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    Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools. 
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    Multiscale modeling of brain dynamics: from single neurons and networks to mathematical tools.

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    Published Version
    Embargoed until: 5555-01-01
    Reason: Publisher Embargo
    Volume
    8
    Pagination
    438 - 458
    DOI
    10.1002/wsbm.1348
    Journal
    Wiley Interdiscip Rev Syst Biol Med
    Issue
    5
    Metadata
    Show full item record
    Abstract
    The extreme complexity of the brain naturally requires mathematical modeling approaches on a large variety of scales; the spectrum ranges from single neuron dynamics over the behavior of groups of neurons to neuronal network activity. Thus, the connection between the microscopic scale (single neuron activity) to macroscopic behavior (emergent behavior of the collective dynamics) and vice versa is a key to understand the brain in its complexity. In this work, we attempt a review of a wide range of approaches, ranging from the modeling of single neuron dynamics to machine learning. The models include biophysical as well as data-driven phenomenological models. The discussed models include Hodgkin-Huxley, FitzHugh-Nagumo, coupled oscillators (Kuramoto oscillators, Rössler oscillators, and the Hindmarsh-Rose neuron), Integrate and Fire, networks of neurons, and neural field equations. In addition to the mathematical models, important mathematical methods in multiscale modeling and reconstruction of the causal connectivity are sketched. The methods include linear and nonlinear tools from statistics, data analysis, and time series analysis up to differential equations, dynamical systems, and bifurcation theory, including Granger causal connectivity analysis, phase synchronization connectivity analysis, principal component analysis (PCA), independent component analysis (ICA), and manifold learning algorithms such as ISOMAP, and diffusion maps and equation-free techniques. WIREs Syst Biol Med 2016, 8:438-458. doi: 10.1002/wsbm.1348 For further resources related to this article, please visit the WIREs website.
    Authors
    Siettos, C; Starke, J
    URI
    http://qmro.qmul.ac.uk/xmlui/handle/123456789/15364
    Collections
    • Applied Mathematics [140]
    Language
    eng
    Licence information
    Original publication is available at http://onlinelibrary.wiley.com/doi/10.1002/wsbm.1348/full
    Copyright statements
    © 2016 Wiley Periodicals, Inc
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