Critical slowing down in networks generating temporal complexity

Mt, Beig; Bologna, Mauro; Bj, West; Grigolini, Paolo

doi:10.1103/physreve.91.012907

Cited by 12 publications

(36 citation statements)

References 23 publications

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“…It is important to notice that in the case of criticality generated by a fine tuning parameter the fluctuations of the mean field around the equilibrium value have an increasing intensity upon decrease of the number of units (Beig et al, 2015). We show that this property is shared by the SOTC.…”

Section: Self-organizationmentioning

confidence: 99%

“…In the case of the criticality with a fine tuning parameter of Beig et al (2015), ν = 0.25. Presently we do not have a theory to determine ν for SOTC, but it is interesting to notice that the numerical calculations illustrated in Figure 2 show that ν = 0.5, making fluctuation intensity of ζ( t ) more significant than in the case of the ordinary criticality of Beig et al (2015).…”

Section: Self-organizationmentioning

confidence: 99%

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Self-organizing Complex Networks: individual versus global rules

2017

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We introduce a form of Self-Organized Criticality (SOC) inspired by the new generation of evolutionary game theory, which ranges from physiology to sociology. The single individuals are the nodes of a composite network, equivalent to two interacting subnetworks, one leading to strategy choices made by the individuals under the influence of the choices of their nearest neighbors and the other measuring the Prisoner's Dilemma Game payoffs of these choices. The interaction between the two networks is established by making the imitation strength K increase or decrease according to whether the last two payoffs increase or decrease upon increasing or decreasing K. Although each of these imitation strengths is selected selfishly, and independently of the others as well, the social system spontaneously evolves toward the state of cooperation. Criticality is signaled by temporal complexity, namely the occurrence of non-Poisson renewal events, the time intervals between two consecutive crucial events being given by an inverse power law index μ = 1.3 rather than by avalanches with an inverse power law distribution as in the original form of SOC. This new phenomenon is herein labeled self-organized temporal criticality (SOTC). We compare this bottom-up self-organization process to the adoption of a global choice rule based on assigning to all the units the same value K, with the time evolution of common K being determined by consciousness of the social benefit, a top-down process implying the action of a leader. In this case self-organization is impeded by large intensity fluctuations and the global social benefit turns out to be much weaker. We conclude that the SOTC model fits the requests of a manifesto recently proposed by a number of European social scientists.

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Section: Self-organizationmentioning

confidence: 99%

Section: Self-organizationmentioning

confidence: 99%

Self-organizing Complex Networks: individual versus global rules

2017

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“…When working with DMM at criticality, is the mean field , with = 0, ] = 0.25 [23]. In the case of SOTC [3], with = , see Section 2, we find ] = 0.5.…”

Section: Complexitymentioning

confidence: 99%

“…To stress the occurrence of crucial events in a social system resting on the bottom-up emergence of altruism, we have to extend the method used for criticality generated by the fine tuning of the control parameter . In that case, at criticality the mean field fluctuates around the vanishing value and the crucial events correspond to the occurrence of this vanishing value [15,23]. We follow [36] and evaluate the fluctuations around the proper nonvanishing mean value of = 1.5.…”

Section: Complexitymentioning

confidence: 99%

Self‐Organized Temporal Criticality: Bottom‐Up Resilience versus Top‐Down Vulnerability

2018

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We propose a social model of spontaneous self-organization generating criticality and resilience, called Self-Organized Temporal Criticality (SOTC). The criticality-induced long-range correlation favors the societal benefit and can be interpreted as the social system becoming cognizant of the fact that altruism generates societal benefit. We show that when the spontaneous bottom-up emergence of altruism is replaced by a top-down process, mimicking the leadership of an elite, the crucial events favoring the system's resilience are turned into collapses, corresponding to the falls of the leading elites. We also show with numerical simulation that the top-down SOTC lacks the resilience of the bottom-up SOTC. We propose this theoretical model to contribute to the mathematical foundation of theoretical sociology illustrated in 1901 by Pareto to explain the rise and fall of elites.

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“…This condition is denoted as fractal intermittency (Paradisi et al, 2012b;Paradisi et al, 2013;Allegrini et al, 2013;Paradisi et al, 2015b;Paradisi and Allegrini, 2015). This complex behavior is also known as Temporal Complexity (Grigolini, 2015;Beig et al, 2015;Turalska et al, 2011;Grigolini and Chialvo, 2013), a term that was introduced to underline the difference of the intermittency-based approach to complexity, focused on the study of the temporal structure of selforganization, with the more extensively investigated approach associated with the estimation of topological and spatial indicators of complexity (e.g., the degree distribution in a complex network, the avalanche size distribution) (Beggs and Plenz, 2003;Plenz and Thiagarjan, 2007;Fraiman et al, 2009;Chialvo, 2010;Grigolini and Chialvo, 2013). In summary, when a system is characterized by fractal intermittency, the essential dynamics are an alternation of metastable states, with strong coherence and long life-times, and transition (intermittent) events that occur randomly in time, develop in very short time, can be considered instantaneous and are associated with a fast memory drop.…”

Section: The Paradigm Of Fractal Intermittency In Complexitymentioning

confidence: 99%

The Challenge of Brain Complexity - A Brief Discussion about a Fractal Intermittency-based Approach

Paradisi¹,

Righi²,

Barcaro³

2016

Proceedings of the 3rd International Conference on Physiological Computing Systems

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Abstract:In the last years, the complexity paradigm is gaining momentum in many research fields where large multidimensional datasets are made available by the advancements in instrumental technology. A complex system is a multi-component system with a large number of units characterized by cooperative behavior and, consequently, emergence of well-defined self-organized structures, such as communities in a complex network. The self-organizing behavior of the brain neural network is probably the most important prototype of complexity and is studied by means of physiological signals such as the ElectroEncephaloGram (EEG). Physiological signals are typically intermittent, i.e., display non-smooth rapid variations or crucial events (e.g., cusps or abrupt jumps) that occur randomly in time, or whose frequency changes randomly. In this work, we introduce a complexity-based approach to the analysis and modeling of physiological data that is focused on the characterization of intermittent events. Recent findings about self-similar or fractal intermittency in human EEG are reviewed. The definition of brain event is a crucial aspect of this approach that is discussed in the last part of the paper, where we also propose and discuss a first version of a general-purpose event detection algorithm for EEG signals.

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Critical slowing down in networks generating temporal complexity

Cited by 12 publications

References 23 publications

Self-organizing Complex Networks: individual versus global rules

Self-organizing Complex Networks: individual versus global rules

Self‐Organized Temporal Criticality: Bottom‐Up Resilience versus Top‐Down Vulnerability

The Challenge of Brain Complexity - A Brief Discussion about a Fractal Intermittency-based Approach

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