Neuronal avalanches of a self-organized neural network with active-neuron-dominant structure

Neuronal avalanche is a spontaneous neuronal activity which obeys a power-law distribution of population event sizes with an exponent of -3/2. It has been observed in the superficial layers of cortex both \emph{in vivo} and \emph{in vitro}. In this paper we analyze the information transmission of a novel self-organized neural network with active-neuron-dominant structure. Neuronal avalanches can be observed in this network with appropriate input intensity. We find that the process of network learning via spike-timing dependent plasticity dramatically increases the complexity of network structure, which is finally self-organized to be active-neuron-dominant connectivity. Both the entropy of activity patterns and the complexity of their resulting post-synaptic inputs are maximized when the network dynamics are propagated as neuronal avalanches. This emergent topology is beneficial for information transmission with high efficiency and also could be responsible for the large information capacity of this network compared with alternative archetypal networks with different neural connectivity.Comment: Non-final version submitted to Chao

Emergent complex neural dynamics

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain

Learning as a phenomenon occurring in a critical state

Recent physiological measurements have provided clear evidence about scale-free avalanche brain activity and EEG spectra, feeding the classical enigma of how such a chaotic system can ever learn or respond in a controlled and reproducible way. Models for learning, like neural networks or perceptrons, have traditionally avoided strong fluctuations. Conversely, we propose that brain activity having features typical of systems at a critical point, represents a crucial ingredient for learning. We present here a study which provides novel insights toward the understanding of the problem. Our model is able to reproduce quantitatively the experimentally observed critical state of the brain and, at the same time, learns and remembers logical rules including the exclusive OR (XOR), which has posed difficulties to several previous attempts. We implement the model on a network with topological properties close to the functionality network in real brains. Learning occurs via plastic adaptation of synaptic strengths and exhibits universal features. We find that the learning performance and the average time required to learn are controlled by the strength of plastic adaptation, in a way independent of the specific task assigned to the system. Even complex rules can be learned provided that the plastic adaptation is sufficiently slow.Comment: 5 pages, 5 figure

Neocortical activity is stimulus- and scale-invariant

Mounting evidence supports the hypothesis that the cortex operates near a critical state, defined as the transition point between order (large-scale activity) and disorder (small-scale activity). This criticality is manifested by power law distribution of the size and duration of spontaneous cascades of activity, which are referred as neuronal avalanches. The existence of such neuronal avalanches has been confirmed by several studies both in vitro and in vivo, among different species and across multiple spatial scales. However, despite the prevalence of scale free activity, still very little is known concerning whether and how the scale-free nature of cortical activity is altered during external stimulation. To address this question, we performed in vivo two-photon population calcium imaging of layer 2/3 neurons in primary visual cortex of behaving mice during visual stimulation and conducted statistical analyses on the inferred spike trains. Our investigation for each mouse and condition revealed power law distributed neuronal avalanches, and irregular spiking individual neurons. Importantly, both the avalanche and the spike train properties remained largely unchanged for different stimuli, while the cross-correlation structure varied with stimuli. Our results establish that microcircuits in the visual cortex operate near the critical regime, while rearranging functional connectivity in response to varying sensory inputs

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

PRINCIPLES OF INFORMATION PROCESSING IN NEURONAL AVALANCHES

How the brain processes information is poorly understood. It has been suggested that the imbalance of excitation and inhibition (E/I) can significantly affect information processing in the brain. Neuronal avalanches, a type of spontaneous activity recently discovered, have been ubiquitously observed in vitro and in vivo when the cortical network is in the E/I balanced state. In this dissertation, I experimentally demonstrate that several properties regarding information processing in the cortex, i.e. the entropy of spontaneous activity, the information transmission between stimulus and response, the diversity of synchronized states and the discrimination of external stimuli, are optimized when the cortical network is in the E/I balanced state, exhibiting neuronal avalanche dynamics. These experimental studies not only support the hypothesis that the cortex operates in the critical state, but also suggest that criticality is a potential principle of information processing in the cortex. Further, we study the interaction structure in population neuronal dynamics, and discovered a special structure of higher order interactions that are inherent in the neuronal dynamics

Neural criticality from effective latent variables

Observations of power laws in neural activity data have raised the intriguing notion that brains may operate in a critical state. One example of this critical state is "avalanche criticality," which has been observed in a range of systems, including cultured neurons, zebrafish, and human EEG. More recently, power laws have also been observed in neural populations in the mouse under a coarse-graining procedure, and they were explained as a consequence of the neural activity being coupled to multiple latent dynamical variables. An intriguing possibility is that avalanche criticality emerges due to a similar mechanism. Here, we determine the conditions under which dynamical latent variables give rise to avalanche criticality. We find that a single, quasi-static latent variable can generate critical avalanches, but that multiple latent variables lead to critical behavior in a broader parameter range. We identify two regimes of avalanches, both of which are critical, but differ in the amount of information carried about the latent variable. Our results suggest that avalanche criticality arises in neural systems in which there is an emergent dynamical variable or shared inputs creating an effective latent dynamical variable, and when this variable can be inferred from the population activity.Comment: 18 pages, 5 figure