In this paper, we focus on differential privacy preserving spectral graph analysis. Spectral graph analysis deals with the analysis of the spectra (eigenvalues and eigenvector components) of the graph’s adjacency matrix or its variants. We develop two approaches to computing the ε-differential eigen decomposition of the graph’s adjacency matrix. The first approach, denoted as LNPP, is based on ...

Mr. Editor: It has been only recently possible to validate the Maslach Burnout Inventory-Human Services Survey (MBI-HSS) 1 among health professionals of Cali 2 , an important step for using this instrument with local empirical support in regard to its reliability of scoring and internal structure. However, two aspects of this analysis can be considered as methodological weaknesses. First, the C...

The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each corresponding codimension is the number of conditions which a matrix of the given type must satisfy in order to have the specified multiplicities.

In this paper, a water-vegetation model with the infiltration feedback effect is considered. Firstly, through linear stability analysis, we get parameter area where Turing instability can occur. Next, by maximum principle, priori estimates for positive steady-state solutions are obtained and sufficient conditions nonexistence of nonconstant solution given. Moreover, bifurcations at both simple ...

Modular structure is a typical structure that is observed in most of real networks. Diffusion dynamics in network is getting much attention because of dramatic increasing of the data flows via the www. The diffusion dynamics in network have been well analysed as probabilistic process, but the proposed frameworks still shows the difference from the real observations. In this paper, we analysed s...

ABSTRACT. We provide an exhaustive spectral analysis of the two-dimensional periodic square graph lattice with a magnetic field. We show that the spectrum consists of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum of a certain discrete operator under the discriminant of a suitable KronigPenney Hamiltonian. In particular, between any two Dirichlet eigenvalues the spec...