The critical group K(G) of a directed graph G=(V,E) is the cokernel of the transpose of the Laplacian matrix of G acting on the integer lattice Z^V. For undirected graphs G, this has been considered by Bacher, de la Harpe, and Nagnibeda, and by Biggs. We prove several things, ...
I reached the breaking point and searched for a better solution, but found none. I briefly hopedenum_dispatchwould save me, but discovered otherwise; it mostly behaves like a stack-allocated alternative toBox<dyn ...>. Neither of these can do type-joining operations like the transpose above,...
The Combinatorial BLAS (CombBLAS) is an extensible distributed-memory parallel graph library offering a small but powerful set of linear algebra primitives specifically targeting graph analytics. - PASSIONLab/CombBLAS
The associated PCI measure is symmetrically defined as the eigenvector associated with the second largest eigenvalue of the transpose of the M˜ matrix. Following Hausmann et al. (2014), we standardise the ECI and PCI measures by subtracting their mean values and dividing the result by the ...
Given a directed graph G=(V,E) with a node set V and an edge set E, let Q be its backward transition matrix (that is, the transpose of the column-normalized adjacency matrix), whose entry [Q]i,j=1/in-degree(i) if there is an edge from j to i, and 0 otherwise. Then, Li ...
BNs aim to model conditional dependencies and therefore causation by representing conditional dependencies as edges and random variables as nodes in a directed acyclic graph. The flow of information between two nodes is reflected by the direction of the edges, giving an idea of their causal ...
Dynamics and functions of neural circuits depend on interactions mediated by receptors. Therefore, a comprehensive map of receptor organization across cortical regions is needed. In this study, we used in vitro receptor autoradiography to measure the den
10 nearest neighbors matrix in covariance space. As covariance matrices are PSD, to randomly generatencovariance matrices of 64 × 64 elements, we first samplenrandom 64 × 64 matrices (using the standard normal) and multiply each by its transpose, as a matrix Gramian is always PSD...
‖A‖ refers to the norm of a matrix A defined by ‖A‖=trace(ATA). The notation X≥Y (respectively, X>Y), where X and Y are real symmetric matrices, means that X−Y is positive semi-definite (respectively, positive definite). MT represents the transpose of the matrix M. I ...
Transposing a graph changes the directions of all edges to the opposite. edges(transpose(funcs)) #> from to #> 1 drop_internal get_deps #> 2 get_deps restore #> 3 get_description get_deps #> 4 parse_deps get_deps #> 5 cran_file cran_file #> 6 cran_file download_urls #> 7 do...