Local anaxonic neurons with graded potential release are important ingredients of nervous systems, present in the olfactory bulb system of mammalians, in the human visual system, as well as in arthropods and nematodes. We develop a neuronal network model including both axonic and anaxonic neurons and monitor the activity tuned by the following parameters: The decay length of the graded potential in local neurons, the fraction of local neurons, the largest eigenvalue of the adjacency matrix and the range of connections of the local neurons. Tuning the fraction of local neurons, we derive the phase diagram including two transition lines: A critical line separating subcritical and supercritical regions, characterized by power law distributions of avalanche sizes and durations, and a bifurcation line. We find that the overall behavior of the system is controlled by a parameter tuning the relevance of local neuron transmission with respect to the axonal one. The statistical properties of spontaneous activity are affected by local neurons at large fractions and in the condition that the graded potential transmission dominates the axonal one. In this case the scaling properties of spontaneous activity exhibit continuously varying exponents, rather than the mean field branching model universality class.
Many systems in Nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behaviour of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the sam…
The statistical analysis of the collective neural activity known as avalanches provides insight into the proper behavior of brains across many species. We consider a neural network model based on the work of Lombardi, Herrmann, De Arcangelis et al. that captures the relevant dynamics of neural avalanches, and we show how tuning the fraction of inhibitory neurons in this model alters the connectivity of the network over time, removes exponential cut-offs present in the distributions of avalanche strength and duration, and transitions the power spectral density of the network into an `epileptic'…
Novel Kuramoto model with inhibition dynamics modeling scale-free avalanches and synchronization in neuronal cultures
University of Campania ”Luigi Vanvitelli”（坎帕尼亚路易吉·范维特利大学）；University of Genova（热那亚大学）；Istituto Italiano di Tecnologia (IIT)（意大利理工大学）；RCCS Ospedale Policlinico San Martino（圣马蒂诺大学临床医院）；National Institute for Nuclear Physics (INFN)（意大利国家核物理研究所）
To date, it is still impossible to sample the entire mammalian brain with single-neuron precision. This forces one to either use spikes (focusing on few neurons) or to use coarse-sampled activity (averaging over many neurons, e.g. LFP). Naturally, the sampling technique impacts inference about collective properties. Here, we emulate both sampling techniques on a simple spiking model to quantify how they alter observed correlations and signatures of criticality. We describe a general effect: when the inter-electrode distance is small, electrodes sample overlapping regions in space, which increa…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in contrast, are scale-free cascades of neural activity, often considered as evidence of brain tuning to criticality. While models have been developed to account for oscillations or avalanches separately, they typically do not explain both phenomena, are too complex to analyze analytically, or intractable to infer from data rigorously. Here we propose a non-equil…
The existence of power-law distributions is only a first requirement in the validation of the critical behavior of a system. Long-range spatio-temporal correlations are fundamental for the spontaneous neuronal activity to be the expression of a system acting close to a critical point. This chapter focuses on temporal correlations and avalanche dynamics in the spontaneous activity of cortex slice cultures and in the resting fMRI BOLD signal. Long-range correlations are investigated by means of the scaling of power spectra and of Detrended Fluctuations Analysis. The existence of 1/f decay in the…
Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timingde…
Self-organized criticality (SOC) refers to the ability of complex systems to evolve towards a 2nd-order phase transition at which interactions between system components lead to scale-invariant events beneficial for system performance. For the last two decades, considerable experimental evidence accumulated that the mammalian cortex with its diversity in cell types and connections might exhibit SOC. Here we review experimental findings of isolated, layered cortex preparations to self-organize towards four dynamical motifs identified in the cortex in vivo: up-states, oscillations, neuronal avala…
The critical brain hypothesis has emerged as an attractive framework to understand neuronal activity, but it is still widely debated. In this work, we analyze data from a multi-electrodes array in the rat's cortex and we find that power-law neuronal avalanches satisfying the crackling-noise relation coexist with spatial correlations that display typical features of critical systems. In order to shed a light on the underlying mechanisms at the origin of these signatures of criticality, we introduce a paradigmatic framework with a common stochastic modulation and pairwise linear interactions inf…
Allometric scaling of brain activity explained by avalanche criticality
University of Campania “Luigi Vanvitelli”（坎帕尼亚路易吉范维特利大学）；Universidade Federal do Ceará（塞阿拉联邦大学）；Center for Complexity and Biosystems, Department of Physics, University of Milan（米兰大学复杂系统与生物系统中心）；CNR - Consiglio Nazionale delle Ricerche, Istituto di Chimica della Materia Condensata e di Tecnologie per l’Energia（国家研究委员会凝聚态化学与能源技术研究所）
We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-LIF neurons in the presence of short-term synaptic plasticity. By varying the coupling strength among neurons, we show that a complex chaotic dynamics arises, characterized by scale free avalanches. The origin of this phenomenon in the c-LIF can be related to the order symmetry breaking in neurons spike-times, which corresponds to the onset of a bro…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of {\it structure-driven activity} has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonl…
