Додаток E — Список рекомендованої літератури

[1]
R.V. Donner, M. Small, J.F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths, Recurrence-based time series analysis by means of complex network methods, International Journal of Bifurcation and Chaos 21 (2011) 1019–1046. https://doi.org/10.1142/s0218127411029021.
[2]
L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J.C. Nuño, From time series to complex networks: The visibility graph, Proceedings of the National Academy of Sciences 105 (2008) 4972–4975. https://doi.org/10.1073/pnas.0709247105.
[3]
A.O. Bielinskyi, O.A. Serdyuk, S.O. Semerikov, V.N. Soloviev, Econophysics of cryptocurrency crashes: A systematic review, in: A.E. Kiv, V.N. Soloviev, S.O. Semerikov (Eds.), 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, CEUR-WS.org, 2021: pp. 31–133. https://ceur-ws.org/Vol-3048/paper03.pdf.
[4]
B. Luque, L. Lacasa, F. Ballesteros, J. Luque, Horizontal visibility graphs: Exact results for random time series, Phys. Rev. E 80 (2009) 046103. https://doi.org/10.1103/PhysRevE.80.046103.
[5]
X. Lan, H. Mo, S. Chen, Q. Liu, Y. Deng, Fast transformation from time series to visibility graphs, Chaos: An Interdisciplinary Journal of Nonlinear Science 25 (2015) 083105. https://doi.org/10.1063/1.4927835.
[6]
I.V. Bezsudnov, A.A. Snarskii, From the time series to the complex networks: The parametric natural visibility graph, Physica A: Statistical Mechanics and Its Applications 414 (2014) 53–60. https://doi.org/10.1016/j.physa.2014.07.002.
[7]
T.T. Zhou, N.D. Jin, Z.K. Gao, Y.B. Luo, Limited penetrable visibility graph for establishing complex network from time series, Acta Physica Sinica 61 (2012) 030506. https://doi.org/10.7498/aps.61.030506.
[8]
Q. Xuan, J. Zhou, K. Qiu, D. Xu, S. Zheng, X. Yang, CLPVG: Circular limited penetrable visibility graph as a new network model for time series, Chaos: An Interdisciplinary Journal of Nonlinear Science 32 (2022) 013130. https://doi.org/10.1063/5.0048243.
[9]
F.R.K. Chung, Spectral graph theory, American Mathematical Society, 1997. https://mathweb.ucsd.edu/~fan/research/revised.html.
[10]
N. Biggs, Spectral graph theory (CBMS regional conference series in mathematics 92), Bulletin of the London Mathematical Society 30 (1998) 197–199. https://doi.org/10.1112/S0024609397223611.
[11]
S. Butler, Interlacing for weighted graphs using the normalized laplacian, Electronic Journal of Linear Algebra 16 (2007) 90–98. https://doi.org/10.13001/1081-3810.1185.
[12]
G. Bounova, O. de Weck, Overview of metrics and their correlation patterns for multiple-metric topology analysis on heterogeneous graph ensembles, Phys. Rev. E 85 (2012) 016117. https://doi.org/10.1103/PhysRevE.85.016117.
[13]
I. Gutman, The energy of a graph, (1978).
[14]
W. Jun, M. Barahona, T. Yue-Jin, D. Hong-Zhong, Natural connectivity of complex networks, Chinese Physics Letters 27 (2010) 078902. https://doi.org/10.1088/0256-307X/27/7/078902.
[15]
E. Estrada, Spectral scaling and good expansion properties in complex networks, Europhysics Letters 73 (2006) 649. https://doi.org/10.1209/epl/i2005-10441-3.
[16]
J. Wu, M. Barahona, Y.-J. Tan, H.-Z. Deng, Spectral measure of structural robustness in complex networks, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 41 (2011) 1244–1252. https://doi.org/10.1109/TSMCA.2011.2116117.
[17]
D.M. Cvetkovic, M. Doob, H. Sachs, Spectra of graphs. Theory and application, (1980).
[18]
A. Berman, R.J. Plemmons, Nonnegative matrices in the mathematical sciences, Society for Industrial; Applied Mathematics, 1994. https://doi.org/10.1137/1.9781611971262.
[19]
I.J. Schoenberg, Publications of edmund landau, in: P. Turán (Ed.), Number Theory and Analysis: A Collection of Papers in Honor of Edmund Landau (1877–1938), Springer US, Boston, MA, 1969: pp. 335–355. https://doi.org/10.1007/978-1-4615-4819-5_23.
[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 (1955) 43–62. http://www.jstor.org/stable/3001479 (accessed January 28, 2024).
[22]
C. Berge, Théorie des graphes et ses applications, Dunod, 1958.
[23]
P. Bonacich, Technique for analyzing overlapping memberships, Sociological Methodology 4 (1972) 176–185. http://www.jstor.org/stable/270732 (accessed January 28, 2024).
[24]
Wikipedia, Arnoldi iteration,. https://en.wikipedia.org/wiki/Arnoldi_iteration.
[25]
K. Stephenson, M. Zelen, Rethinking centrality: Methods and examples, Social Networks 11 (1989) 1–37. https://doi.org/10.1016/0378-8733(89)90016-6.
[26]
R. Pastor-Satorras, A. Vázquez, A. Vespignani, Dynamical and correlation properties of the internet, Phys. Rev. Lett. 87 (2001) 258701. https://doi.org/10.1103/PhysRevLett.87.258701.
[27]
S. Maslov, K. Sneppen, Specificity and stability in topology of protein networks, Science 296 (2002) 910–913. https://doi.org/10.1126/science.1065103.
[28]
M.E.J. Newman, Assortative mixing in networks, Phys. Rev. Lett. 89 (2002) 208701. https://doi.org/10.1103/PhysRevLett.89.208701.
[29]
D.J. Watts, S.H. Strogatz, Collective dynamics of ’small-world’ networks, Nature 393 (1998) 440–442. https://doi.org/10.1038/30918.
[30]
A. Barrat, M. Weigt, On the properties of small-world network models, The European Physical Journal B-Condensed Matter and Complex Systems 13 (2000) 547–560. https://doi.org/10.1007/s100510050067.
[31]
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports 424 (2006) 175–308. https://doi.org/10.1016/j.physrep.2005.10.009.
[32]
P. Holme, C.R. Edling, F. Liljeros, Structure and time evolution of an internet dating community, Social Networks 26 (2004) 155–174. https://doi.org/10.1016/j.socnet.2004.01.007.
[33]
P. Holme, F. Liljeros, C.R. Edling, B.J. Kim, Network bipartivity, Phys. Rev. E 68 (2003) 056107. https://doi.org/10.1103/PhysRevE.68.056107.
[34]
P.G. Lind, M.C. González, H.J. Herrmann, Cycles and clustering in bipartite networks, Phys. Rev. E 72 (2005) 056127. https://doi.org/10.1103/PhysRevE.72.056127.
[35]
P. Zhang, J. Wang, X. Li, M. Li, Z. Di, Y. Fan, Clustering coefficient and community structure of bipartite networks, Physica A: Statistical Mechanics and Its Applications 387 (2008) 6869–6875. https://doi.org/10.1016/j.physa.2008.09.006.
[36]
J.S. Richman, J.R. Moorman, Physiological time-series analysis using approximate entropy and sample entropy, American Journal of Physiology-Heart and Circulatory Physiology 278 (2000) H2039–H2049. https://doi.org/10.1152/ajpheart.2000.278.6.H2039.
[37]
C. Bandt, B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102. https://doi.org/10.1103/PhysRevLett.88.174102.
[38]
H. Kantz, T. Schreiber, Nonlinear time series analysis, Cambridge University Press, 2004.
[39]
S.J. Roberts, W. Penny, I. Rezek, Temporal and spatial complexity measures for electroencephalogram based brain-computer interfacing, Medical & Biological Engineering & Computing 37 (1999) 93–98. https://doi.org/10.1007/BF02513272.
[40]
M. Rostaghi, H. Azami, Dispersion entropy: A measure for time-series analysis, IEEE Signal Processing Letters 23 (2016) 610–614. https://doi.org/10.1109/LSP.2016.2542881.
[41]
J.C. Crepeau, L.K. Isaacson, Journal of Non-Equilibrium Thermodynamics 16 (1991) 137–152. https://doi.org/10.1515/jnet.1991.16.2.137.
[42]
S.M. Pincus, I.M. Gladstone, R.A. Ehrenkranz, A regularity statistic for medical data analysis, Journal of Clinical Monitoring 7 (1991) 335–345. https://doi.org/10.1007/BF01619355.
[43]
S.M. Pincus, Approximate entropy as a measure of system complexity, Proceedings of the National Academy of Sciences 88 (1991) 2297–2301. https://doi.org/10.1073/pnas.88.6.2297.
[44]
W. Chen, Z. Wang, H. Xie, W. Yu, Characterization of surface EMG signal based on fuzzy entropy, IEEE Transactions on Neural Systems and Rehabilitation Engineering 15 (2007) 266–272. https://doi.org/10.1109/TNSRE.2007.897025.
[45]
H.-B. Xie, W.-X. He, H. Liu, Measuring time series regularity using nonlinear similarity-based sample entropy, Physics Letters A 372 (2008) 7140–7146. https://doi.org/10.1016/j.physleta.2008.10.049.
[46]
V. Plerou, P. Gopikrishnan, B. Rosenow, L.A. Nunes Amaral, H.E. Stanley, Universal and nonuniversal properties of cross correlations in financial time series, Phys. Rev. Lett. 83 (1999) 1471–1474. https://doi.org/10.1103/PhysRevLett.83.1471.
[47]
T. Guhr, A. Müller–Groeling, H.A. Weidenmüller, Random-matrix theories in quantum physics: Common concepts, Physics Reports 299 (1998) 189–425. https://doi.org/10.1016/S0370-1573(97)00088-4.
[48]
Y.V. Fyodorov, A.D. Mirlin, Analytical derivation of the scaling law for the inverse participation ratio in quasi-one-dimensional disordered systems, Phys. Rev. Lett. 69 (1992) 1093–1096. https://doi.org/10.1103/PhysRevLett.69.1093.
[49]
E.P. Wigner, On the statistical distribution of the widths and spacings of nuclear resonance levels, Mathematical Proceedings of the Cambridge Philosophical Society 47 (1951) 790–798. https://doi.org/10.1017/S0305004100027237.
[50]
E.P. Wigner, On a class of analytic functions from the quantum theory of collisions, Annals of Mathematics 53 (1951) 36–67. http://www.jstor.org/stable/1969342 (accessed January 29, 2024).
[51]
F.J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. I, Journal of Mathematical Physics 3 (2004) 140–156. https://doi.org/10.1063/1.1703773.
[52]
F.J. Dyson, M.L. Mehta, Statistical Theory of the Energy Levels of Complex Systems. IV, Journal of Mathematical Physics 4 (2004) 701–712. https://doi.org/10.1063/1.1704008.
[53]
M.L. Mehta, F.J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. V, Journal of Mathematical Physics 4 (2004) 713–719. https://doi.org/10.1063/1.1704009.
[54]
M.L. Mehta, Random matrices, Academic Press, 1991.
[55]
T.A. Brody, J. Flores, J.B. French, P.A. Mello, A. Pandey, S.S.M. Wong, Random-matrix physics: Spectrum and strength fluctuations, Rev. Mod. Phys. 53 (1981) 385–479. https://doi.org/10.1103/RevModPhys.53.385.
[56]
L. Laloux, P. Cizeau, J.-P. Bouchaud, M. Potters, Noise dressing of financial correlation matrices, Phys. Rev. Lett. 83 (1999) 1467–1470. https://doi.org/10.1103/PhysRevLett.83.1467.
[57]
Aspects of multivariate statistical theory, Wiley, New York, 1982. https://doi.org/10.1002/9780470316559.
[58]
F.J. Dyson, Distribution of eigenvalues for a class of real symmetric matrices, Revista Mexicana de Fisica 20 (1971) 231–237.
[59]
A.M. Sengupta, P.P. Mitra, Distributions of singular values for some random matrices, Phys. Rev. E 60 (1999) 3389–3392. https://doi.org/10.1103/PhysRevE.60.3389.
[60]
C.E. Shannon, A mathematical theory of communication, Bell System Technical Journal 27 (1948) 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.
[61]
R.A. Fisher, 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 (1922) 309–368. https://doi.org/10.1098/rsta.1922.0009.
[62]
B. Hjorth, EEG analysis based on time domain properties, Electroencephalography and Clinical Neurophysiology 29 (1970) 306–310. https://doi.org/10.1016/0013-4694(70)90143-4.
[63]
F. Mormann, T. Kreuz, C. Rieke, R.G. Andrzejak, A. Kraskov, P. David, C.E. Elger, K. Lehnertz, On the predictability of epileptic seizures, Clinical Neurophysiology 116 (2005) 569–587. https://doi.org/10.1016/j.clinph.2004.08.025.
[64]
V. Marmelat, K. Torre, D. Delignieres, Relative roughness: An index for testing the suitability of the monofractal model, Frontiers in Physiology 3 (2012). https://doi.org/10.3389/fphys.2012.00208.
[65]
T.M. Cover, Elements of information theory, John Wiley & Sons, 1999.
[66]
A.N. Kolmogorov, Three approaches to the quantitative definition of information, International Journal of Computer Mathematics 2 (1968) 157–168. https://doi.org/10.1080/00207166808803030.
[67]
M.S. Kanwal, J.A. Grochow, N. Ay, Comparing information-theoretic measures of complexity in boltzmann machines, Entropy 19 (2017). https://doi.org/10.3390/e19070310.
[68]
M. Li, P. Vitányi, Preliminaries, in: An Introduction to Kolmogorov Complexity and Its Applications, Springer New York, New York, NY, 2008: pp. 1–99. https://doi.org/10.1007/978-0-387-49820-1_1.
[69]
D.G. Bonchev, Information theoretic complexity measures, in: R.A. Meyers (Ed.), Encyclopedia of Complexity and Systems Science, Springer New York, New York, NY, 2009: pp. 4820–4839. https://doi.org/10.1007/978-0-387-30440-3_285.
[70]
L.T. Lui, G. Terrazas, H. Zenil, C. Alexander, N. Krasnogor, Complexity Measurement Based on Information Theory and Kolmogorov Complexity, Artificial Life 21 (2015) 205–224. https://doi.org/10.1162/ARTL_a_00157.
[71]
J.-L. Blanc, L. Pezard, A. Lesne, Delay independence of mutual-information rate of two symbolic sequences, Phys. Rev. E 84 (2011) 036214. https://doi.org/10.1103/PhysRevE.84.036214.
[72]
S. Zozor, P. Ravier, O. Buttelli, On lempel–ziv complexity for multidimensional data analysis, Physica A: Statistical Mechanics and Its Applications 345 (2005) 285–302. https://doi.org/10.1016/j.physa.2004.07.025.
[73]
E. Estevez-Rams, R. Lora Serrano, B. Aragón Fernández, I. Brito Reyes, On the non-randomness of maximum Lempel Ziv complexity sequences of finite size, Chaos: An Interdisciplinary Journal of Nonlinear Science 23 (2013) 023118. https://doi.org/10.1063/1.4808251.
[74]
A. Lempel, J. Ziv, On the complexity of finite sequences, IEEE Transactions on Information Theory 22 (1976) 75–81. https://doi.org/10.1109/TIT.1976.1055501.
[75]
R. Giglio, R. Matsushita, A. Figueiredo, I. Gleria, S.D. Silva, Algorithmic complexity theory and the relative efficiency of financial markets, Europhysics Letters 84 (2008) 48005. https://doi.org/10.1209/0295-5075/84/48005.
[76]
C. Taufemback, R. Giglio, 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 (2011) 1631–1647. https://ideas.repec.org/a/ebl/ecbull/eb-11-00319.html.
[77]
R. Giglio, S. Da Silva, Ranking the stocks listed on bovespa according to their relative efficiency, University Library of Munich, Germany, 2009. https://EconPapers.repec.org/RePEc:pra:mprapa:22720.
[78]
Y. Bai, Z. Liang, X. Li, A permutation lempel-ziv complexity measure for EEG analysis, Biomedical Signal Processing and Control 19 (2015) 102–114. https://doi.org/https://doi.org/10.1016/j.bspc.2015.04.002.
[79]
M. Borowska, Multiscale permutation lempel–ziv complexity measure for biomedical signal analysis: Interpretation and application to focal EEG signals, Entropy 23 (2021). https://doi.org/10.3390/e23070832.
[80]
B.K. Hillen, G.T. Yamaguchi, J.J. Abbas, 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 (2013) 1–15. https://doi.org/10.1186/1743-0003-10-97.
[81]
M.D. Costa, C.-K. Peng, A.L. Goldberger, Multiscale analysis of heart rate dynamics: Entropy and time irreversibility measures, Cardiovascular Engineering 8 (2008) 88–93.
[82]
R. Clausius, T.A. Hirst, 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.
[83]
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. https://doi.org/10.1007/978-3-322-84986-1_3.
[84]
M.J. Katz, Fractals and the analysis of waveforms, Computers in Biology and Medicine 18 (1988) 145–156. https://doi.org/10.1016/0010-4825(88)90041-8.
[85]
C. Sevcik, A procedure to estimate the fractal dimension of waveforms, (2010). https://arxiv.org/abs/1003.5266.
[86]
A. Kalauzi, T. Bojić, L. Rakić, Extracting complexity waveforms from one-dimensional signals, Nonlinear Biomedical Physics 3 (2009) 1–11. https://doi.org/10.1186/1753-4631-3-8.
[87]
F. Hasselman, When the blind curve is finite: Dimension estimation and model inference based on empirical waveforms, Frontiers in Physiology 4 (2013). https://doi.org/10.3389/fphys.2013.00075.
[88]
R.F. Voss, Fractals in nature: From characterization to simulation, in: H.-O. Peitgen, D. Saupe (Eds.), The Science of Fractal Images, Springer New York, New York, NY, 1988: pp. 21–70. https://doi.org/10.1007/978-1-4612-3784-6_1.
[89]
P. Grassberger, I. Procaccia, Measuring the strangeness of strange attractors, Physica D: Nonlinear Phenomena 9 (1983) 189–208. https://doi.org/10.1016/0167-2789(83)90298-1.
[90]
P. Grassberger, I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983) 346–349. https://doi.org/10.1103/PhysRevLett.50.346.
[91]
P. Grassberger, Generalized dimensions of strange attractors, Physics Letters A 97 (1983) 227–230. https://doi.org/https://doi.org/10.1016/0375-9601(83)90753-3.
[92]
T. Higuchi, Approach to an irregular time series on the basis of the fractal theory, Physica D: Nonlinear Phenomena 31 (1988) 277–283. https://doi.org/10.1016/0167-2789(88)90081-4.
[93]
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. https://doi.org/10.1109/CBMS.1995.465426.
[94]
R. Esteller, G. Vachtsevanos, J. Echauz, B. Litt, A comparison of waveform fractal dimension algorithms, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 48 (2001) 177–183. https://doi.org/10.1109/81.904882.
[95]
C. Goh, B. Hamadicharef, G.T. Henderson, 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. https://inria.hal.science/inria-00442374.
[96]
C.F. Vega, J. Noel, Parameters analyzed of higuchi’s fractal dimension for EEG brain signals, in: 2015 Signal Processing Symposium (SPSympo), 2015: pp. 1–5. https://doi.org/10.1109/SPS.2015.7168285.
[97]
B.B. Mandelbrot, J.A. Wheeler, The Fractal Geometry of Nature, American Journal of Physics 51 (1983) 286–287. https://doi.org/10.1119/1.13295.
[98]
H.E. Hurst, Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116 (1951) 770–799. https://doi.org/10.1061/TACEAT.0006518.
[99]
H.E. Hurst, A suggested statistical model of some time series which occur in nature, Nature 180 (1957) 494–494. https://doi.org/10.1038/180494a0.
[100]
C.-K. Peng, S.V. Buldyrev, S. Havlin, M. Simons, H.E. Stanley, A.L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685–1689. https://doi.org/10.1103/PhysRevE.49.1685.
[101]
Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, Testing the weak-form efficiency of the WTI crude oil futures market, Physica A: Statistical Mechanics and Its Applications 405 (2014) 235–244. https://doi.org/10.1016/j.physa.2014.02.042.
[102]
S.V. Bozhokin, D.A. Parshin, Fractals and multifractals: textbook, Scientific; Publishing Center "Regular; Chaotic Dynamics", 2001.
[103]
B.B. Mandelbrot, C.J.G. Evertsz, Y. Hayakawa, Exactly self-similar left-sided multifractal measures, Phys. Rev. A 42 (1990) 4528–4536. https://doi.org/10.1103/PhysRevA.42.4528.
[104]
H.F. Jelinek, N. Elston, B. Zietsch, Fractal analysis: Pitfalls and revelations in neuroscience, in: G.A. Losa, D. Merlini, T.F. Nonnenmacher, E.R. Weibel (Eds.), Fractals in Biology and Medicine, Birkhäuser Basel, Basel, 2005: pp. 85–94.
[105]
B.B. Mandelbrot, B.B. Mandelbrot, The fractal geometry of nature, WH freeman New York, 1982.
[106]
H. Steinhaus, Length, shape and area, in: Colloquium Mathematicum, Polska Akademia Nauk. Instytut Matematyczny PAN, 1954: pp. 1–13.
[107]
A. Vulpiani, Lewis fry richardson: Scientist, visionary and pacifist, Lettera Matematica 2 (2014) 121–128. https://doi.org/10.1007/s40329-014-0063-z.
[108]
B. Hayes, Computing science: Statistics of deadly quarrels, American Scientist 90 (2002) 10–15. http://www.jstor.org/stable/27857587 (accessed January 30, 2024).
[109]
B. Mandelbrot, How long is the coast of britain? Statistical self-similarity and fractional dimension, Science 156 (1967) 636–638. https://doi.org/10.1126/science.156.3775.636.
[110]
C. Tsallis, Possible generalization of boltzmann-gibbs statistics, Journal of Statistical Physics 52 (1988) 479–487. https://doi.org/10.1007/BF01016429.
[111]
C. Tsallis, Dynamical scenario for nonextensive statistical mechanics, Physica A: Statistical Mechanics and Its Applications 340 (2004) 1–10. https://doi.org/10.1016/j.physa.2004.03.072.
[112]
C. Tsallis, M. Gell-Mann, 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 (2005) 15377–15382. https://doi.org/10.1073/pnas.0503807102.
[113]
C. Tsallis, Economics and finance: Q-statistical stylized features galore, Entropy 19 (2017). https://doi.org/10.3390/e19090457.
[114]
G. Nicolis, I. Prigogine, W.H. Freeman, Company, Exploring complexity: An introduction, W.H. Freeman, 1989.
[115]
C. Tsallis, Beyond boltzmann–gibbs–shannon in physics and elsewhere, Entropy 21 (2019). https://doi.org/10.3390/e21070696.
[116]
E.G. Pavlos, O.E. Malandraki, O.V. Khabarova, L.P. Karakatsanis, G.P. Pavlos, 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). https://doi.org/10.3390/e21070648.
[117]
R. de Oliveira, S. Brito, L. da Silva, C. Tsallis, Connecting complex networks to nonadditive entropies, Scientific Reports 11 (2021) 1130.
[118]
G. Pavlos, A. Iliopoulos, L. Karakatsanis, M. Xenakis, E. Pavlos, Complexity of economical systems., Journal of Engineering Science & Technology Review 8 (2015). https://www.academia.edu/download/37828856/Complexity_of_Economical_Systems.pdf.
[119]
A. Bielinskyi, S. Semerikov, O. Serdyuk, V. Solovieva, V.N. Soloviev, L. Pichl, Econophysics of sustainability indices, in: A. Kiv (Ed.), 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, CEUR-WS.org, 2020: pp. 372–392. https://ceur-ws.org/Vol-2713/paper41.pdf.
[120]
G.L. Ferri, M.F. Reynoso Savio, A. Plastino, Tsallis’ q-triplet and the ozone layer, Physica A: Statistical Mechanics and Its Applications 389 (2010) 1829–1833. https://doi.org/https://doi.org/10.1016/j.physa.2009.12.020.
[121]
C. Anteneodo, C. Tsallis, Breakdown of exponential sensitivity to initial conditions: Role of the range of interactions, Phys. Rev. Lett. 80 (1998) 5313–5316. https://doi.org/10.1103/PhysRevLett.80.5313.
[122]
C. TSALLIS, Some open problems in nonextensive statistical mechanics, International Journal of Bifurcation and Chaos 22 (2012) 1230030. https://doi.org/10.1142/S0218127412300303.
[123]
S. Umarov, C. Tsallis, S. Steinberg, On aq-central limit theorem consistent with nonextensive statistical mechanics, Milan Journal of Mathematics 76 (2008) 307–328. https://doi.org/10.1007/s00032-008-0087-y.
[124]
D. Stosic, D. Stosic, T.B. Ludermir, T. Stosic, Nonextensive triplets in cryptocurrency exchanges, Physica A: Statistical Mechanics and Its Applications 505 (2018) 1069–1074. https://doi.org/https://doi.org/10.1016/j.physa.2018.04.066.
[125]
A.O. Bielinskyi, A.V. Matviychuk, O.A. Serdyuk, S.O. Semerikov, V.V. Solovieva, V.N. Soloviev, Correlational and non-extensive nature of carbon dioxide pricing market, in: O. Ignatenko, V. Kharchenko, V. Kobets, H. Kravtsov, Y. Tarasich, V. Ermolayev, D. Esteban, V. Yakovyna, A. Spivakovsky (Eds.), ICTERI 2021 Workshops, Springer International Publishing, Cham, 2022: pp. 183–199. https://doi.org/10.1007/978-3-031-14841-5_12.
[126]
S.G. Stavrinides, M.P. Hanias, M.B. Gonzalez, F. Campabadal, Y. Contoyiannis, S.M. Potirakis, M.M. Al Chawa, C. de Benito, R. Tetzlaff, R. Picos, L.O. Chua, On the chaotic nature of random telegraph noise in unipolar RRAM memristor devices, Chaos, Solitons & Fractals 160 (2022) 112224. https://doi.org/https://doi.org/10.1016/j.chaos.2022.112224.
[127]
A.M. Fraser, H.L. Swinney, Independent coordinates for strange attractors from mutual information, Phys. Rev. A 33 (1986) 1134–1140. https://doi.org/10.1103/PhysRevA.33.1134.
[128]
J. Theiler, Statistical precision of dimension estimators, Phys. Rev. A 41 (1990) 3038–3051. https://doi.org/10.1103/PhysRevA.41.3038.
[129]
M. Casdagli, S. Eubank, J.D. Farmer, J. Gibson, State space reconstruction in the presence of noise, Physica D: Nonlinear Phenomena 51 (1991) 52–98. https://doi.org/https://doi.org/10.1016/0167-2789(91)90222-U.
[130]
M.T. Rosenstein, J.J. Collins, C.J. De Luca, A practical method for calculating largest lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena 65 (1993) 117–134. https://doi.org/https://doi.org/10.1016/0167-2789(93)90009-P.
[131]
M.T. Rosenstein, J.J. Collins, C.J. De Luca, Reconstruction expansion as a geometry-based framework for choosing proper delay times, Physica D: Nonlinear Phenomena 73 (1994) 82–98. https://doi.org/https://doi.org/10.1016/0167-2789(94)90226-7.
[132]
H.S. Kim, R. Eykholt, J.D. Salas, Nonlinear dynamics, delay times, and embedding windows, Physica D: Nonlinear Phenomena 127 (1999) 48–60. https://doi.org/https://doi.org/10.1016/S0167-2789(98)00240-1.
[133]
J.V. Lyle, M. Nandi, P.J. Aston, Symmetric projection attractor reconstruction: Sex differences in the ECG, Frontiers in Cardiovascular Medicine 8 (2021). https://doi.org/10.3389/fcvm.2021.709457.
[134]
T. Gautama, D. Mandic, M. Van Hulle, A differential entropy based method for determining the optimal embedding parameters of a signal, Proceedings 6 (2003) 29–32.
[135]
M.B. Kennel, R. Brown, H.D.I. Abarbanel, Determining embedding dimension for phase-space reconstruction using a geometrical construction, Phys. Rev. A 45 (1992) 3403–3411. https://doi.org/10.1103/PhysRevA.45.3403.
[136]
L. Cao, Practical method for determining the minimum embedding dimension of a scalar time series, Physica D: Nonlinear Phenomena 110 (1997) 43–50. https://doi.org/https://doi.org/10.1016/S0167-2789(97)00118-8.
[137]
A. Krakovská, K. Mezeiová, H. Budáčová, Use of false nearest neighbours for selecting variables and embedding parameters for state space reconstruction, Journal of Complex Systems 2015 (2015).
[138]
C. Rhodes, M. Morari, The false nearest neighbors algorithm: An overview, Computers & Chemical Engineering 21 (1997) S1149–S1154. https://doi.org/https://doi.org/10.1016/S0098-1354(97)87657-0.
[139]
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. https://doi.org/http://dx.doi.org/10.18452/18797.
[140]
F. Takens, Detecting strange attractors in turbulence, in: D. Rand, L.-S. Young (Eds.), Dynamical Systems and Turbulence, Warwick 1980, Springer Berlin Heidelberg, Berlin, Heidelberg, 1981: pp. 366–381.
[141]
N.H. Packard, J.P. Crutchfield, J.D. Farmer, R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712–716. https://doi.org/10.1103/PhysRevLett.45.712.
[142]
K. Shockley, M. Riley, In recurrence quantification analysis: Theory and best practices, 1st ed., Springer, New York, 2015. https://doi.org/10.1007/978-3-319-07155-8.
[143]
J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, Recurrence plots of dynamical systems, Europhysics Letters 4 (1987) 973. https://doi.org/10.1209/0295-5075/4/9/004.
[144]
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence-plot-based measures of complexity and their application to heart-rate-variability data, Phys. Rev. E 66 (2002) 026702. https://doi.org/10.1103/PhysRevE.66.026702.
[145]
C.L. Webber, J.P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies, Journal of Applied Physiology 76 (1994) 965–973. https://doi.org/10.1152/jappl.1994.76.2.965.
[146]
J.P. Zbilut, C.L. Webber, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A 171 (1992) 199–203. https://doi.org/https://doi.org/10.1016/0375-9601(92)90426-M.
[147]
A. Tomashin, G. Leonardi, S. Wallot, Four methods to distinguish between fractal dimensions in time series through recurrence quantification analysis, Entropy 24 (2022). https://doi.org/10.3390/e24091314.
[148]
T. Gneiting, H. Ševčíková, D.B. Percival, Estimators of Fractal Dimension: Assessing the Roughness of Time Series and Spatial Data, Statistical Science 27 (2012) 247–277. https://doi.org/10.1214/11-STS370.
[149]
K. Falconer, Fractal geometry: Mathematical foundations and applications, John Wiley & Sons, 2003. https://doi.org/10.1002/0470013850.
[150]
A. Kalauzi, T. Bojić, L. Rakić, Extracting complexity waveforms from one-dimensional signals, Nonlinear Biomedical Physics 3 (2009). https://doi.org/10.1186/1753-4631-3-8.
[151]
A.A. Anis, E.H. Lloyd, The expected value of the adjusted rescaled hurst range of independent normal summands, Biometrika 63 (1976) 111. https://doi.org/10.2307/2335090.
[152]
A. Hacine-Gharbi, P. Ravier, A binning formula of bi-histogram for joint entropy estimation using mean square error minimization, Pattern Recognition Letters 101 (2018) 21–28. https://doi.org/10.1016/j.patrec.2017.11.007.
[153]
A. Orozco-Duque, D. Novak, V. Kremen, J. Bustamante, Multifractal analysis for grading complex fractionated electrograms in atrial fibrillation, Physiological Measurement 36 (2015) 2269–2284. https://doi.org/10.1088/0967-3334/36/11/2269.
[154]
A. Faini, G. Parati, 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 (2021) 20200254. https://doi.org/10.1098/rsta.2020.0254.
[155]
M. Costa, A.L. Goldberger, C.-K. Peng, Multiscale entropy analysis of biological signals, Phys. Rev. E 71 (2005) 021906. https://doi.org/10.1103/PhysRevE.71.021906.
[156]
I. Prigogine, E.N. Hiebert, From Being to Becoming: Time and Complexity in the Physical Sciences, Physics Today 35 (1982) 69–70. https://doi.org/10.1063/1.2890013.
[157]
J. F.Donges, R.V. Donner, J. Kurths, Testing time series irreversibility using complex network methods, Europhysics Letters 102 (2013) 10004. https://doi.org/10.1209/0295-5075/102/10004.
[158]
M. Zanin, A. Rodríguez-González, E. Menasalvas Ruiz, D. Papo, Assessing time series reversibility through permutation patterns, Entropy 20 (2018). https://doi.org/10.3390/e20090665.
[159]
R. Flanagan, L. Lacasa, Irreversibility of financial time series: A graph-theoretical approach, Physics Letters A 380 (2016) 1689–1697. https://doi.org/https://doi.org/10.1016/j.physleta.2016.03.011.
[160]
A. Puglisi, D. Villamaina, Irreversible effects of memory, Europhysics Letters 88 (2009) 30004. https://doi.org/10.1209/0295-5075/88/30004.
[161]
C. Diks, J.C. van Houwelingen, F. Takens, J. DeGoede, Reversibility as a criterion for discriminating time series, Physics Letters A 201 (1995) 221–228. https://doi.org/https://doi.org/10.1016/0375-9601(95)00239-Y.
[162]
C.S. Daw, C.E.A. Finney, M.B. Kennel, Symbolic approach for measuring temporal “irreversibility,” Phys. Rev. E 62 (2000) 1912–1921. https://doi.org/10.1103/PhysRevE.62.1912.
[163]
P. Guzik, J. Piskorski, T. Krauze, A. Wykretowicz, H. Wysocki, Heart rate asymmetry by poincaré plots of RR intervals, Biomedical Engineering / Biomedizinische Technik 51 (2006) 272–275. https://doi.org/doi:10.1515/BMT.2006.054.
[164]
A. Porta, S. Guzzetti, N. Montano, T. Gnecchi-Ruscone, R. Furlan, 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. https://ieeexplore.ieee.org/document/4511792.
[165]
L. Lacasa, A. Nuñez, É. Roldán, J.M.R. Parrondo, B. Luque, Time series irreversibility: A visibility graph approach, The European Physical Journal B 85 (2012). https://doi.org/10.1140/epjb/e2012-20809-8.
[166]
M. Costa, A.L. Goldberger, C.-K. Peng, Broken asymmetry of the human heartbeat: Loss of time irreversibility in aging and disease, Phys. Rev. Lett. 95 (2005) 198102. https://doi.org/10.1103/PhysRevLett.95.198102.
[167]
C.L. Ehlers, J. Havstad, D. Prichard, J. Theiler, Low doses of ethanol reduce evidence for nonlinear structure in brain activity, The Journal of Neuroscience 18 (1998) 7474–7486. https://doi.org/10.1523/jneurosci.18-18-07474.1998.
[168]
C. Yan, P. Li, L. Ji, L. Yao, C. Karmakar, C. Liu, Area asymmetry of heart rate variability signal, BioMedical Engineering OnLine 16 (2017). https://doi.org/10.1186/s12938-017-0402-3.
[169]
C.K. Karmakar, A. Khandoker, M. Palaniswami, Phase asymmetry of heart rate variability signal, Physiological Measurement 36 (2015) 303. https://doi.org/10.1088/0967-3334/36/2/303.
[170]
I. Grosse, P. Bernaola-Galván, P. Carpena, R. Román-Roldán, J. Oliver, H.E. Stanley, Analysis of symbolic sequences using the jensen-shannon divergence, Physical Review E 65 (2002). https://doi.org/10.1103/physreve.65.041905.
[171]
L. Lacasa, R. Flanagan, Time reversibility from visibility graphs of nonstationary processes, Phys. Rev. E 92 (2015) 022817. https://doi.org/10.1103/PhysRevE.92.022817.
[172]
E.P. White, B.J. Enquist, J.L. Green, On estimating the exponent of power-law frequency distributions, Ecology 89 (2008) 905–912. https://doi.org/https://doi.org/10.1890/07-1288.1.
[173]
C.J. Gavilán-Moreno, G. Espinosa-Paredes, Using largest lyapunov exponent to confirm the intrinsic stability of boiling water reactors, Nuclear Engineering and Technology 48 (2016) 434–447. https://doi.org/https://doi.org/10.1016/j.net.2016.01.002.
[174]
A. Prieto-Guerrero, G. Espinosa-Paredes, Dynamics of BWRs and mathematical models, in: A. Prieto-Guerrero, G. Espinosa-Paredes (Eds.), Linear and Non-Linear Stability Analysis in Boiling Water Reactors, Woodhead Publishing, 2019: pp. 193–268. https://doi.org/https://doi.org/10.1016/B978-0-08-102445-4.00005-9.
[175]
D. Nychka, S. Ellner, A.R. Gallant, D. McCaffrey, Finding chaos in noisy systems, Journal of the Royal Statistical Society. Series B (Methodological) 54 (1992) 399–426. http://www.jstor.org/stable/2346135 (accessed February 5, 2024).
[176]
A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Determining lyapunov exponents from a time series, Physica D: Nonlinear Phenomena 16 (1985) 285–317. https://doi.org/https://doi.org/10.1016/0167-2789(85)90011-9.
[177]
M. Sano, Y. Sawada, Measurement of the lyapunov spectrum from a chaotic time series, Phys. Rev. Lett. 55 (1985) 1082–1085. https://doi.org/10.1103/PhysRevLett.55.1082.
[178]
J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A 34 (1986) 4971–4979. https://doi.org/10.1103/PhysRevA.34.4971.
[179]
U. Parlitz, Identification of true and spurious lyapunov exponents from time series, International Journal of Bifurcation and Chaos 02 (1992) 155–165. https://doi.org/10.1142/S0218127492000148.
[180]
M. Balcerzak, D. Pikunov, A. Dabrowski, The fastest, simplified method of lyapunov exponents spectrum estimation for continuous-time dynamical systems, Nonlinear Dynamics 94 (2018) 3053–3065. https://doi.org/10.1007/s11071-018-4544-z.
[181]
J.W. Kantelhardt, E. Koscielny-Bunde, H.H.A. Rego, S. Havlin, A. Bunde, Detecting long-range correlations with detrended fluctuation analysis, Physica A: Statistical Mechanics and Its Applications 295 (2001) 441–454. https://doi.org/https://doi.org/10.1016/S0378-4371(01)00144-3.
[182]
J.W. Kantelhardt, Fractal and multifractal time series, in: R.A. Meyers (Ed.), Mathematics of Complexity and Dynamical Systems, Springer New York, New York, NY, 2011: pp. 463–487. https://doi.org/10.1007/978-1-4614-1806-1_30.
[183]
J.W. Kantelhardt, S.A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H.E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and Its Applications 316 (2002) 87–114. https://doi.org/https://doi.org/10.1016/S0378-4371(02)01383-3.
[184]
C.-K. Peng, S. Havlin, H.E. Stanley, A.L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos: An Interdisciplinary Journal of Nonlinear Science 5 (1995) 82–87. https://doi.org/10.1063/1.166141.
[185]
S. Dutta, Multifractal properties of ECG patterns of patients suffering from congestive heart failure, Journal of Statistical Mechanics: Theory and Experiment 2010 (2010) P12021. https://doi.org/10.1088/1742-5468/2010/12/P12021.
[186]
E. Maiorino, L. Livi, A. Giuliani, A. Sadeghian, A. Rizzi, Multifractal characterization of protein contact networks, Physica A: Statistical Mechanics and Its Applications 428 (2015) 302–313. https://doi.org/https://doi.org/10.1016/j.physa.2015.02.026.
[187]
P.H. Figueirêdo, E. Nogueira, M.A. Moret, S. Coutinho, Multifractal analysis of polyalanines time series, Physica A: Statistical Mechanics and Its Applications 389 (2010) 2090–2095. https://doi.org/https://doi.org/10.1016/j.physa.2009.11.045.
[188]
G.R. Jafari, P. Pedram, L. Hedayatifar, Erratum: Long-range correlation and multifractality in bach’s inventions pitches, Journal of Statistical Mechanics: Theory and Experiment 2012 (2012) E03001. https://doi.org/10.1088/1742-5468/2012/03/E03001.
[189]
Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, D. Sornette, Multifractal analysis of financial markets: A review, Reports on Progress in Physics 82 (2019) 125901. https://doi.org/10.1088/1361-6633/ab42fb.
[190]
L. Telesca, V. Lapenna, M. Macchiato, Multifractal fluctuations in earthquake-related geoelectrical signals, New Journal of Physics 7 (2005) 214. https://doi.org/10.1088/1367-2630/7/1/214.
[191]
E.G. Yee Leung, Z. Yu, Temporal scaling behavior of avian influenza a (H5N1): The multifractal detrended fluctuation analysis, Annals of the Association of American Geographers 101 (2011) 1221–1240. https://doi.org/10.1080/00045608.2011.592733.
[192]
F. Liao, 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 (2011) 787. https://doi.org/10.1682/jrrd.2010.08.0145.
[193]
L. Telesca, V. Lapenna, M. Macchiato, Multifractal fluctuations in seismic interspike series, Physica A: Statistical Mechanics and Its Applications 354 (2005) 629–640. https://doi.org/https://doi.org/10.1016/j.physa.2005.02.053.
[194]
M.S. Movahed, F. Ghasemi, S. Rahvar, M.R.R. Tabar, Long-range correlation in cosmic microwave background radiation, Phys. Rev. E 84 (2011) 021103. https://doi.org/10.1103/PhysRevE.84.021103.
[195]
P. Mali, S. Sarkar, S. Ghosh, A. Mukhopadhyay, G. Singh, Multifractal detrended fluctuation analysis of particle density fluctuations in high-energy nuclear collisions, Physica A: Statistical Mechanics and Its Applications 424 (2015) 25–33. https://doi.org/https://doi.org/10.1016/j.physa.2014.12.037.
[196]
I.T. Pedron, Correlation and multifractality in climatological time series, Journal of Physics: Conference Series 246 (2010) 012034. https://doi.org/10.1088/1742-6596/246/1/012034.
[197]
R. Rak, S. Drożdż, J. Kwapień, P. Oświȩcimka, Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies, Europhysics Letters 112 (2015) 48001. https://doi.org/10.1209/0295-5075/112/48001.
[198]
M. Wątorek, S. Drożdż, J. Kwapień, L. Minati, P. Oświęcimka, M. Stanuszek, Multiscale characteristics of the emerging global cryptocurrency market, Physics Reports 901 (2021) 1–82. https://doi.org/https://doi.org/10.1016/j.physrep.2020.10.005.
[199]
T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Fractal measures and their singularities: The characterization of strange sets, Nuclear Physics B - Proceedings Supplements 2 (1987) 501–511. https://doi.org/https://doi.org/10.1016/0920-5632(87)90036-3.
[200]
T.C. Halsey, M.H. Jensen, L.P. Kadanoff, I. Procaccia, B.I. Shraiman, Fractal measures and their singularities: The characterization of strange sets, Phys. Rev. A 33 (1986) 1141–1151. https://doi.org/10.1103/PhysRevA.33.1141.
[201]
U. Frisch, 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.
[202]
E.A. Ihlen, Introduction to multifractal detrended fluctuation analysis in matlab, Frontiers in Physiology 3 (2012). https://doi.org/10.3389/fphys.2012.00141.
[203]
P. Oświȩcimka, L. Livi, S. Drożdż, Right-side-stretched multifractal spectra indicate small-worldness in networks, Communications in Nonlinear Science and Numerical Simulation 57 (2018) 231–245. https://doi.org/https://doi.org/10.1016/j.cnsns.2017.09.022.
[204]
S. Drożdż, P. Oświȩcimka, Detecting and interpreting distortions in hierarchical organization of complex time series, Phys. Rev. E 91 (2015) 030902. https://doi.org/10.1103/PhysRevE.91.030902.
[205]
S. Drożdż, R. Kowalski, P. Oświȩcimka, R. Rak, R. Gȩbarowski, Dynamical variety of shapes in financial multifractality, Complexity 2018 (2018) 1–13. https://doi.org/10.1155/2018/7015721.
[206]
M. Dai, C. Zhang, D. Zhang, Multifractal and singularity analysis of highway volume data, Physica A: Statistical Mechanics and Its Applications 407 (2014) 332–340. https://doi.org/https://doi.org/10.1016/j.physa.2014.04.005.
[207]
M. Dai, J. Hou, 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 (2016) 722–731. https://doi.org/https://doi.org/10.1016/j.physa.2015.10.073.
[208]
X. Sun, H. Chen, Z. Wu, Y. Yuan, Multifractal analysis of hang seng index in hong kong stock market, Physica A: Statistical Mechanics and Its Applications 291 (2001) 553–562. https://doi.org/https://doi.org/10.1016/S0378-4371(00)00606-3.
[209]
E. Canessa, Multifractality in time series, Journal of Physics A: Mathematical and General 33 (2000) 3637. https://doi.org/10.1088/0305-4470/33/19/302.
[210]
A. Kasprzak, R. Kutner, J. Perelló, J. Masoliver, Higher-order phase transitions on financial markets, The European Physical Journal B: Condensed Matter and Complex Systems 76 (2010) 513–527. https://EconPapers.repec.org/RePEc:spr:eurphb:v:76:y:2010:i:4:p:513-527.
[211]
H.D.I. Abarbanel, R. Brown, J.J. Sidorowich, L.Sh. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys. 65 (1993) 1331–1392. https://doi.org/10.1103/RevModPhys.65.1331.
[212]
J.-P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617–656. https://doi.org/10.1103/RevModPhys.57.617.
[213]
E.L. Platt, Network science with python and NetworkX quick start guide: Explore and visualize network data effectively, Packt Publishing, 2019. https://www.packtpub.com/product/network-science-with-python-and-networkx-quick-start-guide/9781789955316.
[214]
T.H. Cormen, C.E. Leiserson, R.L. Rivest, C. Stein, Introduction to algorithms, fourth edition, MIT Press, 2022. https://mitpress.mit.edu/9780262046305/introduction-to-algorithms/.
[215]
P. Lévy, Calcul des probabilités, par paul lévy, ..., Gauthier-Villars, 1925.
[216]
S. Mittnik, S.T. rachev, T. Doganoglu, D. Chenyao, Maximum likelihood estimation of stable paretian models, Mathematical and Computer Modelling 29 (1999) 275–293. https://doi.org/https://doi.org/10.1016/S0895-7177(99)00110-7.
[217]
E.F. Fama, R. Roll, Parameter estimates for symmetric stable distributions, Journal of the American Statistical Association 66 (1971) 331–338. https://doi.org/https://doi.org/10.1080/01621459.1971.10482264.
[218]
J.H. McCulloch, Simple consistent estimators of stable distribution parameters, Communications in Statistics - Simulation and Computation 15 (1986) 1109–1136. https://doi.org/https://doi.org/10.1080/03610918608812563.
[219]
J.H. McCulloch, 13 financial applications of stable distributions, in: Statistical Methods in Finance, Elsevier, 1996: pp. 393–425. https://doi.org/https://doi.org/10.1016/S0169-7161(96)14015-3.
[220]
J.P. Nolan, Maximum likelihood estimation and diagnostics for stable distributions, in: O.E. Barndorff-Nielsen, S.I. Resnick, T. Mikosch (Eds.), Lévy Processes: Theory and Applications, Birkhäuser Boston, Boston, MA, 2001: pp. 379–400. https://doi.org/https://doi.org/10.1007/978-1-4612-0197-7_17.
[221]
A. Alvarez, P. Olivares, Méthodes d’estimation pour des lois stables avec des applications en finance, Journal de La Société Française de Statistique 146 (2005) 23–54. http://www.numdam.org/item/JSFS_2005__146_4_23_0/.
[222]
J.P. Nolan, An algorithm for evaluating stable densities in zolotarev’s (m) parameterization, Mathematical and Computer Modelling 29 (1999) 229–233. https://doi.org/https://doi.org/10.1016/S0895-7177(99)00105-3.
[223]
V.M. Zolotarev, One-dimensional stable distributions, American Mathematical Society, 1986.
[224]
D. Salas-Gonzalez, J.M. Górriz, J. Ramírez, M. Schloegl, E.W. Lang, A. Ortiz, Parameterization of the distribution of white and grey matter in MRI using the α-stable distribution, Computers in Biology and Medicine 43 (2013) 559–567. https://doi.org/https://doi.org/10.1016/j.compbiomed.2013.01.003.
[225]
P. Lévy, Theorie de l’addition des variables aleatoires, Gauthier-Villars, 1954.
[226]
T.J. Kozubowski, M.M. Meerschaert, A.K. Panorska, H.-P. Scheffler, Operator geometric stable laws, Journal of Multivariate Analysis 92 (2005) 298–323. https://doi.org/https://doi.org/10.1016/j.jmva.2003.09.004.
[227]
B.V. Gnedenko, A.N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley, 1968.
[228]
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 (1973) 469–477. https://doi.org/https://doi.org/10.1080/01621459.1973.10482458.
[229]
V.N. Soloviev, A. Belinskyi, Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors, in: V. Ermolayev, M.C. Suárez-Figueroa, V. Yakovyna, V.S. Kharchenko, V. Kobets, H. Kravtsov, V.S. Peschanenko, Y. Prytula, M.S. Nikitchenko, A. Spivakovsky (Eds.), 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, CEUR-WS.org, 2018: pp. 116–127. http://ceur-ws.org/Vol-2104/paper_175.pdf.
[230]
A. Bielinskyi, V.N. Soloviev, S. Semerikov, V. Solovieva, Detecting stock crashes using levy distribution, in: A. Kiv, S. Semerikov, V.N. Soloviev, L. Kibalnyk, H. Danylchuk, A. Matviychuk (Eds.), 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, CEUR-WS.org, 2019: pp. 420–433. https://ceur-ws.org/Vol-2422/paper34.pdf.
[231]
V.N. Soloviev, A. Bielinskyi, V. Solovieva, Entropy analysis of crisis phenomena for DJIA index, in: V. Ermolayev, F. Mallet, V. Yakovyna, V.S. Kharchenko, V. Kobets, A. Kornilowicz, H. Kravtsov, M.S. Nikitchenko, S. Semerikov, A. Spivakovsky (Eds.), 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, CEUR-WS.org, 2019: pp. 434–449. https://ceur-ws.org/Vol-2393/paper_375.pdf.
[232]
V.N. Soloviev, A. Bielinskyi, O. Serdyuk, V. Solovieva, S. Semerikov, Lyapunov exponents as indicators of the stock market crashes, in: O. Sokolov, G. Zholtkevych, V. Yakovyna, Y. Tarasich, V. Kharchenko, V. Kobets, O. Burov, S. Semerikov, H. Kravtsov (Eds.), 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, CEUR-WS.org, 2020: pp. 455–470. https://ceur-ws.org/Vol-2732/20200455.pdf.
[233]
V.N. Soloviev, A. Belinskiy, Complex systems theory and crashes of cryptocurrency market, in: V. Ermolayev, M.C. Suárez-Figueroa, V. Yakovyna, H.C. Mayr, M. Nikitchenko, A. Spivakovsky (Eds.), Information and Communication Technologies in Education, Research, and Industrial Applications, Springer International Publishing, Cham, 2019: pp. 276–297. https://doi.org/https://doi.org/10.1007/978-3-030-13929-2_14.
[234]
A.O. Bielinskyi, S.V. Hushko, A.V. Matviychuk, O.A. Serdyuk, S.O. Semerikov, V.N. Soloviev, Irreversibility of financial time series: A case of crisis, in: A.E. Kiv, V.N. Soloviev, S.O. Semerikov (Eds.), 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, CEUR-WS.org, 2021: pp. 134–150. https://ceur-ws.org/Vol-3048/paper04.pdf.
[235]
V.N. Soloviev, A.O. Bielinskyi, N.A. Kharadzjan, Coverage of the coronavirus pandemic through entropy measures, in: A.E. Kiv, S.O. Semerikov, V.N. Soloviev, A.M. Striuk (Eds.), 3rd Workshop for Young Scientists in Computer Science and Software Engineering (CS and SE and SW 2020), Kryvyi Rih, Ukraine, November 27, 2020, CEUR-WS.org, 2021: pp. 24–42. https://ceur-ws.org/Vol-2832/paper02.pdf.
[236]
A.O. Bielinskyi, V.N. Soloviev, S.O. Semerikov, V.V. Solovieva, IDENTIFYING STOCK MARKET CRASHES BY FUZZY MEASURES OF COMPLEXITY, Neuro-Fuzzy Modeling Techniques in Economics 10 (2021) 3–45. https://doi.org/http://doi.org/10.33111/nfmte.2021.003.
[237]
A.O. Bielinskyi, A.E. Kiv, Y.O. Prikhozha, M.A. Slusarenko, V.N. Soloviev, Complex systems and physics education, in: A.E. Kiv, S.O. Semerikov, M.P. Shyshkina (Eds.), Proceedings of the 9th Workshop on Cloud Technologies in Education, CTE 2021, Kryvyi Rih, Ukraine, December 17, 2021, CEUR-WS.org, 2021: pp. 56–80. https://doi.org/https://doi.org/10.55056/cte.103.
[238]
A.O. Bielinskyi, V.N. Soloviev, Complex network precursors of crashes and critical events in the cryptocurrency market, in: S.O. Semerikov, A.M. Striuk, V.N. Soloviev, A.E. Kiv (Eds.), Proceedings of St Student Workshop on Computer Science and Software Engineering, CS and SE@SW 2018, Kryvyi Rih, Ukraine, November 30, 2018, CEUR-WS.org, 2028: pp. 37–45. https://ceur-ws.org/Vol-2292/paper02.pdf.
[239]
A. Kiv, A. Bryukhanov, A. Bielinskyi, V. Soloviev, T. Kavetskyy, D. Dyachok, I. Donchev, V. Lukashin, Irreversibility of plastic deformation processes in metals, in: E. Faure, O. Danchenko, M. Bondarenko, Y. Tryus, C. Bazilo, G. Zaspa (Eds.), Information Technology for Education, Science, and Technics, Springer Nature Switzerland, Cham, 2023: pp. 425–445. https://doi.org/https://doi.org/10.1007/978-3-031-35467-0_26.
[240]
A. Bielinskyi, V. Soloviev, V. Solovieva, A. Matviychuk, S. Semerikov, The analysis of multifractal cross-correlation connectedness between bitcoin and the stock market, in: E. Faure, O. Danchenko, M. Bondarenko, Y. Tryus, C. Bazilo, G. Zaspa (Eds.), Information Technology for Education, Science, and Technics, Springer Nature Switzerland, Cham, 2023: pp. 323–345. https://doi.org/https://doi.org/10.1007/978-3-031-35467-0_21.
[241]
A.O. Bielinskyi, V.N. Soloviev, V. Solovieva, S.O. Semerikov, M.A. Radin, Recurrence quantification analysis of energy market crises: A nonlinear approach to risk management, in: H.B. Danylchuk, S.O. Semerikov (Eds.), 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, CEUR-WS.org, 2022: pp. 110–131. https://ceur-ws.org/Vol-3465/paper14.pdf.
[242]
A.O. Bielinskyi, V.N. Soloviev, S.V. Hushko, A.E. Kiv, A.V. Matviychuk, High-order network analysis for financial crash identification, in: H.B. Danylchuk, S.O. Semerikov (Eds.), 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, CEUR-WS.org, 2022: pp. 132–149. https://ceur-ws.org/Vol-3465/paper15.pdf.
[243]
A. Kiv, A. Bryukhanov, V. Soloviev, A. Bielinskyi, T. Kavetskyy, D. Dyachok, I. Donchev, V. Lukashin, Complex network methods for plastic deformation dynamics in metals, Dynamics 3 (2023) 34–59. https://doi.org/https://doi.org/10.3390/dynamics3010004.
[244]
A.A.B. Pessa, 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 (2021) 063110. https://doi.org/https://doi.org/10.1063/5.0049901.
[245]
R. Albert, A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002) 47–97. https://doi.org/https://doi.org/10.1103/RevModPhys.74.47.
[246]
A.-L. Barabási, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509–512. https://doi.org/10.1126/science.286.5439.509.
[247]
J. Travers, S. Milgram, An experimental study of the small world problem, in: S. Leinhardt (Ed.), Social Networks, Academic Press, 1977: pp. 179–197. https://doi.org/https://doi.org/10.1016/B978-0-12-442450-0.50018-3.
[248]
N.N. Taleb, Statistical consequences of fat tails: Real world preasymptotics, epistemology, and applications, (2022). https://arxiv.org/abs/2001.10488.
[249]
N.N. Taleb, The black swan: Second edition: The impact of the highly improbable fragility, Random House Publishing Group, 2010.
[250]
V. Latora, M. Marchiori, Efficient behavior of small-world networks, Phys. Rev. Lett. 87 (2001) 198701. https://doi.org/10.1103/PhysRevLett.87.198701.
[251]
K. Humphries Mark D. AND Gurney, Network ‘small-world-ness‘: A quantitative method for determining canonical network equivalence, PLOS ONE 3 (2008) 1–10. https://doi.org/10.1371/journal.pone.0002051.
[252]
J. Kim, T. Wilhelm, What is a complex graph?, Physica A: Statistical Mechanics and Its Applications 387 (2008) 2637–2652. https://doi.org/https://doi.org/10.1016/j.physa.2008.01.015.
[253]
S. Dasgupta, C.H. Papadimitriou, U. Vazirani, Algorithms, McGraw-Hill Education, New York, NY, USA, 2006.
[254]
C.H. Papadimitriou, The euclidean travelling salesman problem is NP-complete, Theoretical Computer Science 4 (1977) 237–244. https://doi.org/https://doi.org/10.1016/0304-3975(77)90012-3.