We introduce a dynamic model for complexity control (CC) between systems, represented by time series characterized by different temporal complexity measures, as indicated by their respective inverse power law (IPL) indices. Given the apparent straight forward character of the model and the generality of the result, we formulate a hypothesis based on the closeness of the scaling measures of the model to the empirical complexity measures of the human brain. The main differences between the empirical Complexity Matching and Management Effect (CMME) model and the current CC model are: 1) CC is based on reinforcement learning (RL), while CMME is a quantum mechanical effect based on linear response theory. 2) CC depends on the interaction's nature, while CMME is independent of the strength of the perturbation 3) In CC, the complexity of the interacting networks changes over time whereas in CMMEs, they remain unchanged during the perturbation. 4) CC is manifest on single organ-network (ON) time series (ONTS), while CMMEs only appear at the level of large ensemble averages and at the asymptotic regime. Consequently, CC is a proper model for describing the recent experimental results, such as the rehabilitation in walking arm-in-arm and the complexity synchronization (CS) effect between the ONTS. The CC effect can lead to the design of mutual-adaptive signals to restore the misaligned complexity of maladjusted ONs or, on the other hand, to disrupt the complexity of a malicious system and lower its intelligence.

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.

Introduction:We present a theoretical foundation based on the spontaneous self-organized temporal criticality (SOTC) and multifractal dimensionality μ to model complex neurophysiological and behavioral systems to infer the optimal empirical transfer of information among them. We hypothesize that heterogeneous time series characterizing the brain, heart, and lung organ-networks (ONs) are necessarily multifractal, whose level of complexity and, therefore, their information content is measured by their multifractal dimensions. Methods:We apply modified diffusion entropy analysis (MDEA) to assess multifractal dimensions of ON time series (ONTS), and complexity synchronization (CS) analysis to infer information transfer among ONs that are part of a network-of-organ-networks (NoONs). An automated parameter selection process is proposed that relies on the Kolmogorov-Smirnov statistic to properly choose stripe sizes which are crucial in the MDEA analysis using synthetic duration times derived from the Mittag-Leffler map, shows the strength of KS-based stripe size selection to track changes in the IPL parameter μ . The purpose of this paper is to advance the validation, standardization, and reconstruct-ability of MDEA and CS analysis of heterogeneous neurophysiological time series data. Results:Results from processing these datasets show that the complexity of brain, heart, and lung ONTS co-vary over time during cognitive task performance in 44% of subjects, while complexity of brain-heart interactions significantly co-vary in 85% of subjects. Discussion:We conclude that certain principles, guidelines, and strategies for the application of MDEA analysis need further consideration. We conclude with a summary of the MDEA's limitations and future research directions.

We introduce a dynamic model for complexity control (CC) between systems, represented by time series characterized by different temporal complexity measures, as indicated by their respective inverse power law (IPL) indices. Given the apparent straightforward character of the model and the generality of the result, we formulate a hypothesis based on the closeness of the scaling measures of the model to the empirical complexity measures of the human brain. CC is a proper model for describing the recent experimental results, such as the rehabilitation in walking arm in arm and the complexity synchronization effect. The CC effect can lead to the design of mutual-adaptive signals to restore the misaligned complexity of maladjusted organ networks or, on the other hand, to disrupt the complexity of a malicious system and lower its intelligent behavior.

In this work, we use a simple multi-agent-based-model (MABM) of a social network, implementing selfish algorithm (SA) agents, to create an adaptive environment and show, using a modified diffusion entropy analysis (DEA), that the mutual-adaptive interaction between the parts of such a network manifests complexity synchronization (CS). CS has been shown to exist by processing simultaneously measured time series from among organ-networks (ONs) of the brain (neurophysiology), lungs (respiration), and heart (cardiovascular reactivity) and to be explained theoretically as a synchronization of the multifractal dimension (MFD) scaling parameters characterizing each time series. Herein, we find the same kind of CS in the emergent intelligence of groups formed in a self-organized social interaction without macroscopic control but with biased self-interest between two groups of agents playing an anti-coordination game. This computational result strongly suggests the existence of the same CS in real-world social phenomena and in human-machine interactions as that found empirically in ONs.

This paper introduces a non-standard research technique to clarify how complex phenomena, such as those that are abundantly present in human physiology, can be faithfully described using fractal dynamical models with and without stochastic forces. This method for conducting research involves tracing the historical evolution of understanding an empirical medical process facilitated by the fractal-order calculus perspective. Herein, we trace the analysis of the time series for heart rate variability (HRV) developed for diagnosing the cardiovascular health of a patient. This is performed herein by introducing four (one empirical, which entails three theoretical fractal models) distinct but related fractal models, each one introduced to solve a particular problem arising from a fundamental defect in the previous model, but in generalizing a model at one stage to resolve the problem associated with the defect, another is invariably introduced by the replacement model. It is through the utilization of the fractal-order calculus that the necessity for rethinking how to systematically incorporate additional layers of complexity is revealed, ultimately resulting in a ‘complete’ description of its empirical dynamics in fractal terms.

The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Lévy random walks is presented herein. We study such walks occurring on a two-dimensional plane where the walk is similar to the motion of a bird flying with a constant velocity, but with random changes of direction in time. The intelligence of the bird is signaled by the instantaneous changes of flying direction, which become invisible in the time series obtained by projecting the 2D walk either on the x-axis or y-axis. We establish that the projected 1D time series share the statistical complexity of time series frequently used to monitor physiological processes, shedding light on the role of crucial events (CE-s) in pathophysiology. Such CE-s are signified by abrupt changes of flying direction which are invisible in the 1D physiological time series. We establish a connection between the complex scaling index δ generated by the CE-s through μR=2−δ, where μR is the inverse power law index of the probability density function of the time interval between consecutive failures of the process of interest. We argue that the identification of empirical indices along with their theoretical relations afford important measures to control cancer.

Herein we examine the paradox faced by an individual after joining a large or ganization.The paradox is related to the phenomenon of the Organization Man, rst identi ed in the middle of the last century and is addressed herein using a large-scale numerical calculation of the network dynamics modeling the or ganization. This network model reduces to a fractal-order Langevin equation model of the dynamics for a single individual embedded in a complex network. An analytic solution for describing the subtle, yet dramatic, in uence of the organization (complex network) on the decision making behavior of an individ ual member of the organization is obtained. Furthermore, this adoption of the organizational behavior by the individual is the result of the way people interact with one another and is not necessarily a consequence of any overt e¤ort on the part of the organization to in uence individual behavior. In fact it is shown that a top-down approach to controlling individual behavior is unstable, whereas a bottom-up approach is resilient.

We apply modified diffusion entropy analysis (MDEA) to assess multifractal dimensions of ON time series (ONTS) and complexity synchronization (CS) analysis to infer information transfer among ONs that are part of a network of organ networks (NoONs). The purpose of this paper is to advance the validation, standardization, and repeatability of MDEA and CS analysis of heterogeneous neurophysiological time series data. Results from processing these datasets show that the complexity of brain, heart, and lung ONTS significantly co-vary over time during cognitive task performance but that certain principles, guidelines, and strategies for the application of MDEA analysis need consideration.

Fractal time series have been argued to be ubiquitous in human physiology and some of the implications of that ubiquity are quite remarkable. One consequence of the omnipresent fractality is complexity synchronization (CS) observed in the interactions among simultaneously recorded physiologic time series discussed herein. This new kind of synchronization has been revealed in the interaction triad of organ-networks (ONs) consisting of the mutually interacting time series generated by the brain (electroencephalograms, EEGs), heart (electrocardiograms, ECGs), and lungs (Respiration). The scaled time series from each member of the triad look nothing like one another and yet they bear a deeply recorded synchronization invisible to the naked eye. The theory of scaling statistics is used to explain the source of the CS observed in the information exchange among these multifractal time series. The multifractal dimension (MFD) of each time series is a measure of the time-dependent complexity of that time series, and it is the matching of the MFD time series that provides the synchronization referred to as CS. The CS is one manifestation of the hypothesis given by a “Law of Multifractal Dimension Synchronization” (LMFDS) which is supported by data. Therefore, the review aspects of this paper are chosen to make the extended range of the LMFDS hypothesis sufficiently reasonable to warrant further empirical testing.

Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for understanding complexity in such systems. We utilize the first-passage time technique and coordinate transformations to study the dynamics of the system and identify crucial events. Furthermore, we employ Diffusion Entropy Analysis, a powerful statistical tool, to characterize the complexity of the system and quantify the information content of the identified events. Our results show that the emergence of crucial events is closely related to the complexity of the system and can provide insight into its behavior. This approach may have applications in diverse fields, such as climate modeling, financial markets, and biological systems, where understanding the emergence of crucial events is of great importance.

Posturography is routinely used to qualitatively assess one of the cardinal symptoms of Parkinson's disease -- postural instability. While most measures of balance control are derived from displacement of the center of pressure there is evidence that such control is more likely to be velocity-based. We performed static posturographic tests (eyes open and eyes closed) during quiet standing in narrow stance for n=30 patients with Parkinson's disease (PDP) in the ON state and compared the results with those of n=30 age-matched senior controls (HSC) and n=60 young controls (HYC). We used differentiator filters to generate time series of low-frequency fluctuations of sway velocity and calculated their Lempel-Ziv complexity (LZC). With eyes closed, the mediolateral LZC of HSC 0.21 (0.02) was significantly higher than those of HYC 0.19 (0.02) and PDP 0.18 (002). Thus aging and PD have opposite effects on mediolateral LZC which strongly differentiates between HSC and PDP (92% sensitivity and 87% specificity).

INTRODUCTION:Detrended fluctuation analysis (DFA) is a well-established method to evaluate scaling indices of time series, which categorize the dynamics of complex systems. In the literature, DFA has been used to study the fluctuations of reaction time Y(n) time series, where n is the trial number.METHODS:Herein we propose treating each reaction time as a duration time that changes the representation from operational (trial number) time n to event (temporal) time t, or X(t). The DFA algorithm was then applied to the X(t) time series to evaluate scaling indices. The dataset analyzed is based on a Go-NoGo shooting task that was performed by 30 participants under low and high time-stress conditions in each of six repeated sessions over a 3-week period.RESULTS:This new perspective leads to quantitatively better results in (1) differentiating scaling indices between low versus high time-stress conditions and (2) predicting task performance outcomes.CONCLUSION:We show that by changing from operational time to event time, the DFA allows discrimination of time-stress conditions and predicts performance outcomes.

Absence seizures-generalized rhythmic spike-and-wave discharges (SWDs) are the defining property of childhood (CAE) and juvenile (JAE) absence epilepsies. Such seizures are the most compelling examples of pathological neuronal hypersynchrony. All the absence detection algorithms proposed so far have been derived from the properties of individual SWDs. In this work, we investigate EEG phase synchronization in patients with CAE/JAE and healthy subjects to explore the possibility of using the wavelet phase synchronization index to detect seizures and quantify their disorganization (fragmentation). The overlap of the ictal and interictal probability density functions was high enough to preclude effective seizure detection based solely on changes in EEG synchronization. We used a machine learning classifier with the phase synchronization index (calculated for 1 s data segments with 0.5 s overlap) and the normalized amplitude as features to detect generalized SWDs. Using 19 channels (10-20 setup), we identified 99.2% of absences. However, the overlap of the segments classified as ictal with seizures was only 83%. The analysis showed that seizures were disorganized in approximately half of the 65 subjects. On average, generalized SWDs lasted about 80% of the duration of abnormal EEG activity. The disruption of the ictal rhythm can manifest itself as the disappearance of epileptic spikes (with high-amplitude delta waves persisting), transient cessation of epileptic discharges, or loss of global synchronization. The detector can analyze a real-time data stream. Its performance is good for a six-channel setup (Fp1, Fp2, F7, F8, O1, O2), which can be implemented as an unobtrusive EEG headband. False detections are rare for controls and young adults (0.03% and 0.02%, respectively). In patients, they are more frequent (0.5%), but in approximately 82% cases, classification errors are caused by short epileptiform discharges. Most importantly, the proposed detector can be applied to parts of EEG with abnormal EEG activity to quantitatively determine seizure fragmentation. This property is important because a previous study reported that the probability of disorganized discharges is eight times higher in JAE than in CAE. Future research must establish whether seizure properties (frequency, length, fragmentation, etc.) and clinical characteristics can help distinguish CAE and JAE.

Herein theoretical ideas are presented to demonstrate the utility of CEs in uncovering what is often hidden in multiply interacting ON time series. We focus on what can be learned about ONs’ resilience using what we know about modified diffusion entropy analysis (MDEA) to reveal the influence of CEs on an ON’s ability to perform its healthy function. We emphasize processing empirical time series hosting invisible CEs that consists of a mix of CEs and non-CEs. These notions have recently been applied to heart rate variability (HRV) time series, and we review those applications to convince the reader of their wider range of utility in the form of CERT. The utility of CE time series is explored to determine the efficacy of a noninvasive type of rehabilitation for certain kinds of neurodegenerative diseases. We hypothesize how complexity matching among complex dynamic ONs can be used to define this kind of rehabilitation, one that mimics nature’s own strategy for healing injuries and recovering from disease based on the noninvasive driving of a morbid ON by a healthy ON of the same kind. The first question we need to answer is: How can invisible CEs be detected?

We study a growth process using the logistic equation in the presence of multiplicative fluctuations. It is well known that this model has a noise-induced phase transition that has attracted the attention of many researchers in the last 40 years. We study this problem and show that it generates physical effects characterized by the emergence of an inverse power law with power-law index µ = 32 , found more recently in complex phenomena, for instance in the physics of blinking quantum dots. We investigate whether this index is a manifestation of complex dynamics, such as µ = 53 , generated by the Kardar-Parisi-Zhang dynamics, or whether it is a manifestation of an ordinary diffusion process. In the first case, the anomalous diffusion is a manifestation of crucial events, in the second case it is generated by pseudo-crucial events. To realize this goal we adopt the technique of Diffusion Entropy Analysis (DEA) in a form used in the past to analyze physiological processes, for instance the heartbeats of patients, to establish the risk of heart attack. We find that noise-induced phase transitions generate pseudo-crucial events. These results were obtained using a coordinate transformation replacing the multiplicative fluctuations with additive fluctuations and by the adoption of the first-passage-time technique.

Herein we address the measurable consequences of the network effect (NE) on time series generated by different parts of the brain, heart, and lung organ-networks (ONs), which are directly related to their inter-network and intra-network interactions. Moreover, these same physiologic ONs have been shown to generate crucial event (CE) time series, and herein are shown, using modified diffusion entropy analysis (MDEA) to have scaling indices with quasiperiodic changes in complexity, as measured by scaling indices, over time. Such time series are generated by different parts of the brain, heart, and lung ONs, and the results do not depend on the underlying coherence properties of the associated time series but demonstrate a generalized synchronization of complexity. This high-order synchrony among the scaling indices of EEG (brain), ECG (heart), and respiratory time series is governed by the quantitative interdependence of the multifractal behavior of the various physiological ONs' dynamics. This consequence of the NE opens the door for an entirely general characterization of the dynamics of complex networks in terms of complexity synchronization (CS) independently of the scientific, engineering, or technological context. CS is truly a transdisciplinary effect.