A diversity of localized timescales in network activity
- Yale University, United States
- Jacobs University Bremen, Germany
- New York University, United States
Figures
Figure 1
The activity of a linear network can be decomposed into contributions from a set of eigenvectors.
On the right is shown a sample network along with the activity of two nodes (cyan and yellow). The activity of this network is the combination of a set of eigenvectors whose spatial distributions …
Figure 2
Local connectivity is insufficient to yield localized eigenvectors.
(A) The network consists of 100 nodes, arranged in a ring. Connection strength decays exponentially with distance, with characteristic length of one node, and is sharply localized. The network …
Figure 3 with 1 supplement
Localized eigenvectors in a network with a gradient of local connectivity.
(A) The network is a chain of 100 nodes. Network topology is shown as a schematic with a subset of nodes and only nearest-neighbor connections. The plot above the chain shows the connectivity …
Figure 3—figure supplement 1
Co-existence of localized and delocalized eigenvectors in a network with a weak gradient of local connectivity.
(A) Left panel: eigenvalues of the network (filled circles) along with the region of the complex plane in which α2 > 0 (gray shaded region). Eigenvectors corresponding to eigenvalues within this …
Figure 4
Second-order expansion for partially-delocalized eigenvectors.
Same model with a gradient of local connectivity as in Figure 3. (A) Schematic of the predicted shape. Eigenvectors (black) are the product of an exponential (blue) and an Airy function (red). The …
Figure 5
Localized eigenvectors in a network with a gradient of connectivity range.
(A) The network consists of a chain of 50 identical nodes, shown here by a schematic. Spatial length of feedforward connections (from earlier to later nodes) decreases along the chain while the …
Figure 6
Localized eigenvectors in a network with random self-coupling.
(A) The network consists of 100 nodes arranged in a chain. The plot above the chain shows the connectivity profile. Self-coupling is random, as indicated by the shading. The network is described by E…
Figure 7
Strong long-range connections can delocalize a subset of eigenvectors.
(A) Left panel: connectivity of the network in Figure 3 with long-range connections of strength 0.05 added between 10% of the nodes. The gradient of self-coupling is shown along the diagonal on …
Additional files
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Supplementary file 1
Mathematical appendix.
- https://doi.org/10.7554/eLife.01239.011
