arXiv subjects

Paolo Grigolini

Publications and source records attributed to Paolo Grigolini.

At least 19 recordsLinked to original sources

arXiv2026

Complexity synchronization as a diagnostic and control principle for adaptive systems

Adaptive systems can exhibit similar levels of performance while relying on fundamentally different internal modes of coordination. Standard metrics such as average cooperation or payoff indicate whether a system succeeds, but do not reveal how coordination is organized across interacting components or which adaptive variables should be targeted when performance fails. Here we propose complexity synchronization (CS), the synchronization of evolving temporal complexity across coupled variables, as a diagnostic and intervention guiding principle for adaptive systems. We test this idea in an adaptive multi agent system composed of Selfish Algorithm agents interacting in a reduced Predator Prey model with a Prisoners Dilemma like payoff structure. Temporal complexity is quantified using sliding window modified diffusion entropy analysis (MDEA) and detrended fluctuation analysis (DFA). CS is defined as the correlation between the resulting time dependent scaling exponents. In the high-interaction regime, MDEA-based CS increases with cooperative performance, whereas DFA based CS captures a distinct persistence dominated coordination mode. Our results show that CS can reveal functionally relevant subsystems and provide a principled basis for targeted repair. More broadly, CS offers a general diagnostic and engineering framework for understanding and controlling coordination in biological, social, human machine, and other adaptive systems.

nlin.AO↗

arXiv2024

Complexity synchronization analysis of neurophysiological data: Theory and 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). 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.

q-bio.NC↗

arXiv2024

Complexity Control

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.

nlin.AO↗

arXiv2024

Cell Motility in Cancer, Crucial Events, Criticality, and Lévy Walks

The analysis of glioblastoma (GB) cell locomotion and its modeling inspired by Levy 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 the 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 δgenerated by the CE-s through μ_{R} = 2 - δ, where μ_{R} 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.

nlin.AO↗

arXiv2023

Search for crucial events in physiological processes

The main purpose of this paper is to attract the attention of researchers working in the field of physiological processes, towards crucial events. Crucial events are often confused with extreme events thereby generating the misleading impression that their treatment should be based on quantum mechanical formalism. We show that crucial events are invisible and should not be confused with catastrophes. Crucial events are generated by self-organization processes yielding a form of swarm intelligence, and signal their action with fluctuations characterized by anomalous scaling and 1/f spectrum. The existence or the lack of crucial events can be revealed with an entropic method of analysis called the Diffusion Entropy Analysis (DEA). However, anomalous scaling and 1/f spectrum are not a compelling signature of efficient self-organization, and physiological processes with anomalous scaling and 1/f noise spectrum without crucial events are a signature of collapsing physiological organizations. In the case of physiological processes like cancer dynamics, the existence of crucial events is a signal of intelligence that must be destroyed rather than reinforced.

nlin.AO↗

arXiv2023

Influence of an environment changing in time on Crucial Events: the earthquake prototype

This paper is devoted to the study of the interaction between two distinct forms of non-stationary processes, which we will refer to as non-stationarity of first and second kind. The non-stationarity of first kind is caused by criticality-generated events that we call crucial events. Crucial events signal ergodicity breaking emerging from the interaction between the units of the complex system under study, indicating that the non stationarity of first kind has internal origin. The non-stationarity of second kind is due to the influence on the system of interest of an environment changing in time, thereby implying an external origin. In this paper we show that the non-stationarity of first kind, measured by an inverse power law index μ is characterized by singularities at μ = 2 and μ = 3. We realize the interaction between the non-stationarity of first kind and the non-stationarity of second kind with a model frequently adopted to study earthquakes, namely, a system of mainshocks, assumed to be crucial events, generating a cascade of after-shocks simulating the changing in time environment. We prove that the after-shocks significantly affects the detection of anomalous scaling, with this effect weakening as the value μ approaches μ = 2.5. We argue that this result is a consequence of the fact that the states μ = 2 and μ = 3 are the borders between different statistical regimes, where a sort of phase transition occurs, with μ = 2.5 being a state sufficiently far from both transition regimes. We conclude this paper with the observation that the earthquakes should be interpreted as resulting from the interaction between many geophysical units generating criticality, with the non-stationary events of second kind affecting conveniently short time regions between two consecutive crucial events.

physics.geo-ph↗

arXiv2023

Complexity Synchronization in Emergent Intelligence

In this work, we use a simple multi-agent-based model (MABM), implementing selfish algorithm (SA) agents, to create an adaptive environment and show, using modified diffusion entropy analysis (MDEA), that the mutual-adaptive interaction between the parts of such a network manifests complexity synchronization (CS). CS has been experimentally shown to exist 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 scaling parameters characterizing each time series. Herein, we find the same kind of CS in the emergent intelligence (i.e., without macroscopic control and based on self-interest) between two groups of agents playing an anti-coordination game, thereby suggesting the potential for the same CS in real-world social phenomena and in human-machine interactions.

nlin.AO↗

arXiv2023

Unveiling Pseudo-Crucial Events in Noise-Induced Phase Transitions

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.

physics.data-an↗

arXiv2022

Complexity Synchronization

The observational ubiquity of inverse power law spectra (IPL) in complex phenomena entails theory for dynamic fractal phenomena capturing their fractal dimension, dynamics, and statistics. These and other properties are consequences of the complexity resulting from nonlinear dynamic networks collectively summarized for biomedical phenomena as the Network Effect (NE) or focused more narrowly as Network Physiology. Herein we address the measurable consequences of the NE on time series generated by different parts of the brain, heart, and lung organ networks, which are directly related to their inter-network and intra-network interactions. Moreover, these same physiologic organ networks 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 organ networks, 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 organs' network 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.

nlin.AO↗

arXiv2022

Noise-induced intermittence

We study a form of noise-induced intermittence originated by an out of equilibrium process yielding events in time with a survival probability that in the case of an infinitely aged condition coincides with the Mittag-Leffler function. In contrast with the Pomeau-Manneville intermittence, the aging process does not have any effect on the inverse power law of the large time scale but on the short-time stretched exponential regime.

physics.bio-ph↗

arXiv2021

From Social to Epidemic Criticality and Back

We study the spread of a simulated epidemic in a network of individuals who may either contract a disease through sexual contact with an infected nearest neighbor or use safe sex practices under the influence of neighbors who are already adopting precautions. We show that both interaction between susceptible and infected individuals and the imitation of opinions concerning safe sex practices between individuals in favor of using such practices and those opposed to them leads to a phase transition. If the parameters of the epidemic are in the supercritical state, corresponding to an unlimited growth of infection, the interaction parameter of the sociological debate must also be in the supercritical state to control the spread of infection, and bring the system to criticality. Adopting a theoretical perspective like that of multilayer complex networks, we study the case where the epidemic network is under the influence of the above-mentioned sociological debate. We show that at criticality this debate generates clusters of individuals in favor of safe sex practices and clusters of individuals opposing their use. We study the influence of a sociological debate on whether to use safe sex or not, on the spreading of sexually transmitted infections. We show that due to this debate in the epidemic network a pattern mirroring the structures of the sociological network appears. Finally, we introduce a feedback of the epidemic network on the sociological network and prove that due to this feedback the sociological system undergoes a process of self-organization keeping it at criticality. We hope that these results have the effect of giving interesting suggestions to behavioral psychologists and information scientists actively involved in the analysis of the social debate on the moral issues connected to sexual activities.

physics.soc-ph↗

arXiv2019

Intelligence of small groups

Dunbar hypothesized that $150$ is the maximal number of people with whom one can maintain stable social relationships. We explain this effect as being a consequence of a process of self-organization between $N$ units leading their social system to the edge of phase transition, usually termed criticality. Criticality generates events, with an inter-event time interval distribution characterized by an inverse power law (IPL) index $μ_{S}<2$. These events break ergodicity and we refer to them as crucial events. The group makes decisions and the time persistence of each decision is given by another IPL distribution with IPL index $μ_{R}$, which is different from $μ_{S}$ if $N\neq 150$. We prove that when the number of interacting individuals is equal to $150$, these two different IPL indexes become identical, with the effect of generating the Kardar Parisi Zhang (KPZ) scaling $δ=1/3$. We argue this to be an enhanced form of intelligence, which generates efficient information transmission within the group. We prove the inflrmation transmission efficiency is maximal when $N=150$, the Dunbar number.

nlin.AO↗

arXiv2019

Interacting Faults in California and Hindu Kush

We study seismic fluctuations in California and Hindu Kush using Diffusion Entropy Analysis (DEA), a technique designed to detect the action of crucial events in time series generated by complex dynamical systems. The time distance between two consecutive crucial events is described by an inverse power law distribution density with a power index $μ$ close to the value $μ= 2$, corresponding to an ideal $1/f$ noise. DEA was used in the recent past to study neurophysiological processes that in the healthy condition are found to generate $1/f$ noise and $μ$ close to $2$. In this paper we find that the seismic fluctuations in both California and Hindu-Kush of extended areas implying the action of many faults, $μ\approx 2.1$, while in regions involving the action of only one fault, or of a very small number of faults, $μ\approx 2.4$. This observation led us the conjectures that the seismic criticality is due to the interaction of many faults. To support this conjecture we adopted a dynamical model for fault dynamics proposed by Brown and Tosatti and we have extended it to describe the interaction between many faults. The DEA applied to surrogate sequences generated by this dynamical model, yields $μ= 2.1$ for a single fault and $μ= 2,4$ for many interacting faults, in a good agreement with the observation of real seismic fluctuations. This result supports our conjecture and suggests interesting applications to neurophysiological and sociological processes.

nlin.AO↗

arXiv2019

Complexity Matching and Requisite Variety

Complexity matching characterizes the role of information in interactions between systems and can be traced back to the 1957 Introduction to Cybernetics by Ross Ashby. We argue that complexity can be expressed in terms of crucial events, which are generated by the processes of spontaneous self-organization. Complex processes, ranging from biological to sociological, must satisfy the homeodynamic condition and host crucial events that have recently been shown to drive the information transport between complex systems. We adopt a phenomenological approach, based on the subordination to periodicity that makes it possible to combine homeodynamics and self-organization induced crucial events. The complexity of crucial events is defined by the waiting-time probability density function (PDF) of the intervals between consecutive crucial events, which have an inverse power law (IPL) PDF $ψ(τ)\propto 1/(τ)^{μ}$ with $1<μ<3$. We show that the action of crucial events has an effect compatible with the shared notion of complexity-induced entropy reduction, while making the synchronization between systems sharing the same complexity different from chaos synchronization. We establish the coupling between two temporally complex systems using a phenomenological approach inspired by models of swarm cognition and prove that complexity matching, namely sharing the same IPL index $μ$, facilitates the transport of information, generating perfect synchronization. This new form of complexity matching is expected to contribute significantly to progress in understanding and improving biofeedback therapies.

nlin.AO↗

arXiv2017

On the Dynamical Foundation of Multifractality

The crucial aspect of this demonstration is the discovery of renewal events, hidden in the computed dynamics of a multifractal metronome, which enables the replacement of the phenomenon of strong anticipation with a time delayed cross-correlation between the driven and the driving metronome. We establish that the phenomenon of complexity matching, which is the theme of an increasing number of research groups, has two distinct measures. One measure is the sensitivity of a complex system to environmental multi-fractality; another is the level of information transfer, between two complex networks at criticality. The cross-correlation function is evaluated in the ergodic long-time limit, but its delayed maximal value is the signature of information transfer occurring in the non ergodic short-time regime. It is shown that a more complex system transfers its multifractality to a less complex system while the reverse case is not possible.

nlin.AO↗

arXiv2017

Non-Poisson Renewal Events and Memory

We study two different forms of fluctuation-dissipation processes generating anomalous relaxations to equilibrium of an initial out of equilibrium condition, the former being based on a stationary although very slow correlation function and the latter characterized by the occurrence of crucial events, namely, non-Poisson renewal events, incompatible with the stationary condition. Both forms of regression to equilibrium have the same non-exponential Mittag-Leffler structure. We analyze the single trajectories of the two processes by recording the time distances between two consecutive origin re-crossings and establishing the corresponding waiting time probability density function (PDF), $ψ(t)$. In the former case, with no crucial events, $ψ(t)$ is exponential and in the latter case, with crucial events, $ψ(t)$ is an inverse power law PDF with a diverging first moment. We discuss the consequences that this result is expected to have for the correct interpretation of some anomalous relaxation processes.

physics.data-an↗

arXiv2017

Crucial events, randomness and multi-fractality in heartbeats

We study the connection between multi-fractality and crucial events. Multi-fractality is frequently used as a measure of physiological variability. Crucial events are known to play a fundamental role in the transport of information between complex networks. To establish a connection we focus on the special case of heartbeat time series and on the search for a diagnostic prescription to distinguish healthy from pathologic subjects. Over the last twenty years two apparently different diagnostic techniques have been established: the first is based on the observation that the multi-fractal spectrum of healthy patients is broader than the multi-fractal spectrum of pathologic subjects; the second is based on the observation that heartbeat dynamics are a superposition of crucial and Poisson events, with pathologic patients hosting Poisson events with larger probability than the healthy patients. In this paper, we prove that increasing the percentage of Poisson events hosted by heartbeats has the effect of making their multi-fractal spectrum narrower, thereby establishing that the two different diagnostic techniques are compatible with one another and, at the same time, establishing a dynamic interpretation of multi-fractal processes that has been previously overlooked.

nlin.AO↗

arXiv2016

Neuronal Avalanches: Where Temporal Complexity and Criticality Meet

The model of the current paper is an extension of a previous publication, wherein we used the leaky integrate-and-fire model on a regular lattice with periodic boundary conditions, and introduced the temporal complexity as a genuine signature of criticality. In that work, the power-law distribution of neural avalanches was manifestation of supercriticality rather than criticality. Here, however, we show that continuous solution of the model and replacing the stochastic noise with a Gaussian zero-mean noise leads to the coincidence of power-law display of temporal complexity and spatiotemporal patterns of neural avalanches at the critical point. We conclude that the source of inconsistency may in fact be a numerical artifact originated by the discrete description of the model, which may imply slow numerical convergence of avalanche distribution compared to temporal complexity.

cond-mat.dis-nn↗