Calculating effective resistances on underlying networks of association schemes

Recently, in Refs. \cite{jsj} and \cite{res2}, calculation of effective resistances on distance-regular networks was investigated, where in the first paper, the calculation was based on stratification and Stieltjes function associated with the network, whereas in the latter one a recursive formula for effective resistances was given based on the Christoffel-Darboux identity. In this paper, evaluation of effective resistances on more general networks which are underlying networks of association schemes is considered, where by using the algebraic combinatoric structures of association schemes such as stratification and Bose-Mesner algebras, an explicit formula for effective resistances on these networks is given in terms of the parameters of corresponding association schemes. Moreover, we show that for particular underlying networks of association schemes with diameter $d$ such that the adjacency matrix $A$ possesses $d+1$ distinct eigenvalues, all of the other adjacency matrices $A_i$, $i\neq 0,1$ can be written as polynomials of $A$, i.e., $A_i=P_i(A)$, where $P_i$ is not necessarily of degree $i$. Then, we use this property for these particular networks and assume that all of the conductances except for one of them, say $c\equiv c_1=1$, are zero to give a procedure for evaluating effective resistances on these networks. The preference of this procedure is that one can evaluate effective resistances by using the structure of their Bose-Mesner algebra without any need to know the spectrum of the adjacency matrices.Comment: 41 page

Perfect transfer of m-qubit GHZ states

By using some techniques such as spectral distribution and stratification associated with the graphs, employed in [1,2] for the purpose of Perfect state transfer (PST) of a single qubit over antipodes of distance-regular spin networks and PST of a $d$-level quantum state over antipodes of pseudo-distance regular networks, PST of an m-qubit GHZ state is investigated. To do so, we employ the particular distance-regular networks (called Johnson networks) J(2m,m) to transfer an m-qubit GHZ state initially prepared in an arbitrary node of the network (called the reference node) to the corresponding antipode, perfectly. Keywords: Perfect state transferenc, GHZ states, Johnson network, Stratification, Spectral distribution PACs Index: 01.55.+b, 02.10.YnComment: 17 page

Renal ganglioneuromas in a pediatric patient: Case report and review of the literature

AbstractGanglioneuromas are rare benign tumors originating from the sympathetic nervous system and neural crest cells. A 4-year-old girl presented with numerous urinary tract infections. Ultrasound and computed tomography revealed a large mass within the right kidney. A right nephrectomy and sampling of surrounding lymph nodes were performed. Pathology confirmed that the mass was a mature ganglioneuroma. The patient remains disease-free, more than 2 years after surgery. We present this rare case of renal ganglioneuroma as well as a review of the literature