The characterization of Laplacian eigenvalues and eigenvectors the Kronecker product graphs using spectra factors turned out to be quite challenging has remained an open problem date. Several approaches for estimation spectrum have been proposed in recent years. However, it turns that not all methods are practical apply network science models, particularly context multilayer networks. Here we d...

The development of neural network models has greatly enhanced the comprehension of cognitive phenomena. Here, we show that models using multiplicative processing of inputs are both powerful and simple to train and understand. We believe they are valuable tools for cognitive explorations. Our model can be viewed as a subclass of networks built on sigma-pi units and we show how to derive the Kron...

Generalizing a result of [24] , [8] about elliptic modular forms, we give closed formula for the sum all Hilbert Hecke eigenforms over totally real number field with strict class 1, multiplied by their period polynomials, as single product Kronecker series.

Summary The Kronecker product covariance structure provides an efficient way to model the inter-correlations of matrix-variate data. In this paper, we propose test statistics for matrix based on linear spectral renormalized sample matrices. A central limit theorem is proved statistics, with explicit formulas mean and functions, thereby filling a gap in literature. We then show theoretically tha...

The generalized defect D(U) of a unitary N ×N matrix U with no zero entries is the dimension of the real space of directions, moving into which from U we do not disturb the moduli |Ui,j | as well as the Gram matrix U∗U in the first order. Then the defect d(U) is equal to D(U) − (2N − 1), that is the generalized defect diminished by the dimension of the manifold {DrUDc : Dr,Dc unitary diagonal}....

Recently, quaternion orthogonal designs (QODs) were introduced as a mathematical construct with the potential for applications in wireless communications. The potential applications require new methods for constructing QODs, as most of the known methods of construction do not produce QODs with the exact properties required for implementation in wireless systems. This paper uses real amicable or...