Додаток E — Список рекомендованої літератури

[1]
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).
[2]
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).
[3]
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.
[4]
B. Luque, L. Lacasa, F. Ballesteros, and J. Luque, Horizontal visibility graphs: Exact results for random time series, Phys. Rev. E 80, 046103 (2009).
[5]
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).
[6]
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).
[7]
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).
[8]
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).
[9]
F. R. K. Chung, Spectral Graph Theory (American Mathematical Society, 1997).
[10]
N. Biggs, Spectral graph theory (CBMS regional conference series in mathematics 92), Bulletin of the London Mathematical Society 30, 197 (1998).
[11]
S. Butler, Interlacing for weighted graphs using the normalized laplacian, Electronic Journal of Linear Algebra 16, 90 (2007).
[12]
[13]
I. Gutman, The energy of a graph, (1978).
[14]
W. Jun, M. Barahona, T. Yue-Jin, and D. Hong-Zhong, Natural connectivity of complex networks, Chinese Physics Letters 27, 078902 (2010).
[15]
E. Estrada, Spectral scaling and good expansion properties in complex networks, Europhysics Letters 73, 649 (2006).
[16]
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).
[17]
D. M. Cvetkovic, M. Doob, and H. Sachs, Spectra of graphs. Theory and application, (1980).
[18]
A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Society for Industrial; Applied Mathematics, 1994).
[19]
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.
[20]
T. H. Wei, The Algebraic Foundations of Ranking Theory (University of Cambridge, 1952).
[21]
M. G. Kendall, Further contributions to the theory of paired comparisons, Biometrics 11, 43 (1955).
[22]
C. Berge, Théorie Des Graphes Et Ses Applications (Dunod, 1958).
[23]
P. Bonacich, Technique for analyzing overlapping memberships, Sociological Methodology 4, 176 (1972).
[24]
Wikipedia, Arnoldi iteration.
[25]
K. Stephenson and M. Zelen, Rethinking centrality: Methods and examples, Social Networks 11, 1 (1989).
[26]
V. Latora and M. Marchiori, Efficient behavior of small-world networks, Phys. Rev. Lett. 87, 198701 (2001).
[27]
R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Dynamical and correlation properties of the internet, Phys. Rev. Lett. 87, 258701 (2001).
[28]
S. Maslov and K. Sneppen, Specificity and stability in topology of protein networks, Science 296, 910 (2002).
[29]
M. E. J. Newman, Assortative mixing in networks, Phys. Rev. Lett. 89, 208701 (2002).
[30]
D. J. Watts and S. H. Strogatz, Collective dynamics of ’small-world’ networks, Nature 393, 440 (1998).
[31]
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).
[32]
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports 424, 175 (2006).
[33]
P. Holme, C. R. Edling, and F. Liljeros, Structure and time evolution of an internet dating community, Social Networks 26, 155 (2004).
[34]
P. Holme, F. Liljeros, C. R. Edling, and B. J. Kim, Network bipartivity, Phys. Rev. E 68, 056107 (2003).
[35]
P. G. Lind, M. C. González, and H. J. Herrmann, Cycles and clustering in bipartite networks, Phys. Rev. E 72, 056127 (2005).
[36]
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).
[37]
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).
[38]
C. Bandt and B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett. 88, 174102 (2002).
[39]
H. Kantz and T. Schreiber, Nonlinear Time Series Analysis (Cambridge University Press, 2004).
[40]
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).
[41]
M. Rostaghi and H. Azami, Dispersion entropy: A measure for time-series analysis, IEEE Signal Processing Letters 23, 610 (2016).
[42]
[43]
S. M. Pincus, I. M. Gladstone, and R. A. Ehrenkranz, A regularity statistic for medical data analysis, Journal of Clinical Monitoring 7, 335 (1991).
[44]
S. M. Pincus, Approximate entropy as a measure of system complexity, Proceedings of the National Academy of Sciences 88, 2297 (1991).
[45]
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).
[46]
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).
[47]
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).
[48]
T. Guhr, A. Müller–Groeling, and H. A. Weidenmüller, Random-matrix theories in quantum physics: Common concepts, Physics Reports 299, 189 (1998).
[49]
[50]
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).
[51]
E. P. Wigner, On a class of analytic functions from the quantum theory of collisions, Annals of Mathematics 53, 36 (1951).
[52]
F. J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. I, Journal of Mathematical Physics 3, 140 (2004).
[53]
F. J. Dyson and M. L. Mehta, Statistical Theory of the Energy Levels of Complex Systems. IV, Journal of Mathematical Physics 4, 701 (2004).
[54]
M. L. Mehta and F. J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. V, Journal of Mathematical Physics 4, 713 (2004).
[55]
M. L. Mehta, Random Matrices (Academic Press, 1991).
[56]
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).
[57]
L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Noise dressing of financial correlation matrices, Phys. Rev. Lett. 83, 1467 (1999).
[58]
[59]
F. J. Dyson, Distribution of eigenvalues for a class of real symmetric matrices, Revista Mexicana de Fisica 20, 231 (1971).
[60]
A. M. Sengupta and P. P. Mitra, Distributions of singular values for some random matrices, Phys. Rev. E 60, 3389 (1999).
[61]
C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal 27, 379 (1948).
[62]
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).
[63]
B. Hjorth, EEG analysis based on time domain properties, Electroencephalography and Clinical Neurophysiology 29, 306 (1970).
[64]
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).
[65]
V. Marmelat, K. Torre, and D. Delignieres, Relative roughness: An index for testing the suitability of the monofractal model, Frontiers in Physiology 3, (2012).
[66]
T. M. Cover, Elements of Information Theory (John Wiley & Sons, 1999).
[67]
A. N. Kolmogorov, Three approaches to the quantitative definition of information, International Journal of Computer Mathematics 2, 157 (1968).
[68]
M. S. Kanwal, J. A. Grochow, and N. Ay, Comparing information-theoretic measures of complexity in boltzmann machines, Entropy 19, (2017).
[69]
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.
[70]
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.
[71]
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).
[72]
J.-L. Blanc, L. Pezard, and A. Lesne, Delay independence of mutual-information rate of two symbolic sequences, Phys. Rev. E 84, 036214 (2011).
[73]
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).
[74]
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).
[75]
A. Lempel and J. Ziv, On the complexity of finite sequences, IEEE Transactions on Information Theory 22, 75 (1976).
[76]
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).
[77]
[78]
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.
[79]
Y. Bai, Z. Liang, and X. Li, A permutation lempel-ziv complexity measure for EEG analysis, Biomedical Signal Processing and Control 19, 102 (2015).
[80]
[81]
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).
[82]
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).
[83]
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).
[84]
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.
[85]
M. J. Katz, Fractals and the analysis of waveforms, Computers in Biology and Medicine 18, 145 (1988).
[86]
[87]
A. Kalauzi, T. Bojić, and L. Rakić, Extracting complexity waveforms from one-dimensional signals, Nonlinear Biomedical Physics 3, 1 (2009).
[88]
[89]
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.
[90]
P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D: Nonlinear Phenomena 9, 189 (1983).
[91]
P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50, 346 (1983).
[92]
P. Grassberger, Generalized dimensions of strange attractors, Physics Letters A 97, 227 (1983).
[93]
T. Higuchi, Approach to an irregular time series on the basis of the fractal theory, Physica D: Nonlinear Phenomena 31, 277 (1988).
[94]
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.
[95]
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).
[96]
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).
[97]
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.
[98]
B. B. Mandelbrot and J. A. Wheeler, The Fractal Geometry of Nature, American Journal of Physics 51, 286 (1983).
[99]
H. E. Hurst, Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116, 770 (1951).
[100]
[101]
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).
[102]
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).
[103]
S. V. Bozhokin and D. A. Parshin, Fractals and Multifractals: Textbook (Scientific; Publishing Center "Regular; Chaotic Dynamics", 2001).
[104]
B. B. Mandelbrot, C. J. G. Evertsz, and Y. Hayakawa, Exactly self-similar left-sided multifractal measures, Phys. Rev. A 42, 4528 (1990).
[105]
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.
[106]
B. B. Mandelbrot and B. B. Mandelbrot, The Fractal Geometry of Nature, Vol. 1 (WH freeman New York, 1982).
[107]
H. Steinhaus, Length, Shape and Area, in Colloquium Mathematicum, Vol. 3 (Polska Akademia Nauk. Instytut Matematyczny PAN, 1954), pp. 1–13.
[108]
A. Vulpiani, Lewis fry richardson: Scientist, visionary and pacifist, Lettera Matematica 2, 121 (2014).
[109]
B. Hayes, Computing science: Statistics of deadly quarrels, American Scientist 90, 10 (2002).
[110]
[111]
C. Tsallis, Possible generalization of boltzmann-gibbs statistics, Journal of Statistical Physics 52, 479 (1988).
[112]
C. Tsallis, Dynamical scenario for nonextensive statistical mechanics, Physica A: Statistical Mechanics and Its Applications 340, 1 (2004).
[113]
C. Tsallis, M. Gell-Mann, and Y. Sato, Asymptotically scale-invariant occupancy of phase space makes the entropy <i>s<sub>q</sub></i> extensive, Proceedings of the National Academy of Sciences 102, 15377 (2005).
[114]
[115]
G. Nicolis, I. Prigogine, W. H. Freeman, and Company, Exploring Complexity: An Introduction (W.H. Freeman, 1989).
[116]
[117]
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 ejection-heliospheric current sheet interaction, Entropy 21, (2019).
[118]
R. de Oliveira, S. Brito, L. da Silva, and C. Tsallis, Connecting complex networks to nonadditive entropies, Scientific Reports 11, 1130 (2021).
[119]
G. Pavlos, A. Iliopoulos, L. Karakatsanis, M. Xenakis, and E. Pavlos, Complexity of economical systems., Journal of Engineering Science & Technology Review 8, (2015).
[120]
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.
[121]
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).
[122]
C. Anteneodo and C. Tsallis, Breakdown of exponential sensitivity to initial conditions: Role of the range of interactions, Phys. Rev. Lett. 80, 5313 (1998).
[123]
C. TSALLIS, Some open problems in nonextensive statistical mechanics, International Journal of Bifurcation and Chaos 22, 1230030 (2012).
[124]
S. Umarov, C. Tsallis, and S. Steinberg, On aq-central limit theorem consistent with nonextensive statistical mechanics, Milan Journal of Mathematics 76, 307 (2008).
[125]
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).
[126]
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.
[127]
S. G. Stavrinides et al., On the chaotic nature of random telegraph noise in unipolar RRAM memristor devices, Chaos, Solitons & Fractals 160, 112224 (2022).
[128]
A. M. Fraser and H. L. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33, 1134 (1986).
[129]
J. Theiler, Statistical precision of dimension estimators, Phys. Rev. A 41, 3038 (1990).
[130]
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).
[131]
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).
[132]
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).
[133]
H. S. Kim, R. Eykholt, and J. D. Salas, Nonlinear dynamics, delay times, and embedding windows, Physica D: Nonlinear Phenomena 127, 48 (1999).
[134]
J. V. Lyle, M. Nandi, and P. J. Aston, Symmetric projection attractor reconstruction: Sex differences in the ECG, Frontiers in Cardiovascular Medicine 8, (2021).
[135]
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).
[136]
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).
[137]
[138]
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).
[139]
C. Rhodes and M. Morari, The false nearest neighbors algorithm: An overview, Computers & Chemical Engineering 21, S1149 (1997).
[140]
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.
[141]
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.
[142]
N. H. Packard, J. P. Crutchfield, J. D. Farmer, and R. S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45, 712 (1980).
[143]
K. Shockley and M. Riley, In Recurrence Quantification Analysis: Theory and Best Practices, 1st ed. (Springer, New York, 2015).
[144]
J.-P. Eckmann, S. O. Kamphorst, and D. Ruelle, Recurrence plots of dynamical systems, Europhysics Letters 4, 973 (1987).
[145]
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, and J. Kurths, Recurrence-plot-based measures of complexity and their application to heart-rate-variability data, Phys. Rev. E 66, 026702 (2002).
[146]
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).
[147]
J. P. Zbilut and C. L. Webber, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A 171, 199 (1992).
[148]
[149]
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).
[150]
K. Falconer, Fractal Geometry: Mathematical Foundations and Applications (John Wiley & Sons, 2003).
[151]
A. Kalauzi, T. Bojić, and L. Rakić, Extracting complexity waveforms from one-dimensional signals, Nonlinear Biomedical Physics 3, (2009).
[152]
[153]
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).
[154]
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).
[155]
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).
[156]
M. Costa, A. L. Goldberger, and C.-K. Peng, Multiscale entropy analysis of biological signals, Phys. Rev. E 71, 021906 (2005).
[157]
I. Prigogine and E. N. Hiebert, From Being to Becoming: Time and Complexity in the Physical Sciences, Physics Today 35, 69 (1982).
[158]
J. F.Donges, R. V. Donner, and J. Kurths, Testing time series irreversibility using complex network methods, Europhysics Letters 102, 10004 (2013).
[159]
M. Zanin, A. Rodríguez-González, E. Menasalvas Ruiz, and D. Papo, Assessing time series reversibility through permutation patterns, Entropy 20, (2018).
[160]
R. Flanagan and L. Lacasa, Irreversibility of financial time series: A graph-theoretical approach, Physics Letters A 380, 1689 (2016).
[161]
A. Puglisi and D. Villamaina, Irreversible effects of memory, Europhysics Letters 88, 30004 (2009).
[162]
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).
[163]
C. S. Daw, C. E. A. Finney, and M. B. Kennel, Symbolic approach for measuring temporal “irreversibility”, Phys. Rev. E 62, 1912 (2000).
[164]
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).
[165]
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, Valencia, Spain, September 17-20, 2006 (IEEE, 2006), pp. 77–80.
[166]
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).
[167]
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).
[168]
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).
[169]
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).
[170]
C. K. Karmakar, A. Khandoker, and M. Palaniswami, Phase asymmetry of heart rate variability signal, Physiological Measurement 36, 303 (2015).
[171]
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).
[172]
L. Lacasa and R. Flanagan, Time reversibility from visibility graphs of nonstationary processes, Phys. Rev. E 92, 022817 (2015).
[173]
E. P. White, B. J. Enquist, and J. L. Green, On estimating the exponent of power-law frequency distributions, Ecology 89, 905 (2008).
[174]
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).
[175]
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.
[176]
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).
[177]
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).
[178]
M. Sano and Y. Sawada, Measurement of the lyapunov spectrum from a chaotic time series, Phys. Rev. Lett. 55, 1082 (1985).
[179]
J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, and S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A 34, 4971 (1986).
[180]
U. Parlitz, Identification of true and spurious lyapunov exponents from time series, International Journal of Bifurcation and Chaos 02, 155 (1992).
[181]
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).
[182]
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).
[183]
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.
[184]
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).
[185]
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).
[186]
S. Dutta, Multifractal properties of ECG patterns of patients suffering from congestive heart failure, Journal of Statistical Mechanics: Theory and Experiment 2010, P12021 (2010).
[187]
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).
[188]
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).
[189]
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).
[190]
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).
[191]
L. Telesca, V. Lapenna, and M. Macchiato, Multifractal fluctuations in earthquake-related geoelectrical signals, New Journal of Physics 7, 214 (2005).
[192]
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).
[193]
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).
[194]
L. Telesca, V. Lapenna, and M. Macchiato, Multifractal fluctuations in seismic interspike series, Physica A: Statistical Mechanics and Its Applications 354, 629 (2005).
[195]
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).
[196]
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).
[197]
I. T. Pedron, Correlation and multifractality in climatological time series, Journal of Physics: Conference Series 246, 012034 (2010).
[198]
R. Rak, S. Drożdż, J. Kwapień, and P. Oświȩcimka, Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies, Europhysics Letters 112, 48001 (2015).
[199]
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).
[200]
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).
[201]
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).
[202]
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).
[203]
E. A. Ihlen, Introduction to multifractal detrended fluctuation analysis in matlab, Frontiers in Physiology 3, (2012).
[204]
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).
[205]
S. Drożdż and P. Oświȩcimka, Detecting and interpreting distortions in hierarchical organization of complex time series, Phys. Rev. E 91, 030902 (2015).
[206]
S. Drożdż, R. Kowalski, P. Oświȩcimka, R. Rak, and R. Gȩbarowski, Dynamical variety of shapes in financial multifractality, Complexity 2018, 1 (2018).
[207]
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).
[208]
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).
[209]
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).
[210]
E. Canessa, Multifractality in time series, Journal of Physics A: Mathematical and General 33, 3637 (2000).
[211]
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).
[212]
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).
[213]
J.-P. Eckmann and D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57, 617 (1985).
[214]
[215]
T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, Fourth Edition (MIT Press, 2022).
[216]
P. Lévy, Calcul Des Probabilités, Par Paul lévy, ... (Gauthier-Villars, 1925).
[217]
S. Mittnik, S. T. rachev, T. Doganoglu, and D. Chenyao, Maximum likelihood estimation of stable paretian models, Mathematical and Computer Modelling 29, 275 (1999).
[218]
E. F. Fama and R. Roll, Parameter estimates for symmetric stable distributions, Journal of the American Statistical Association 66, 331 (1971).
[219]
J. H. McCulloch, Simple consistent estimators of stable distribution parameters, Communications in Statistics - Simulation and Computation 15, 1109 (1986).
[220]
J. H. McCulloch, 13 Financial Applications of Stable Distributions, in Statistical Methods in Finance, Vol. 14 (Elsevier, 1996), pp. 393–425.
[221]
J. P. Nolan, Maximum Likelihood Estimation and Diagnostics for Stable Distributions, in Lévy Processes: Theory and Applications, edited by O. E. Barndorff-Nielsen, S. I. Resnick, and T. Mikosch (Birkhäuser Boston, Boston, MA, 2001), pp. 379–400.
[222]
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).
[223]
J. P. Nolan, An algorithm for evaluating stable densities in zolotarev’s (m) parameterization, Mathematical and Computer Modelling 29, 229 (1999).
[224]
V. M. Zolotarev, One-Dimensional Stable Distributions (American Mathematical Society, 1986).
[225]
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).
[226]
P. Lévy, Theorie de l’addition Des Variables Aleatoires (Gauthier-Villars, 1954).
[227]
T. J. Kozubowski, M. M. Meerschaert, A. K. Panorska, and H.-P. Scheffler, Operator geometric stable laws, Journal of Multivariate Analysis 92, 298 (2005).
[228]
B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, 1968).
[229]
[230]
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. Suárez-Figueroa, V. Yakovyna, V. S. Kharchenko, V. Kobets, H. Kravtsov, V. S. Peschanenko, Y. Prytula, M. S. Nikitchenko, and A. Spivakovsky, Vol. 2104 (CEUR-WS.org, 2018), pp. 116–127.
[231]
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.
[232]
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.
[233]
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.
[234]
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.
[235]
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.
[236]
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.
[237]
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).
[238]
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.
[239]
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.
[240]
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.
[241]
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.
[242]
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.
[243]
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.
[244]
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).
[245]
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).
[246]
R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74, 47 (2002).
[247]
A.-L. Barabási and R. Albert, Emergence of scaling in random networks, Science 286, 509 (1999).
[248]
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.
[249]
[250]
N. N. Taleb, The Black Swan: Second Edition: The Impact of the Highly Improbable Fragility (Random House Publishing Group, 2010).