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

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

The self-organization of combinatoriality and phonotactics in vocalization systems

This paper shows how a society of agents can self-organize a shared vocalization system that is discrete, combinatorial and has a form of primitive phonotactics, starting from holistic inarticulate vocalizations. The originality of the system is that: (1) it does not include any explicit pressure for communication; (2) agents do not possess capabilities of coordinated interactions, in particular they do not play language games; (3) agents possess no specific linguistic capacities; and (4) initially there exists no convention that agents can use. As a consequence, the system shows how a primitive speech code may bootstrap in the absence of a communication system between agents, i.e. before the appearance of language

A topological approximation of the nonlinear Anderson model

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance-overlap in phase space, ranging from a fully developed chaos involving Levy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on a Cayley tree. It is found in vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha, with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of stripes propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for publication in Physical Review

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