A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators

Self-organized quasi periodicity is one of the most puzzling dynamical phases observed in systems of non linear coupled oscillators. The single dynamical units are not locked to the periodic mean field they produce, but they still feature a coherent behavior, through an unexplained complex form of correlation. We consider a class of leaky integrate-and-fire oscillators on random sparse and massive networks with dynamical synapses, featuring self-organized quasi periodicity, and we show how complex collective oscillations arise from constructive interference of microscopic dynamics. In particular, we find a simple quantitative relationship between two relevant microscopic dynamical time scales and the macroscopic time scale of the global signal. We show that the proposed relation is a general property of collective oscillations, common to all the partially synchronous dynamical phases analyzed. We argue that an analogous mechanism could be at the origin of similar network dynamics.Comment: to appear in Phys. Rev.

Neutral theory and scale-free neural dynamics

Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether such scaling laws stem from the underlying neural dynamics operating at the edge of a phase transition is a fascinating possibility, as systems poised at criticality have been argued to exhibit a number of important functional advantages. Here we employ a well-known model for neural dynamics with synaptic plasticity, to elucidate an alternative scenario in which neuronal avalanches can coexist, overlapping in time, but still remaining scale-free. Remarkably their scale-invariance does not stem from underlying criticality nor self-organization at the edge of a continuous phase transition. Instead, it emerges from the fact that perturbations to the system exhibit a neutral drift --guided by demographic fluctuations-- with respect to endogenous spontaneous activity. Such a neutral dynamics --similar to the one in neutral theories of population genetics-- implies marginal propagation of activity, characterized by power-law distributed causal avalanches. Importantly, our results underline the importance of considering causal information --on which neuron triggers the firing of which-- to properly estimate the statistics of avalanches of neural activity. We discuss the implications of these findings both in modeling and to elucidate experimental observations, as well as its possible consequences for actual neural dynamics and information processing in actual neural networks.Comment: Main text: 8 pages, 3 figures. Supplementary information: 5 pages, 4 figure

Unveiling the intrinsic dynamics of biological and artificial neural networks: from criticality to optimal representations

Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics should operate at the brink of a phase transition, i.e., at the edge between different collective phases, to entail a rich dynamical repertoire and optimize functional capabilities. In recent years, research guided by the advent of high-throughput data and new theoretical developments has contributed to making a quantitative validation of such a hypothesis. Here we review recent advances in this field, stressing our contributions. In particular, we use data from thousands of individually recorded neurons in the mouse brain and tools such as a phenomenological renormalization group analysis, theory of disordered systems, and random matrix theory. These combined approaches provide novel evidence of quasi-universal scaling and near-critical behavior emerging in different brain regions. Moreover, we design artificial neural networks under the reservoir-computing paradigm and show that their internal dynamical states become near critical when we tune the networks for optimal performance. These results not only open new perspectives for understanding the ultimate principles guiding brain function but also towards the development of brain-inspired, neuromorphic computation

Scattering lengths and universality in superdiffusive L\'evy materials

We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensionsComment: 6 pages, 8 figure

Quasiuniversal scaling in mouse-brain neuronal activity stems from edge-of-instability critical dynamics

The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the brain transmits, processes, and stores information. An inspiring, albeit controversial, conjecture proposes that some statistical characteristics of empirically observed neuronal activity can be understood by assuming that brain networks operate in a dynamical regime with features, including the emergence of scale invariance, resembling those seen typically near phase transitions. Here, we present a data-driven analysis based on simultaneous high-throughput recordings of the activity of thousands of individual neurons in various regions of the mouse brain. To analyze these data, we construct a unified theoretical framework that synergistically combines a phenomenological renormalization group approach and techniques that infer the general dynamical state of a neural population, while designing complementary tools. This strategy allows us to uncover strong signatures of scale invariance that are “quasiuniversal” across brain regions and experiments, revealing that all the analyzed areas operate, to a greater or lesser extent, near the edge of instabilitySpanish Ministry and Agencia Estatal de investigación (AEI) through Project ofI+D+iRef. PID2020-113681GBI00MICIN/AEI/10.13039/501100011033 and FEDER "A way to make Europe"Junta de Andalucía and European Regional Development Fund, Project references A-FQM-175-UGR18P20-0017

Time-series thresholding and the definition of avalanche size

Avalanches whose sizes and durations are distributed as power laws appear in many contexts, from physics to geophysics and biology. Here we show that there is a hidden peril in thresholding continuous times series-from either empirical or synthetic data-for the identification of avalanches. In particular, we consider two possible alternative definitions of avalanche size used, e.g., in the empirical determination of avalanche exponents in the analysis of neural-activity data. By performing analytical and computational studies of an Ornstein-Uhlenbeck process (taken as a guiding example) we show that (1) if relatively large threshold values are employed to determine the beginning and ending of avalanches and (2) if-as sometimes done in the literature-avalanche sizes are defined as the total area (above zero) of the avalanche, then true asymptotic scaling behavior is not seen, instead the observations are dominated by transient effects. This problem-that we have detected in some recent works-leads to misinterpretations of the resulting scaling regimes.We acknowledge the Spanish Ministry and Agencia Estatal de investigacion (AEI) through Grant No. FIS2017-84256-P (European Regional Development Fund (ERDF)) for financial support. This study has been partially financed by the Consejeria de Conocimiento, Investigacion y Universidad, Junta de Andalucia and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR as well as to Teach in Parma for support to M.A.M. The study is supported by Fondazione Cariparma, under TeachInParma Project

Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition

Scale-free outbursts of activity are commonly observed in physical, geological, and biological systems. The idea of self-organized criticality (SOC), introduced back in 1987 by Bak, Tang, and Wiesenfeld suggests that, under certain circumstances, natural systems can seemingly self-tune to a critical state with its concomitant power-laws and scaling. Theoretical progress allowed for a rationalization of how SOC works by relating its critical properties to those of a standard non-equilibrium second-order phase transition that separates an active state in which dynamical activity reverberates indefinitely, from an absorbing or quiescent state where activity eventually ceases. The basic mechanism underlying SOC is the alternation of a slow driving process and fast dynamics with dissipation, which generates a feedback loop that tunes the system to the critical point of an absorbing-active continuous phase transition. Here, we briefly review these ideas as well as a recent closely-related concept: self-organized bistability (SOB). In SOB, the very same type of feedback operates in a system characterized by a discontinuous phase transition, which has no critical point but instead presents bistability between active and quiescent states. SOB also leads to scale-invariant avalanches of activity but, in this case, with a different type of scaling and coexisting with anomalously large outbursts. Moreover, SOB explains experiments with real sandpiles more closely than SOC. We review similarities and differences between SOC and SOB by presenting and analyzing them under a common theoretical framework, covering recent results as well as possible future developments. We also discuss other related concepts for "imperfect" self-organization such as "self-organized quasi-criticality" and "self-organized collective oscillations," of relevance in e.g., neuroscience, with the aim of providing an overview of feedback mechanisms for self-organization to the edge of a phase transition.We acknowledge the Spanish Ministry and Agencia Estatal de investigacion (AEI) through grant FIS2017-84256-P European Regional Development Fund (ERDF), as well as the Consejeria de Conocimiento, Investigacion y Universidad, Junta de Andalucia and ERDF, A-FQM -175-UGR18 and SOMM17/6105/UGR and for financial support. We also thank Cariparma for their support through the TEACH IN PARMA project

Jensen’s force and the statistical mechanics of cortical asynchronous states

Cortical networks are shaped by the combined action of excitatory and inhibitory interactions. Among other important functions, inhibition solves the problem of the all-or-none type of response that comes about in purely excitatory networks, allowing the network to operate in regimes of moderate or low activity, between quiescent and saturated regimes. Here, we elucidate a noise-induced effect that we call “Jensen’s force” –stemming from the combined effect of excitation/inhibition balance and network sparsity– which is responsible for generating a phase of self-sustained low activity in excitationinhibition networks. The uncovered phase reproduces the main empirically-observed features of cortical networks in the so-called asynchronous state, characterized by low, un-correlated and highly-irregular activity. The parsimonious model analyzed here allows us to resolve a number of long-standing issues, such as proving that activity can be self-sustained even in the complete absence of external stimuli or driving. The simplicity of our approach allows for a deep understanding of asynchronous states and of the phase transitions to other standard phases it exhibits, opening the door to reconcile, asynchronousstate and critical-state hypotheses, putting them within a unified framework. We argue that Jensen’s forces are measurable experimentally and might be relevant in contexts beyond neuroscience.The study is supported by Fondazione Cariparma, under TeachInParma Project. MAM thanks the Spanish Ministry of Science and the Agencia Española de Investigación (AEI) for financial support under grant FIS2017-84256-P (European Regional Development Fund (ERDF)) as well as the Consejera de Conocimiento, Investigación y Universidad, Junta de Andaluca and European Regional Development Fund (ERDF), ref. SOMM17/6105/UGR. V.B. and R.B. acknowledge funding from the INFN BIOPHYS projec

Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach

Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, such as stochastic resonance, noise induced bistability, and noise-induced oscillations, to name but a few. Here we revisit a mechanism-first investigated in the context of neuroscience-by which relatively small intrinsic (demographic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems from (or is strongly associated with) the existence of a 'non-normal' stability matrix at the deterministic fixed point, which may induce the system to be 'reactive'. By employing a number of analytical and computational approaches, we further investigate this mechanism and explore the interplay between non-normality and intrinsic stochasticity. In particular, we conclude that the resulting dynamics of this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of 'non-linear reactivity', and rationalize the observed values of avalanche exponents.We are grateful to the Spanish-MINECO for financial support (under grants FIS2013-43201-P and FIS2017-84256-P; FEDER funds). MAM also acknowledges the support from TeachinParma and the Cariparma foundation