Related papers: Modelling the brain as a n Apollonian network
We introduce a new family of networks, the Apollonian networks, that are simultaneously scale-free, small world, Euclidean, space-filling and matching graphs. These networks have a wide range of applications ranging from the description of…
In this work, we report the preliminary analysis of the electrophysiological behavior of in vitro neuronal networks to identify when the networks are in a critical state based on the size distribution of network-wide avalanches of activity.…
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…
The $1/f$-like decay observed in the power spectrum of electro-physiological signals, along with scale-free statistics of the so-called neuronal avalanches, constitute evidences of criticality in neuronal systems. Recent in vitro studies…
Scale-invariant neuronal avalanches have been observed in cell cultures and slices as well as anesthetized and awake brains, suggesting that the brain operates near criticality, i.e. within a narrow margin between avalanche propagation and…
The exploration of brain networks has reached an important milestone as relatively large and reliable information has been gathered for connectomes of different species. Analyses of connectome data sets reveal that the structural length and…
Most brain models focus on associative memory or calculation capability, experimentally inaccessible using physiological methods. Here we present a model explaining a basic feature of electroencephalograms (EEG). Our model is based on an…
In this paper we find an exact analytical expression for the number of spanning trees in Apollonian networks. This parameter can be related to significant topological and dynamic properties of the networks, including percolation, epidemic…
Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…
As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has…
Emulating the neural-like information processing dynamics of the brain provides a time and energy efficient approach for solving complex problems. While the majority of neuromorphic hardware currently developed rely on large arrays of…
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…
Neuronal avalanches measured in vitro and in vivo in different cortical networks consistently exhibit power law behaviour for the size and duration distributions with exponents typical for a mean field self-organized branching process.…
Brain-like self-assembled networks can infer and analyze information out of unorganized noisy signals with minimal power consumption. These networks are characterized by spatiotemporal avalanches and their crackling behavior, and their…
Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by…
Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake…
The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting…
Neural avalanches are collective firings of neurons that exhibit emergent scale-free behavior. Understanding the nature and distribution of these avalanches is an important element in understanding how the brain functions. We study a model…
Neuronal networks can present activity described by power-law distributed avalanches presumed to be a signature of a critical state. Here we study a random-neighbor network of excitable cellular automata coupled by dynamical synapses. The…
We show that a network of spiking neurons exhibits robust self-organized criticality if the synaptic efficacies follow realistic dynamics. Deriving analytical expressions for the average coupling strengths and inter-spike intervals, we…