A graph is called symmetric if its full automorphism group acts transitively on the set of arcs. The Cayley graph $Gamma=Cay(G,S)$ on group $G$ is said to be normal symmetric if $N_A(R(G))=R(G)rtimes Aut(G,S)$ acts transitively on the set of arcs of $Gamma$. In this paper, we classify all connected tetravalent normal symmetric Cayley graphs of order $p^2q$ where $p>q$ are prime numbers.

The association of secreted frizzled related protein type 4 (Sfrp4) as an antagonist of Wnt mole-cules in apoptotic events has been reported previously. Moreover, its increased expression has been reported in the ovary of women with polycystic ovary (PCO). We have demonstrated in-creased Sfrp4 in PCO-induced rat ovary related to an increased number of apoptotic follicles showing nuclear ?cateni...

Stability analysis of mathematical models of hematopoiesis (blood cell production process), described by differential equations with delay, needs to locate eigenvalues of characteristic equations that are usually exponential polynomial functions with delay-dependent coefficients. It is then more complicated than for ordinary differential equations to determine conditions for all roots to have n...

In a graph or complex network, communities and anti-communities are node sets whose modularity attains extremely large values, positive and negative, respectively. We consider the simultaneous detection of communities and anti-communities, by looking at spectral methods based on various matrixbased definitions of the modularity of a vertex set. Invariant subspaces associated to extreme eigenval...

Many nonintegrable systems have eigenstates that typically require numerous basis states to represent them. We develop a criterion to judge the extent to which phase space is explored by the spectrum of such a Hamiltonian. Our criterion uses the eigenvalues rather than the eigenfunctions and is based on identifying a direct relation between the intensity of Shnirelman's peak and the localizatio...

We discuss of a ring-shaped soft quantum wire modeled by δ interaction supported by the ring of a generally nonconstant coupling strength. We derive condition which determines the discrete spectrum of such systems, and analyze the dependence of eigenvalues and eigenfunctions on the coupling and ring geometry. In particular, we illustrate that a random component in the coupling leads to a locali...

We present the discovery of a novel and intriguing global geometric structure (interior) transmission eigenfunctions associated with Helmholtz system. It is shown in generic scenarios that there always exists sequence corresponding eigenvalues going to infinity such those are localized around boundary domain. provide comprehensive rigorous justification case within radial geometry, whereas for ...

objectives: the aim of the present study was to assess the auditory lateralization ability in children with (central) auditory processing disorder. methods: participants were divided in two groups: 15 children with central auditory processing disorder (8-10 years) and 80 normal children (8-11 years) from both genders with pure-tone air-conduction thresholds better than 20 db hl bilaterally and ...

a wireless sensor network (wsn) is a wireless decentralized structure network consists of many nodes. nodes can be fixed or mobile. wsn applications typically observe some physical phenomenon through sampling of the environment so determine the location of events is an important issue in wsn. wireless localization used to determine the position of nodes. the precise localization in wsns is a co...

Breast cancer has been reported to account for the maximum cases among all female cancers till date. In order to gain a deeper insight into the complexities of the disease, we analyze the breast cancer network and its normal counterpart at the proteomic level. While the short range correlations in the eigenvalues exhibiting universality provide an evidence towards the importance of random conne...