111 research outputs found
Neural complexity: a graph theoretic interpretation
One of the central challenges facing modern neuroscience is to explain the ability of the nervous system to coherently integrate information across distinct functional modules in the absence of a central executive. To this end Tononi et al. [Proc. Nat. Acad. Sci. USA 91, 5033 (1994)] proposed a measure of neural complexity that purports to capture this property based on mutual information between complementary subsets of a system. Neural complexity, so defined, is one of a family of information theoretic metrics developed to measure the balance between the segregation and integration of a system's dynamics. One key question arising for such measures involves understanding how they are influenced by network topology. Sporns et al. [Cereb. Cortex 10, 127 (2000)] employed numerical models in order to determine the dependence of neural complexity on the topological features of a network. However, a complete picture has yet to be established. While De Lucia et al. [Phys. Rev. E 71, 016114 (2005)] made the first attempts at an analytical account of this relationship, their work utilized a formulation of neural complexity that, we argue, did not reflect the intuitions of the original work. In this paper we start by describing weighted connection matrices formed by applying a random continuous weight distribution to binary adjacency matrices. This allows us to derive an approximation for neural complexity in terms of the moments of the weight distribution and elementary graph motifs. In particular we explicitly establish a dependency of neural complexity on cyclic graph motifs
Granger causality analysis in neuroscience and neuroimaging
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[Letter] Misunderstandings regarding the application of Granger causality in neuroscience
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Dynamical independence: discovering emergent macroscopic processes in complex dynamical systems
We introduce a notion of emergence for coarse-grained macroscopic variables
associated with highly-multivariate microscopic dynamical processes, in the
context of a coupled dynamical environment. Dynamical independence instantiates
the intuition of an emergent macroscopic process as one possessing the
characteristics of a dynamical system "in its own right", with its own
dynamical laws distinct from those of the underlying microscopic dynamics. We
quantify (departure from) dynamical independence by a transformation-invariant
Shannon information-based measure of dynamical dependence. We emphasise the
data-driven discovery of dynamically-independent macroscopic variables, and
introduce the idea of a multiscale "emergence portrait" for complex systems. We
show how dynamical dependence may be computed explicitly for linear systems via
state-space modelling, in both time and frequency domains, facilitating
discovery of emergent phenomena at all spatiotemporal scales. We discuss
application of the state-space operationalisation to inference of the emergence
portrait for neural systems from neurophysiological time-series data. We also
examine dynamical independence for discrete- and continuous-time deterministic
dynamics, with potential application to Hamiltonian mechanics and classical
complex systems such as flocking and cellular automata.Comment: 38 pages, 7 figure
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Solved problems for Granger causality in neuroscience: a response to Stokes and Purdon
Granger-Geweke causality (GGC) is a powerful and popular method for identifying directed functional (‘causal’) connectivity in neuroscience. In a recent paper, Stokes and Purdon (2017b) raise several concerns about its use. They make two primary claims: (1) that GGC estimates may be severely biased or of high variance, and (2) that GGC fails to reveal the full structural/causal mechanisms of a system. However, these claims rest, respectively, on an incomplete evaluation of the literature, and a misconception about what GGC can be said to measure. Here we explain how existing approaches resolve the first issue, and discuss the frequently-misunderstood distinction between functional and effective neural connectivity which underlies Stokes and Purdon's second claim
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