During the search for new structural descriptors we have defined the information-theory operators U(M), V(M), X(M), and Y(M), that are computed from atomic invariants and measure the information content of the elements of molecular matrices. Structural descriptors computed with these four information-theory operators are used to develop structure-property models for the boiling temperature, mol...

The component matrix, Laplacian Distance Peripheral distance of the cyclotomic graphs and some properties are found. D-energy, $D_{p}$-energy, $D^{L}$-energy indices determined. For real symmetric matrices, matrices that attain maximum $L, L_{s}$ minimum S calculated. Hausdorff optimal matching evaluated.

Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study the critical points of this optimization problem using algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.

In this paper we present a method to search q circulant matrices; the concatenation of these circulant matrices with circulant identity matrix generates quasi-cyclic codes with high various code rate q/(q+1) (q an integer). This method searches circulant matrices in order to find the good quasi-cyclic code (QCC) having the largest minimum distance. A modified simulated annealing algorithm is us...

Applying weighted network measures to distance matrices Many approaches to the analysis of weighted networks are not designed for fully connected weighted networks. However, as any distance matrix between objects is a fully connected weighted network, such networks are extremely common. In earlier work we derived an approach for the analysis of weighted networks which also works on fully connec...