40 research outputs found
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 such that the
adjacency matrix possesses distinct eigenvalues, all of the other
adjacency matrices , can be written as polynomials of ,
i.e., , where is not necessarily of degree . Then, we use
this property for these particular networks and assume that all of the
conductances except for one of them, say , 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 -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