Physics Clues on the Mind Substrate and Attributes.

The last decade has witnessed a remarkable progress in our understanding of the brain. This has mainly been based on the scrutiny and modeling of the transmission of activity among neurons across lively synapses. A main conclusion, thus far, is that essential features of the mind rely on collective phenomena that emerge from a willful interaction of many neurons that, mediating other cells, form a complex network whose details keep constantly adapting to their activity and surroundings.

EEGs Disclose Significant Brain Activity Correlated with Synaptic Fickleness.

We here study a network of synaptic relations mingling excitatory and inhibitory neuron nodes that displays oscillations quite similar to electroencephalogram (EEG) brain waves, and identify abrupt variations brought about by swift synaptic mediations. We thus conclude that corresponding changes in EEG series surely come from the slowdown of the activity in neuron populations due to synaptic restrictions. The latter happens to generate an imbalance between excitation and inhibition causing a quick explosive increase of excitatory activity, which turns out to be a (first-order) transition among dynamic mental phases.

Nonlinear preferential rewiring in fixed-size networks as a diffusion process.

We present an evolving network model in which the total numbers of nodes and edges are conserved, but in which edges are continuously rewired according to nonlinear preferential detachment and reattachment. Assuming power-law kernels with exponents alpha and beta , the stationary states which the degree distributions evolve toward exhibit a second-order phase transition-from relatively homogeneous to highly heterogeneous (with the emergence of starlike structures) at alpha=beta . Temporal evolution of the distribution in this critical regime is shown to follow a nonlinear diffusion equation, arriving at either pure or mixed power laws of exponents -alpha and 1-alpha .

Chaotic hopping between attractors in neural networks.

We present a neurobiologically-inspired stochastic cellular automaton whose state jumps with time between the attractors corresponding to a series of stored patterns. The jumping varies from regular to chaotic as the model parameters are modified. The resulting irregular behavior, which mimics the state of attention in which a system shows a great adaptability to changing stimulus, is a consequence in the model of short-time presynaptic noise which induces synaptic depression.