, 063110 (2021). [190] E. P. White, B. J. Enquist, and J. L. Green, On Estimating the Exponent of Power-Law Frequency Distributions, Ecology 89, 905 (2008). [191] N. N. Taleb, The Black Swan: Second Edition: The Impact of the Highly Improbable Fragility (Random House Publishing Group, 2010). [192] P. Lévy, Calcul Des Probabilités, Par Paul lévy, ... (Gauthier-Villars, 1925). [193] P. Lévy, Theorie de l’addition Des Variables Aleatoires (Gauthier-Villars, 1954). [194] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, 1968). [195] T. J. Kozubowski, M. M. Meerschaert, A. K. Panorska, and H.-P. Scheffler, Operator Geometric Stable Laws, Journal of Multivariate Analysis 92, 298 (2005). [196] A. Alvarez and P. Olivares, Méthodes d’estimation Pour Des Lois Stables Avec Des Applications En Finance, Journal de La Société Française de Statistique 146, 23 (2005). [197] J. P. Nolan, An Algorithm for Evaluating Stable Densities in Zolotarev’s (m) Parameterization, Mathematical and Computer Modelling 29, 229 (1999). [198] A. Bielinskyi, V. N. Soloviev, S. Semerikov, and V. Solovieva, Detecting Stock Crashes Using Levy Distribution, in Proceedings of the Selected Papers of the 8th International Conference on Monitoring, Modeling & Management of Emergent Economy, M3E2-EEMLPEED 2019, Odessa, Ukraine, May 22-24, 2019, edited by A. Kiv, S. Semerikov, V. N. Soloviev, L. Kibalnyk, H. Danylchuk, and A. Matviychuk, Vol. 2422 (CEUR-WS.org, 2019), pp. 420–433. [199] D. Salas-Gonzalez, J. M. Górriz, J. Ramírez, M. Schloegl, E. W. Lang, and A. Ortiz, Parameterization of the Distribution of White and Grey Matter in MRI Using the α-Stable Distribution, Computers in Biology and Medicine 43, 559 (2013). [200] V. M. Zolotarev, One-Dimensional Stable Distributions (American Mathematical Society, 1986). [201] E. F. Fama and R. Roll, Parameter Estimates for Symmetric Stable Distributions, Journal of the American Statistical Association 66, 331 (1971). [202] J. H. McCulloch, Simple Consistent Estimators of Stable Distribution Parameters, Communications in Statistics - Simulation and Computation 15, 1109 (1986). [203] J. H. McCulloch, 13 Financial Applications of Stable Distributions, in Statistical Methods in Finance, Vol. 14 (Elsevier, 1996), pp. 393–425. [204] J. P. Nolan, Maximum Likelihood Estimation and Diagnostics for Stable Distributions, in Lévy Processes: Theory and Applications, edited by O. E. BarndorffNielsen, S. I. Resnick, and T. Mikosch (Birkhäuser Boston, Boston, MA, 2001), pp. 379–400. [205] S. Mittnik, S. T. rachev, T. Doganoglu, and D. Chenyao, Maximum Likelihood Estimation of Stable Paretian Models, Mathematical and Computer Modelling 29, 275 (1999). [206] W. H. Dumouchel, Stable Distributions in Statistical Inference: 1. Symmetric Stable Distributions Compared to Other Symmetric Long-Tailed Distributions, Journal of the American Statistical Association 68, 469 (1973). [207] N. N. Taleb, Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications, (2022). [208] D. J. Watts and S. H. Strogatz, Collective Dynamics of ’Small-World’ Networks, Nature 393, 440 (1998). [209] A.-L. Barabási and R. Albert, Emergence of Scaling in Random Networks, Science 286, 509 (1999). [210] R. Albert and A.-L. Barabási, Statistical Mechanics of Complex Networks, Rev. Mod. Phys. 74, 47 (2002). [211] E. L. Platt, Network Science with Python and NetworkX Quick Start Guide: Explore and Visualize Network Data Effectively (Packt Publishing, 2019). [212] T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, Fourth Edition (MIT Press, 2022). [213] J. Travers and S. Milgram, An Experimental Study of the Small World Problem, in Social Networks, edited by S. Leinhardt (Academic Press, 1977), pp. 179–197. [214] A. O. Bielinskyi and V. N. Soloviev, Complex Network Precursors of Crashes and Critical Events in the Cryptocurrency Market, in Proceedings of St Student Workshop on Computer Science and Software Engineering, CS and SE@SW 2018, Kryvyi Rih, Ukraine, November 30, 2018, edited by S. O. Semerikov, A. M. Striuk, V. N. Soloviev, and A. E. Kiv, Vol. 2292 (CEUR-WS.org, 2028), pp. 37–45. [215] A. O. Bielinskyi, V. N. Soloviev, S. V. Hushko, A. E. Kiv, and A. V. Matviychuk, High-Order Network Analysis for Financial Crash Identification, in Proceedings of the Selected and Revised Papers of 10th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2022), Virtual Event, Kryvyi Rih, Ukraine, November 17-18, 2022, edited by H. B. Danylchuk and S. O. Semerikov, Vol. 3465 (CEUR-WS.org, 2022), pp. 132–149. [216] A. Kiv, A. Bryukhanov, V. Soloviev, A. Bielinskyi, T. Kavetskyy, D. Dyachok, I. Donchev, and V. Lukashin, Complex Network Methods for Plastic Deformation Dynamics in Metals, Dynamics 3, 34 (2023). [217] R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, and J. Kurths, Recurrence-Based Time Series Analysis by Means of Complex Network Methods, International Journal of Bifurcation and Chaos 21, 1019 (2011). [218] L. Lacasa, B. Luque, F. Ballesteros, J. Luque, and J. C. Nuño, From Time Series to Complex Networks: The Visibility Graph, Proceedings of the National Academy of Sciences 105, 4972 (2008). [219] A. O. Bielinskyi, O. A. Serdyuk, S. O. Semerikov, and V. N. Soloviev, Econophysics of Cryptocurrency Crashes: A Systematic Review, in Proceedings of the Selected and Revised Papers of 9th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2021), Odessa, Ukraine, May 26-28, 2021, edited by A. E. Kiv, V. N. Soloviev, and S. O. Semerikov, Vol. 3048 (CEUR-WS.org, 2021), pp. 31–133. [220] X. Lan, H. Mo, S. Chen, Q. Liu, and Y. Deng, Fast transformation from time series to visibility graphs, Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 083105 (2015). [221] I. V. Bezsudnov and A. A. Snarskii, From the Time Series to the Complex Networks: The Parametric Natural Visibility Graph, Physica A: Statistical Mechanics and Its Applications 414, 53 (2014). [222] T. T. Zhou, N. D. Jin, Z. K. Gao, and Y. B. Luo, Limited Penetrable Visibility Graph for Establishing Complex Network from Time Series, Acta Physica Sinica 61, 2012-3-030506 (2012). [223] Q. Xuan, J. Zhou, K. Qiu, D. Xu, S. Zheng, and X. Yang, CLPVG: Circular limited penetrable visibility graph as a new network model for time series, Chaos: An Interdisciplinary Journal of Nonlinear Science 32, 013130 (2022). [224] F. R. K. Chung, Spectral Graph Theory (American Mathematical Society, 1997). [225] N. Biggs, Spectral Graph Theory (CBMS Regional Conference Series in Mathematics 92), Bulletin of the London Mathematical Society 30, 197 (1998). [226] S. Butler, Interlacing for Weighted Graphs Using the Normalized Laplacian, Electronic Journal of Linear Algebra 16, 90 (2007). [227] G. Bounova and O. de Weck, Overview of Metrics and Their Correlation Patterns for Multiple-Metric Topology Analysis on Heterogeneous Graph Ensembles, Phys. Rev. E 85, 016117 (2012). [228] I. Gutman, The Energy of a Graph, (1978). [229] D. M. Cvetkovic, M. Doob, and H. Sachs, Spectra of Graphs. Theory and Application, (1980). [230] J. Wu, M. Barahona, Y.-J. Tan, and H.-Z. Deng, Spectral Measure of Structural Robustness in Complex Networks, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 41, 1244 (2011). [231] W. Jun, M. Barahona, T. Yue-Jin, and D. Hong-Zhong, Natural Connectivity of Complex Networks, Chinese Physics Letters 27, 078902 (2010). [232] E. Estrada, Spectral Scaling and Good Expansion Properties in Complex Networks, Europhysics Letters 73, 649 (2006). [233] A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Society for Industrial; Applied Mathematics, 1994). [234] I. J. Schoenberg, Publications of Edmund Landau, in Number Theory and Analysis: A Collection of Papers in Honor of Edmund Landau (1877–1938), edited by P. Turán (Springer US, Boston, MA, 1969), pp. 335–355. [235] T. H. Wei, The Algebraic Foundations of Ranking Theory (University of Cambridge, 1952). [236] M. G. Kendall, Further Contributions to the Theory of Paired Comparisons, Biometrics 11, 43 (1955). [237] C. Berge, Théorie Des Graphes Et Ses Applications (Dunod, 1958). [238] P. Bonacich, Technique for Analyzing Overlapping Memberships, Sociological Methodology 4, 176 (1972). [239] Wikipedia, Arnoldi Iteration. [240] K. Stephenson and M. Zelen, Rethinking Centrality: Methods and Examples, Social Networks 11, 1 (1989). [241] V. Latora and M. Marchiori, Efficient Behavior of Small-World Networks, Phys. Rev. Lett. 87, 198701 (2001). [242] R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Dynamical and Correlation Properties of the Internet, Phys. Rev. Lett. 87, 258701 (2001). [243] S. Maslov and K. Sneppen, Specificity and Stability in Topology of Protein Networks, Science 296, 910 (2002). [244] M. E. J. Newman, Assortative Mixing in Networks, Phys. Rev. Lett. 89, 208701 (2002). [245] A. Barrat and M. Weigt, On the Properties of Small-World Network Models, The European Physical Journal B-Condensed Matter and Complex Systems 13, 547 (2000). [246] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex Networks: Structure and Dynamics, Physics Reports 424, 175 (2006). [247] P. Holme, C. R. Edling, and F. Liljeros, Structure and Time Evolution of an Internet Dating Community, Social Networks 26, 155 (2004). [248] P. Holme, F. Liljeros, C. R. Edling, and B. J. Kim, Network Bipartivity, Phys. Rev. E 68, 056107 (2003). [249] P. G. Lind, M. C. González, and H. J. Herrmann, Cycles and Clustering in Bipartite Networks, Phys. Rev. E 72, 056127 (2005). [250] P. Zhang, J. Wang, X. Li, M. Li, Z. Di, and Y. Fan, Clustering Coefficient and Community Structure of Bipartite Networks, Physica A: Statistical Mechanics and Its Applications 387, 6869 (2008).

Show full item record