It is shown that distance powers of an integral Cayley graph over an abelian group Γ are again integral Cayley graphs over Γ. Moreover, it is proved that distance matrices of integral Cayley graphs over abelian groups have integral spectrum.

let $r$ be a commutative ring and let $m$ be an $r$-module. in this article, we introduce the concept of the zariski socles of submodules of $m$ and investigate their properties. also we study modules with noetherian second spectrum and obtain some related results.

a multicone graph is defined to be join of a clique and a regular graph. a graph $ g $ is  cospectral with  graph $ h $ if their adjacency matrices have the same eigenvalues. a graph $ g $ is  said to be  determined by its spectrum or ds for short, if for any graph $ h $ with $ spec(g)=spec(h)$, we conclude that $ g $ is isomorphic to $ h $. in this paper, we present new classes of  multicone g...

The position of the degree scale feature in the CMB spectrum is determined within the framework of the fractal universe with a power index of 2. The presence of any feature in the cosmic microwave background (CMB) anisotropy spectrum whose physical scale is known provides us with the ability to perform the angular diameter distance test [1]. Any feature progects as an anisotropy onto an angular...

BACKGROUND Aberrant brain connectivity, especially with long-distance underconnectivity, has been recognized as a candidate pathophysiology of autism spectrum disorders. However, a number of diffusion tensor imaging studies investigating people with autism spectrum disorders have yielded inconsistent results. METHODS To test the long-distance underconnectivity hypothesis, we performed a syste...

Let us consider a connected graph G with diameter D. For a given integer k between 0 and D, we say that G is k-walk-regular if the number of walks of length between vertices u, v only depends on the distance between u and v, provided that such a distance does not exceed k. Thus, in particular, a 0-walk-regular graph is the same as a walk-regular graph, where the number of cycles of length roote...

This paper introduces Split Spectrum, which enhances elastic optical networking by splitting a bulk traffic demand into multiple channels, when a single-channel transmission is prohibited by distance or spectrum availability. We performed transmission simulations to determine the maximum reach as a function of modulation format (dual polarization BPSK, QPSK, 16QAM), baud-rate (from 5 to 28 GBd)...

Detecting the signals of the primary users in the wideband spectrum is a key issue for cognitive radio networks. In this paper, we consider the multi-antenna based signal detection in a wideband spectrum scenario where the noise statistical characteristics are assumed to be unknown. We reason that the covariance matrices of the spectrum subbands have structural constraints and that they describ...

In the post genomic era, access to complete genome sequence data for numerous diverse species has opened multiple avenues for examining and comparing primary DNA sequence organization of entire genomes. Previously, the concept of a genomic signature was introduced with the observation of species-type specific Dinucleotide Relative Abundance Profiles (DRAPs); dinucleotides were identified as the...