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

Synchronisation in dynamically coupled maps

The central aim of this thesis is to better understand the dynamics of a set of dynamically coupled map systems previously introduced by Ito & Kaneko in a series of papers (Phys. Rev. Lett. 88 (2002), no. 2, 028701 and Phys. Rev. E 67 (2003), no. 4, 046226). The current work extends Ito & Kaneko’s studies to clarify the changes in macrodynamics induced by the differences in microdynamics between the two systems. A third system is also introduced that has a minor change to the microdynamics from nonlinear to linear output function in the externally coupled system. The dynamics of these three dynamically-coupled maps is also compared with their simplified systems with static coupling. The previous studies of these dynamically-coupled maps showed a partitioning of the parameter space into regions of different macrodynamics. Here, an in-depth study is presented of the behaviour of the systems as they cross the boundary between one region and another. The behaviour across this boundary is shown to be much more complicated than suggested in the previous studies. These three systems of dynamically-coupled maps all differ in the form of their microscopic couplings, yet two of the systems are shown to produce similar macrodynamics, whereas the third differs dramatically by almost any measure of the macrodynamics. The time it takes for the systems to synchronise, both the dynamically-coupled and static-coupled systems, is investigated. It is shown that the introduction of dynamicalcouplings stops the systems from synchronising quasi-instantaneously. Details of potential consequences of this in the field of neuroscience are discussed. A brief study of the effect of driving the systems with external stimuli is presented. The different microscopic coupling forms cause different responses to the external stimuli. Some of the responses are similar to that observed by the visual cortex area of the brain

The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'

Lehtinen and Kuorikoski ([73]) question, provocatively, whether, in the context of Computing the Perfect Model, economists avoid - even positively abhor - reliance on simulation. We disagree with the mildly qualified affirmative answer given by them, whilst agreeing with some of the issues they raise. However there are many economic theoretic, mathematical (primarily recursion theoretic and constructive) - and even some philosophical and epistemological - infelicities in their descriptions, definitions and analysis. These are pointed out, and corrected; for, if not, the issues they raise may be submerged and subverted by emphasis just on the unfortunate, but essential, errors and misrepresentationsSimulation, Computation, Computable, Analysis, Dynamics, Proof, Algorithm