Emergence of localized eigenvectors can cause a failure of standard spectral method for graph partitioning. The spectral method using the non-backtracking matrix was proposed as a way to overcome this problem. The numerical experiments on several examples of real networks show that, indeed, the non-backtracking matrix does not exhibit localization of eigenvectors. We show that, however, localiz...

We show the existence of discrete sets of Raman sidebands which self-consistently establish a Raman coherence and propagate without change in amplitude and relative phase. Equivalently, there exist periodic femtosecond-time-scale, temporal pulse shapes which propagate without change in shape.

Although the spectral properties of random graphs have been a long-standing focus network theory, right eigenvectors directed so far eluded an exact analytic treatment. We present general theory for statistics eigenvector components in with prescribed degree distribution and randomly weighted links. obtain expressions inverse participation ratio show that small average are localized. Remarkably...

background: urinary tract infection (uti) is considered as the most common bacterial infectious disease seen among the pediatric patients. the aim of this study was to investigate the prevalence and antimicrobial susceptibility of bacterial uropathogens isolated from the pediatric patients with urinary tract infections. methods: this descriptive study was conducted in children medial center, te...

For a large class of linear neutral type systems the problem of eigenvalues and eigenvectors assignment is investigated, i.e. finding the system which has the given spectrum and almost all, in some sense, eigenvectors.

Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely...

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.