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

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

Cortical Synchronization and Perceptual Framing

How does the brain group together different parts of an object into a coherent visual object representation? Different parts of an object may be processed by the brain at different rates and may thus become desynchronized. Perceptual framing is a process that resynchronizes cortical activities corresponding to the same retinal object. A neural network model is presented that is able to rapidly resynchronize clesynchronized neural activities. The model provides a link between perceptual and brain data. Model properties quantitatively simulate perceptual framing data, including psychophysical data about temporal order judgments and the reduction of threshold contrast as a function of stimulus length. Such a model has earlier been used to explain data about illusory contour formation, texture segregation, shape-from-shading, 3-D vision, and cortical receptive fields. The model hereby shows how many data may be understood as manifestations of a cortical grouping process that can rapidly resynchronize image parts which belong together in visual object representations. The model exhibits better synchronization in the presence of noise than without noise, a type of stochastic resonance, and synchronizes robustly when cells that represent different stimulus orientations compete. These properties arise when fast long-range cooperation and slow short-range competition interact via nonlinear feedback interactions with cells that obey shunting equations.Office of Naval Research (N00014-92-J-1309, N00014-95-I-0409, N00014-95-I-0657, N00014-92-J-4015); Air Force Office of Scientific Research (F49620-92-J-0334, F49620-92-J-0225)

Oscillations, metastability and phase transitions in brain and models of cognition

Neuroscience is being practiced in many different forms and at many different organizational levels of the Nervous System. Which of these levels and associated conceptual frameworks is most informative for elucidating the association of neural processes with processes of Cognition is an empirical question and subject to pragmatic validation. In this essay, I select the framework of Dynamic System Theory. Several investigators have applied in recent years tools and concepts of this theory to interpretation of observational data, and for designing neuronal models of cognitive functions. I will first trace the essentials of conceptual development and hypotheses separately for discerning observational tests and criteria for functional realism and conceptual plausibility of the alternatives they offer. I will then show that the statistical mechanics of phase transitions in brain activity, and some of its models, provides a new and possibly revealing perspective on brain events in cognition

Topics in social network analysis and network science

This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided

Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model

Systems with long-range interactions often exhibit power-law distributions and can by described by the non-extensive statistical mechanics framework proposed by Tsallis. In this contribution we consider a simple model reproducing continuous transition from the extensive to the non-extensive statistics. The considered model is composed of agents interacting among themselves on a certain network topology. To generate the underlying network we propose a new network formation algorithm, in which the mean degree scales sub-linearly with a number of nodes in the network (the scaling depends on a single parameter). By changing this parameter we are able to continuously transition from short-range to long-range interactions in the agent-based model.Comment: 12 pages, 6 figure

Transport on complex networks: Flow, jamming and optimization

Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics