Universal neural field computation

Turing machines and G\"odel numbers are important pillars of the theory of computation. Thus, any computational architecture needs to show how it could relate to Turing machines and how stable implementations of Turing computation are possible. In this chapter, we implement universal Turing computation in a neural field environment. To this end, we employ the canonical symbologram representation of a Turing machine obtained from a G\"odel encoding of its symbolic repertoire and generalized shifts. The resulting nonlinear dynamical automaton (NDA) is a piecewise affine-linear map acting on the unit square that is partitioned into rectangular domains. Instead of looking at point dynamics in phase space, we then consider functional dynamics of probability distributions functions (p.d.f.s) over phase space. This is generally described by a Frobenius-Perron integral transformation that can be regarded as a neural field equation over the unit square as feature space of a dynamic field theory (DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with rectangular support are mapped onto uniform p.d.f.s with rectangular support, again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with arXiv:1204.546

Noise during rest enables the exploration of the brain's dynamic repertoire.

Contains fulltext : 71144.pdf (publisher's version ) (Open Access)Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire

Determining the properties of gene regulatory networks from expression data.

The expression of genes depends on the physical structure of DNA, how the function of DNA is regulated by the transcription factors expressed by other genes, RNA regulation, such as that through RNA interference, and protein signals mediated by protein-protein interaction networks. We illustrate different approaches to determining information about the network of gene regulation from experimental data. First, we show that we can use statistical information of the mRNA expression values to determine the global topological properties of the gene regulatory network. Second, we show that analyzing the changes in expression due to mutations or different environmental conditions can give us information on the relative importance of the different mechanisms involved in gene regulation

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Item does not contain fulltextFunctionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix

The Human Brain Project-Synergy between neuroscience, computing, informatics, and brain-inspired technologies.

The Human Brain Project (HBP) is a European flagship project with a 10-year horizon aiming to understand the human brain and to translate neuroscience knowledge into medicine and technology. To achieve such aims, the HBP explores the multilevel complexity of the brain in space and time; transfers the acquired knowledge to brain-derived applications in health, computing, and technology; and provides shared and open computing tools and data through the HBP European brain research infrastructure. We discuss how the HBP creates a transdisciplinary community of researchers united by the quest to understand the brain, with fascinating perspectives on societal benefits