Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality

Complexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century w...

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Main Authors: Bruce J. West, Senthil Mudaliar
Format: Article
Language:English
Published: MDPI AG 2025-02-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/27/3/241
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author Bruce J. West
Senthil Mudaliar
author_facet Bruce J. West
Senthil Mudaliar
author_sort Bruce J. West
collection DOAJ
description Complexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century when it came time to determine the solutions to differential equations that were not linear. Consequently, this tutorial is not an essay on the mathematics of complexity nor is it a rigorous review of the recent growth spurt of complexity science, but is rather an exploration of how physiologic time series (PTS) in the life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions are discarded and so-called ordinary statistical events in PTS are replaced with crucial events (CEs) using mutifractal dimensionality as the working measure of complexity. The empirical datasets considered include respiration, electrocardiograms (ECGs), and electroencephalograms (EEGs), and as different as these time series appear from one another when recorded, they are in fact shown to be in synchrony when properly processed using the technique of modified diffusion entropy analysis (MDEA). This processing reveals a new synchronization mechanism among the time series which simultaneously measures their complexity by means of the multifractal dimension of each time series and are shown to track one another across time. These results reveal a set of priciples that capture the manner in which information is exchanged among physiologic organ networks.
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spelling doaj-art-9bf0f27e6f8a40d391fec2997b0e6b712025-08-20T02:42:48ZengMDPI AGEntropy1099-43002025-02-0127324110.3390/e27030241Principles Entailed by Complexity, Crucial Events, and Multifractal DimensionalityBruce J. West0Senthil Mudaliar1Center for Nonlinear Science, University of North Texas, Denton, TX 76203, USAUniformed Services University of the Health Sciences, Bethesda, MD 20817, USAComplexity is one of those descriptive terms adopted in science that we think we understand until it comes time to form a coherent definition upon which everyone can agree. Suddenly, we are awash in conditions that qualify this or that situation, much like we were in the middle of the last century when it came time to determine the solutions to differential equations that were not linear. Consequently, this tutorial is not an essay on the mathematics of complexity nor is it a rigorous review of the recent growth spurt of complexity science, but is rather an exploration of how physiologic time series (PTS) in the life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions are discarded and so-called ordinary statistical events in PTS are replaced with crucial events (CEs) using mutifractal dimensionality as the working measure of complexity. The empirical datasets considered include respiration, electrocardiograms (ECGs), and electroencephalograms (EEGs), and as different as these time series appear from one another when recorded, they are in fact shown to be in synchrony when properly processed using the technique of modified diffusion entropy analysis (MDEA). This processing reveals a new synchronization mechanism among the time series which simultaneously measures their complexity by means of the multifractal dimension of each time series and are shown to track one another across time. These results reveal a set of priciples that capture the manner in which information is exchanged among physiologic organ networks.https://www.mdpi.com/1099-4300/27/3/241complexity synchronization (CS)crucial event (CEs)multifractal dimensionalityempirical principlesfractal architecture (FA)
spellingShingle Bruce J. West
Senthil Mudaliar
Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
Entropy
complexity synchronization (CS)
crucial event (CEs)
multifractal dimensionality
empirical principles
fractal architecture (FA)
title Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
title_full Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
title_fullStr Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
title_full_unstemmed Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
title_short Principles Entailed by Complexity, Crucial Events, and Multifractal Dimensionality
title_sort principles entailed by complexity crucial events and multifractal dimensionality
topic complexity synchronization (CS)
crucial event (CEs)
multifractal dimensionality
empirical principles
fractal architecture (FA)
url https://www.mdpi.com/1099-4300/27/3/241
work_keys_str_mv AT brucejwest principlesentailedbycomplexitycrucialeventsandmultifractaldimensionality
AT senthilmudaliar principlesentailedbycomplexitycrucialeventsandmultifractaldimensionality