Complexity Synchronization and the Fractal calculus

Date: 

Friday, 1 August, 2025 - 15:00 to 16:00

Speaker: Bruce J. West, Dept. of Innovation and Research, North Carolina State University, Raleigh, NC, USA.

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

ZoomA zoom meeitng link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  complexity synchronization (CS); crucial event (CEs); multifractal dimensionality; empirical principles; fractal architecture (FA).

Abstract: Since the turn of the century Network Science and Complexity Theory have been growing dramatically and their nexus has led to profoundly different ways of thinking about physiology, health, disease, and rehabilitation from those based on Newtonian mechanics. The observational ubiquity of inverse power law spectra (IPLS) in complex phenomena entailed a theory for the dynamics capturing the growth of their fractal dimension and statistics. These and other properties, e.g., chaotic and multifractal dimensional (MFD) time series, are consequences of the complexity resulting from nonlinear dynamic networks collectively summarized for biomedical phenomena as the Network Effect (NE). The NE is often described by homogeneous scaling variables with IPL scaling having a time-dependent index δ(t) which determines the MFD of the time series being a direct measure of the network’s evolving complexity and opens the door to a generalized theory of the probability calculus involving ‘fractal’ derivatives.

In this talk I address the measurable consequences of the NE on time series generated by different parts of the brain, heart, and lung ONs, which are directly related to their inter-network and intra-network interactions. Moreover, these same physiological ONs are shown to generate MFD time series using diffusion entropy analysis (DEA) that have scaling indices with quasiperiodic changes in complexity (scaling index) over time. These time series are generated by different parts of the brain, as well as heart and lung ONs and the results do not depend on the coherence properties of ON time series but demonstrate a generalized synchronization of complexity. This high-order synchrony is among the scaling indices of EEG, ECG and respiratory time series which governs the quantitative interdependence of the MFD behavior of the various ON’s dynamics. This consequence of the NE opens the door for an entirely new generalization of the dynamics of complex networks in terms of complexity synchronization (CS) independently of the scientific, engineering, or technological context. CS is a truly transdisciplinary effect whose foundation is determined by the fractal probability calculus, in physics it is referred to as fractal kinetic theory (FKT).

Biography: Dr. Bruce J. West was the Chief Scientist in Mathematical and Information Science at the US Army Research Office (ARO), 1999-2021 (retired 7/1/21); PhD in Physics from the University of Rochester 1970. Over a 50-year career he has published 24 books, including those most closely related to this colloquium: Crucial Event Rehabilitation Therapy (SpringerBriefs in Bioengineering, 2023), Crucial Events (World Scientific, 2021); Fractional Calculus View of Complexity, Tomorrow’s Science (CRC Press, 2016); Nature’s Patterns and the Fractional Calculus (De Gruyer GmbH, 2017). He has published over 400 scientific articles, essays and opinions in referred scientific journals garnering over 24K citations with an h-factor of 80. Before ARO Dr. West was Professor of Physics, University of North Texas, 1989-1999 and Chair of the Department of Physics 1989-1993. He is a Fellow of the American Physical Society, elected in 1992 and of the American Association for the Advancement of Science, elected in 2012. He has multiple awards for his research including the two most prestigious awards given to civilian researchers, those being the Presidential Meritorious Rank Award 2012 (by Obama) and the Presidential Distinguished Rank Award 2017 (by Trump).

Bibliography

[1] K. Mahmoodi, S.E. Kerick, P. Grigolini, P.J. Franaszczuk and B.J. West, “Complexity synchronization: a measure of interaction between the brain, heart and lungs”, Scientific Reports 13 (1), 11433 (2023).

[2] BJ West, P Grigolini, SE Kerick, PJ Franaszczuk, K Mahmoodi,” Complexity Synchronization of Organ Networks”, Entropy 25 (10), 1393 (2023).

[3] B.J. West, E. Geneston & P. Grigolini, “Maximizing information exchange between complex networks”, Physics Reports 468, 1-99 (2008).

[4] D.H. Abney , A. Paxton, R. Dale & C.T.  Kello, "Complexity matching of dyadic conversation", J. Exp. Psychol.: Gen143, 2304 (2014).

[5]  Z.M.H. Almurad, C. Roume & D. Delignières, "Complexity matching in side-by-side walking", Human Movement Science 54, 125 (2017).

[6] B.J. West, G.F. Massari, G. Culbreth, R. Failla, M. Bologna, R.I.M. Dunbar, and P. Grigolini, “Relating Size and Functionality in Human Social Networks through Complexity”, Journal Proceedings of the National Academy of Sciences 11718355-18358 (2020).

[7] B.J. West, “The Fractal Tapestry of Life: III Multifractals Entail the Fractional Calculus”, Fractal Fract. 20226(4), 225; https://doi.org/10.3390/fractalfract6040225

[8]  B.J. West and P. Grigolini, Crucial Events; Why are catastrophes never expected?, Studies of Nonlinear Phenomena in Life Science - Vol. 17, World ScientiÖc, NJ (2021).

[9] G. Aquino, M. Bologna, P. Grigolini and B.J. West, “Beyond the death of linear response theory: criticality of the 1/-noise condition”, Phys. Rev. Lett105, 040601 (2010).

[10] G. Aquino, M. Bologna, P. Grigolini, and B. J. West, "Transmission of information between complex systems: 1/f resonance", Phys. Rev. E 83, 051130 (2011).

[11] N. Piccinini, D. Lambert, B.J. West, M. Bologna and P. Grigolini, "Nonergodic Complexity Management“, Phys. Rev. E 93, 062301 (2016).

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