Network discovery with DCM.
Bottom Line: The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks.The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions.We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies.
Affiliation: The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, UK. email@example.comShow MeSH
Related in: MedlinePlus
Mentions: Put simply, all this means is that the dynamics of any system comprising many elements can be decomposed into a mixture of (orthogonal) patterns over variables describing its state. By necessity, some of these patterns dissipate more quickly than others. Generally, some patterns decay so slowly that they predominate over others that disappear as soon as they are created. Mathematically, this means that P (principal) eigenvalues λp → 0 : p ≤ P are nearly zero and the associated eigenvectors or modes Up(ξ) are slow and unstable. In this case, ζp = Up−ξ : p ≤ P are known as order parameters. Order parameters are mixtures of states encoding the amplitude of the slow (unstable) modes that determine macroscopic behaviour. Other fast (stable) modes ζq = Uq−ξ : q > P have large negative eigenvalues, which means that they decay or dissipate quickly to an invariant attracting set or manifold, h(ζp), such that . In other words, the invariant (centre) manifold h(ζp) attracts trajectories and contains the solutions to Eq. (1). When there is only one order parameter or principal mode, this manifold is a line or curve in state-space and ζ1 could represent the distance along that curve (see Fig. 1). The unstable fast modes decay quickly because the eigenvalue is effectively their rate of decay. One can see this easily by taking a first-order Taylor expansion of Eq. (1) about the centre manifold:(2)ζ˙q≈fqζp,hζp+Uq−IUqζq−hqζp=λqζq−hqζp.
Affiliation: The Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, London, UK. firstname.lastname@example.org