Analysis of Natural and Artificial Phenomena Using Signal Processing and Fractional Calculus

References

[1] L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, Classes of small-world networks. Proc. of the National Academy of Sciences 97, No 21 (2000), 11149-11152. Search in Google Scholar

[2] A. Arenas, L. Danon, A. Diaz-Guilera, P. M. Gleiser, and R. Guimera, Community analysis in social networks. The European Physical J. BCondensed Matter and Complex Systems 38, No 2 (2004), 373-380.Search in Google Scholar

[3] W. B. Arthur, Complexity and the economy. Science 284, No 5411 (1999), 107-109.Search in Google Scholar

[4] D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods. Ser. on Complexity, Nonlinearity and Chaos, World Scientific (2012).10.1142/8180Search in Google Scholar

[5] A.-L. Barabási, H. Jeong, Z. Néda, E. Ravasz, A. Schubert, and T. Vicsek, Evolution of the social network of scientific collaborations. Physica A: Statistical Mechanics and its Applications 311, No 3 (2002), 590-614.Search in Google Scholar

[6] D. S. Bassett and E. Bullmore, Small-world brain networks. The Neuroscientist 12, No 6 (2006), 512-523.Search in Google Scholar

[7] P. Bhattacharya, B. K. Chakrabarti, and Kamal, A fractal model of earthquake occurrence: Theory, simulations and comparisons with the aftershock data. Journal of Physics: Conference Series 319, No 1 (2011), 1012004.Search in Google Scholar

[8] C. M. Bishop, Pattern Recognition and Machine Learning, Springer, New York (2006).Search in Google Scholar

[9] T. F. Cox andM. A. Cox, Multidimensional Scaling, CRC Press (2000). 10.1201/9781420036121Search in Google Scholar

[10] J. Foster, From simplistic to complex systems in economics. Cambridge J. of Economics 29, No 6 (2005), 873-892.Search in Google Scholar

[11] T. J. Foxon, J. Köhler, J. Michie, and C. Oughton, Towards a new complexity economics for sustainability. Cambridge J. of Economics 37, No 1 (2013), 187-208.Search in Google Scholar

[12] A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E.Mietus, G. B. Moody, C.-K. Peng, and H. E. Stanley, Physiobank, physiotoolkit, and physionet components of a new research resource for complex physiologic signals. Circulation 101, No 23 (2000), e215-e220.Search in Google Scholar

[13] F. Guzzetti, B. D. Malamud, D. L. Turcotte, and P. Reichenbach, Power-law correlations of landslide areas in central Italy. Earth and Planetary Science Letters 195, No 3 (2002), 169-183.Search in Google Scholar

[14] H. Haken, Information and Self-Organization: A Macroscopic Approach to Complex Systems. Springer (2006).Search in Google Scholar

[15] W.-Q. Huang, X.-T. Zhuang, and S. Yao, A network analysis of the chinese stock market. Physica A: Statistical Mechanics and its Applications 388, No 14 (2009), 2956-2964.Search in Google Scholar

[16] C. M. Ionescu, The Human Respiratory System: An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics. Springer (2013).Search in Google Scholar

[17] A. K. Jain, Data clustering: 50 years beyond k-means. Pattern Recognition Letters 31, No 8 (2010), 651-666.Search in Google Scholar

[18] N. F. Johnson, P. Jefferies, and P. M. Hui, Financial market complexity. OUP Catalogue (2003).10.1093/acprof:oso/9780198526650.001.0001Search in Google Scholar

[19] A. Kato, J. Murai, S. Katsuno, and T. Asami, An internet traffic data repository: The architecture and the design policy. In: INET’99 Proceedings (1999).Search in Google Scholar

[20] M. S. Keshner, 1/f noise. Proceedings of the IEEE 70, No 3 (1982), 212-218.Search in Google Scholar

[21] K. Kiyono, Z. R. Struzik, N. Aoyagi, F. Togo, and Y. Yamamoto, Phase transition in a healthy human heart rate. Physical Review Letters 95, No 5 (2005), 058101.10.1103/PhysRevLett.95.058101Search in Google Scholar PubMed

[22] S. Lennartz, V. Livina, A. Bunde, and S. Havlin, Long-term memory in earthquakes and the distribution of interoccurrence times. EPL (Europhysics Letters) 81, No 6 (2008), 69001.10.1209/0295-5075/81/69001Search in Google Scholar

[23] W. Li and X. Cai, Statistical analysis of airport network of China. Physical Review E 69, No 4 (2004), 046106.10.1103/PhysRevE.69.046106Search in Google Scholar PubMed

[24] W. Li, X. Zhang, and G. Hu, How scale-free networks and large-scale collective cooperation emerge in complex homogeneous social systems. Physical Review E 76, No 4 (2007), 045102. 10.1103/PhysRevE.76.045102Search in Google Scholar PubMed

[25] G. Lim, S. Kim, J. Kim, P. Kim, Y. Kang, S. Park, I. Park, S.-B. Park, and K. Kim, Structure of a financial cross-correlation matrix under attack. Physica A: Statistical Mechanics and its Applications 388, No 18 (2006), 3851-3858.Search in Google Scholar

[26] M. Lima, J. A. Tenreiro Machado, and A. C. Costa, A multidimensional scaling analysis of musical sounds based on pseudo phase plane. Abstract and Applied Analysis 2012 (2012), 436108.10.1155/2012/436108Search in Google Scholar

[27] A. M. Lopes and J. T. Machado, Dynamical behaviour of multi-particle large-scale systems. Nonlinear Dynamics 69, No 3 (2012), 913-925.Search in Google Scholar

[28] A. M. Lopes and J. Tenreiro Machado, Analysis of temperature timeseries: Embedding dynamics into the mds method. Communications in Nonlinear Science and Numerical Simulation 19, No 4 (2014), 851-871.Search in Google Scholar

[29] J. A. T. Machado and A. M. Lopes, Analysis and visualization of seismic data using mutual information. Entropy 15, No 9 (2013), 3892-3909.Search in Google Scholar

[30] J. T. Machado, And I say to myself: “What a fractional world!”. Fractional Calculus and Applied Analysis 14, No 4 (2011), 635-654; DOI: 10.2478/s13540-011-0037-1; http://link.springer.com/article/10.2478/s13540-011-0037-1.Search in Google Scholar

[31] D. Makowiec, A. Dudkowska, R. Ga_laska, and A. Rynkiewicz, Multifractal estimates of monofractality in RR-heart series in power spectrum ranges. Physica A: Statistical Mechanics and its Applications 388, No 17 (2009), 3486-3502.Search in Google Scholar

[32] B. B. Mandelbrot, The Fractal Geometry of Nature. Macmillan (1983).10.1119/1.13295Search in Google Scholar

[33] B. B. Mandelbrot and J. W. Van Ness, Fractional brownian motions, fractional noises and applications. SIAM Review 10, No 4 (1968), 422-437.Search in Google Scholar

[34] R. Mategna and H. Stanley, An Introduction to Econophysics. Cambridge University (2000).Search in Google Scholar

[35] Z. M’Chirgui, Small-world or scale-free phenomena in internet: What implications for the next-generation networks? Review of European Studies 4, No 1 (2012), 85-93; DOI: 10.5539/res.v4n1p85.10.5539/res.v4n1p85Search in Google Scholar

[36] A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, Spatial Tessellations- Concepts and Applications of Voronoi Diagrams. John Wiley (2000).10.1002/9780470317013Search in Google Scholar

[37] C. Pinto, A. Mendes Lopes, and J. Machado, A review of power laws in real life phenomena. Communications in Nonlinear Science and Numerical Simulation 17, No 9 (2012), 3558-3578.Search in Google Scholar

[38] D. Rind, Complexity and climate. Science 284, No 5411 (1999), 105-107.Search in Google Scholar

[39] T. Robertazzi and P. Sarachik, Self-organizing communication networks. Communications Magazine, IEEE 24, No 1 (1986), 28-33. [40] M. Sachtjen, B. Carreras, and V. Lynch, Disturbances in a power transmission system. Physical Review E 61, No 5 (2000), 4877.Search in Google Scholar

[41] L. A. Schintler, S. P. Gorman, A. Reggiani, R. Patuelli, A. Gillespie, P. Nijkamp, and J. Rutherford, Complex network phenomena in telecommunication systems. Networks and Spatial Economics 5, No 4 (2005), 351-370.Search in Google Scholar

[42] P. Sen, S. Dasgupta, A. Chatterjee, P. Sreeram, G. Mukherjee, and S. Manna, Small-world properties of the indian railway network. Physical Review E 67, No 3 (2003), 036106.10.1103/PhysRevE.67.036106Search in Google Scholar

[43] D. Sornette and V. Pisarenko, Fractal plate tectonics. Geophysical Research Letters 30, No 3 (2003), 1105.10.1029/2002GL015043Search in Google Scholar

[44] S. Stein, M. Liu, E. Calais, and Q. Li, Mid-continent earthquakes as a complex system. Seismological Research Letters 80, No 4 (2009), 551-553.Search in Google Scholar

[45] S. H. Strogatz, Exploring complex networks. Nature 410, No 6825 (2001), 268-276.Search in Google Scholar

[46] J. Tenreiro Machado, Accessing complexity from genome information. Communications in Nonlinear Science and Numerical Simulation 17, No 6 (2012), 2237-2243.Search in Google Scholar

[47] J. Tenreiro Machado and A. M. Lopes, Dynamical analysis of the global warming. Mathematical Problems in Engineering 2012 (2012), Article ID 971641 (12 p).10.1155/2012/971641Search in Google Scholar

[48] J. Tenreiro Machado and A. M. Lopes, The persistence of memory. Nonlinear Dynamics, Online first (Aug. 2014); DOI 10.1007/s11071-014-1645-1.10.1007/s11071-014-1645-1Search in Google Scholar

[49] D. L. Turcotte and B. D. Malamud, 14 earthquakes as a complex system. International Geophysics 81, Part A (2002), 209-227, IV.10.1016/S0074-6142(02)80217-0Search in Google Scholar

[50] J. Wang, Optimized scale-free networks against cascading failures. International J. of Modern Physics C 23, No 11 (2012), 1250075 (12p).10.1142/S0129183112500751Search in Google Scholar

[51] Z. Wu, L. A. Braunstein, V. Colizza, R. Cohen, S. Havlin, and H. E. Stanley, Optimal paths in complex networks with correlated weights: The worldwide airport network. Physical Review E 74, No 5 (2006), 056104.10.1103/PhysRevE.74.056104Search in Google Scholar PubMed

[52] W.-B. Zhang, Theory of complex systems and economic dynamics. Nonlinear Dynamics, Psychology, and Life Sciences 6, No 2 (2002), 83-101.Search in Google Scholar

[53] C. Zhou, L. Zemanová, G. Zamora, C. C. Hilgetag, and J. Kurths, Hierarchical organization unveiled by functional connectivity in complex brain networks. Physical Review Letters 97, No 23 (2006), 238103. 10.1103/PhysRevLett.97.238103Search in Google Scholar PubMed