A modularity based spectral method for simultaneous community and anti-community detection

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrix-based definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenvalues of these matrices provide indications on the presence of both kinds of modular structure in the network. The localization of the relevant invariant subspaces can be estimated by looking at particular matrix angles based on Frobenius inner products

Additional file 7: of TRPA1 channels promote astrocytic Ca2+ hyperactivity and synaptic dysfunction mediated by oligomeric forms of amyloid-β peptide

TRPA1 channels expression is located in thick GFAP-positive processes and in adjacent thin processes lacking GFAP staining. 3D–recontsruct of astrocytic processes objectivized by GFAP staining (magenta) showing that TRPA1 channels (green) expression went over in contiguous processes excluding GFAP staining. Scale bar: 50 nm. (ZIP 1736 kb

Additional file 2: of TRPA1 channels promote astrocytic Ca2+ hyperactivity and synaptic dysfunction mediated by oligomeric forms of amyloid-β peptide

Characterization of Fluo-4-loaded cells in the stratum radiatum of mouse coronal slice. (a) Confocal image of Fluo-4-loaded (cyan) and SR101-labeled (magenta) cells in the CA1 stratum radiatum. Merged image showing the proportion of loaded astrocytes (white), confirming that most of the loaded cells are astrocytes. One hour before slicing, animals were iv injected with SR101 as described previously [51]. Vessels are only labeled with SR101 (white arrow). (b) Z-stack projections of confocal images of a patched astrocyte loaded with Fluo-4 (cyan) and SR101 (magenta). Merged image showing the Fluo-4 diffusion in the whole astrocytic territory. (c) Example of a passive whole-cell current recorded in a stratum radiatum astrocyte. Cell was held at −70 mV and 10 mV hyper- and depolarizing voltage steps of 80 ms duration were applied (−110 to +80 mV). (TIFF 1907 kb