Abstract
We address the issue of criticality that is attracting the attention of an increasing number of neurophysiologists. Our main purpose is to establish the specific nature of some dynamical processes that although physically different, are usually termed as “critical,” and we focus on those characterized by the cooperative interaction of many units. We notice that the term “criticality” has been adopted to denote both noise-induced phase transitions and Self-Organized Criticality (SOC) with no clear connection with the traditional phase transitions, namely the transformation of a thermodynamic system from one state of matter to another. We notice the recent attractive proposal of extended criticality advocated by Bailly and Longo, which is realized through a wide set of critical points rather than emerging as a singularity from a unique value of the control parameter. We study a set of cooperatively firing neurons and we show that for an extended set of interaction couplings the system exhibits a form of temporal complexity similar to that emerging at criticality from ordinary phase transitions. This extended criticality regime is characterized by three main properties: (i) In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity; (ii) For large values of the interaction coupling the periodic nature of the process becomes predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity; (iii) Focusing our attention on firing neuron avalanches, we find two of the popular SOC properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches. We derive the main conclusion that SOC emerges from extended criticality, thereby explaining the experimental observation of Plenz and Beggs: avalanches occur in time with surprisingly regularity, in apparent conflict with the temporal complexity of physical critical points.
Highlights
Bridging psychology and neurophysiology is a challenging issue of the twenty-first century whose origin traces back to the middle nineteenth century
Our main purpose is to establish the specific nature of some dynamical processes that physically different, are usually termed as “critical,” and we focus on those characterized by the cooperative interaction of many units
This extended criticality regime is characterized by three main properties: (i) In the ideal limiting case of infinitely large time period, temporal complexity corresponds to Mittag-Leffler complexity; (ii) For large values of the interaction coupling the periodic nature of the process becomes predominant while maintaining to some extent, in the intermediate time asymptotic region, the signature of complexity; (iii) Focusing our attention on firing neuron avalanches, we find two of the popular Self-Organized Criticality (SOC) properties, namely the power indexes 2 and 1.5 respectively for time length and for the intensity of the avalanches
Summary
Bridging psychology and neurophysiology is a challenging issue of the twenty-first century whose origin traces back to the middle nineteenth century. As pointed out by Kinouchi and Copelli (2006) the work of Weber and Fechner in the middle of the nineteenth century, on how physical stimuli turn into psychological sensation is a fundamental mind-brain problem, which has influenced the foundation of psychology by James (Hawkins, 2011). The basic idea behind the work of Kinouchi and Copelli (2006) is that in biological complex systems the optimal information processing is found near phase transitions, and that the efficiency of biologically relevant processes is optimized at criticality. Criticality of phase transition is one of the most important achievements of the twentieth century physics, thereby implying a transition from the middle nineteenth century to the second half of the twentieth century. In addition to the classical second-order phase transition, where temperature is the control parameter, the term criticality has been used to denote processes as different as noiseinduced phase transitions (Van den Broeck et al, 1994) and Self-Organized Criticality (SOC), whereas the identification of the occurrence of criticality through the observation of time series is considered to be a challenging task requiring special techniques (Varotsos et al, 2011) holding true for both the 2D Ising model and SOC
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