Brain Dynamics across levels of Organization

After presenting evidence that the electrical activity recorded from the brain surface can reflect metastable state transitions of neuronal configurations at the mesoscopic level, I will suggest that their patterns may correspond to the distinctive spatio-temporal activity in the Dynamic Core (DC) and the Global Neuronal Workspace (GNW), respectively, in the models of the Edelman group on the one hand, and of Dehaene-Changeux, on the other. In both cases, the recursively reentrant activity flow in intra-cortical and cortical-subcortical neuron loops plays an essential and distinct role. Reasons will be given for viewing the temporal characteristics of this activity flow as signature of Self-Organized Criticality (SOC), notably in reference to the dynamics of neuronal avalanches. This point of view enables the use of statistical Physics approaches for exploring phase transitions, scaling and universality properties of DC and GNW, with relevance to the macroscopic electrical activity in EEG and EMG

Tuning the average path length of complex networks and its influence to the emergent dynamics of the majority-rule model

We show how appropriate rewiring with the aid of Metropolis Monte Carlo computational experiments can be exploited to create network topologies possessing prescribed values of the average path length (APL) while keeping the same connectivity degree and clustering coefficient distributions. Using the proposed rewiring rules we illustrate how the emergent dynamics of the celebrated majority-rule model are shaped by the distinct impact of the APL attesting the need for developing efficient algorithms for tuning such network characteristics.Comment: 10 figure

On critical State Transitions between different levels in Neural Systems

The framework of Modern Theory of Critical State Transitions considers the relation between different levels of organization in complex systems in terms of Critical State Transitions. A State Transition between levels entails changes of scale of observables and, concurrently, new formats of description at reduced dimensionality. It is here suggested that this principle can be applied to the hierarchic structure of the Nervous system, whereby the relations between different levels of its functional organization can be viewed as successions of State Transitions. Upon State Transition, the lower level presents to the higher level an abstraction of itself, at reduced dimensionality and at a coarser scale. The re-scaling in the State Transitions is associated with new objects of description, displays new properties and obeys new laws, commensurate to the new scale. To illustrate this process, some aspects of the neural events thought to be associated with Cognition and Consciousness are discussed. However, the intent is here also more general in that State Transitions between all levels of organization are proposed as the mechanisms by which successively higher levels of organization emerge from lower levels.Comment: 1

Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis

We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an individual-based microscopic simulator as a black box coarse-grained timestepper and with the aid of simulated annealing we compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level. We also exploit the scheme to perform a rare-events analysis by estimating an effective Fokker-Planck describing the evolving probability density function of the corresponding coarse-grained observables

Culture and generalized inattentional blindness

A recent mathematical treatment of Baars' Global Workspace consciousness model, much in the spirit of Dretske's communication theory analysis of high level mental function, is used to study the effects of embedding cultural heritage on a generalized form of inattentional blindness. Culture should express itself quite distinctly in this basic psychophysical phenomenon, acting across a variety of sensory and other modalities, because the limited syntactic and grammatical 'bandpass' of the topological rate distortion manifold characterizing conscious attention is itself strongly sculpted by the constraints of cultural context

Generalized inattentional blindness from a Global Workspace perspective

We apply Baars' Global Workspace model of consciousness to inattentional blindness, using the groupoid network method of Stewart et al. to explore modular structures defined by information measures associated with cognitive process. Internal cross-talk breaks the fundamental groupoid symmetry, and, if sufficiently strong, creates, in a highly punctuated manner, a linked, shifting, giant component which instantiates the global workspace of consciousness. Embedding, exterior, information sources act as an external field which breaks the groupoid symmetry in a somewhat different manner, definng the slowly-acting contexts of Baars' theory and providing topological constraints on the manifestations of consciousness. This analysis significantly extends recent mathematical treatments of the global workspace, and identifies a shifting, topologically-determined syntactical and grammatical 'bottleneck' as a tunable rate distortion manifold which constrains what sensory or other signals can be brought to conscious attention, typically in a punctuated manner. Sensations outside the limits of that filter's syntactic 'bandpass' have lower probability of detection, regardless of their structure, accounting for generalized forms of inattentional blindness

Metastability, Criticality and Phase Transitions in brain and its Models

This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures