Elementary Proofs Of Two Theorems Involving Arguments Of Eigenvalues Of A Product Of Two Unitary Matrices

We give elementary proofs of two theorems concerning bounds on the maximum argument of the eigenvalues of a product of two unitary matrices --- one by Childs \emph{et al.} [J. Mod. Phys., \textbf{47}, 155 (2000)] and the other one by Chau [arXiv:1006.3614]. Our proofs have the advantages that the necessary and sufficient conditions for equalities are apparent and that they can be readily generalized to the case of infinite-dimensional unitary operators.Comment: 8 pages in Revtex 4.1 preprint format, to appear in Journal of Inequalities and Application

Biased EPR entanglement and its application to teleportation

We consider pure continuous variable entanglement with non-equal correlations between orthogonal quadratures. We introduce a simple protocol which equates these correlations and in the process transforms the entanglement onto a state with the minimum allowed number of photons. As an example we show that our protocol transforms, through unitary local operations, a single squeezed beam split on a beam splitter into the same entanglement that is produced when two squeezed beams are mixed orthogonally. We demonstrate that this technique can in principle facilitate perfect teleportation utilising only one squeezed beam.Comment: 8 pages, 5 figure

Gaussian Post-selection for Continuous Variable Quantum Cryptography

We extend the security proof for continuous variable quantum key distribution protocols using post selection to account for arbitrary eavesdropping attacks by employing the concept of an equivalent protocol where the post-selection is implemented as a series of quantum operations including a virtual distillation. We introduce a particular `Gaussian' post selection and demonstrate that the security can be calculated using only experimentally accessible quantities. Finally we explicitly evaluate the performance for the case of a noisy Gaussian channel in the limit of unbounded key length and find improvements over all pre-existing continuous variable protocols in realistic regimes.Comment: 4+4 pages. arXiv admin note: substantial text overlap with arXiv:1106.082

Topology design and performance analysis of an integrated communication network

A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix

British Sikhs in complementary schooling: the role of heritage language proficiency and ‘culture learning’ in ethnic identity and bicultural adaptation

While the debate regarding bilingual benefits persists within the cognitive sciences, education research has documented various functions that heritage languages (HL) serve their speakers through bicultural adaptation. The present study adopted a mixed-methods approach to gauge HL proficiency and use, cultural participation and ethnic and mainstream identities, and to examine multiple perspectives on HL learning with complementary schooling (CS) among British Sikhs. Seventy-four 6- to 15-year-olds completed scales for perceived oral and literate abilities, language use across contexts, British and Sikh identifications, and participation in cultural activities. Children filled in open-ended items, while parents and teachers discussed in interviews and focus groups, their motivations for HL learning and CS experiences. The majority of children self-reported ‘good’ proficiency, which differed between generations as impacted by home use and was associated with cultural participation and Sikh identification. Most children referred to practical utility while most parents regarded culture retention as the dominant motivation for HL learning. Teachers discussed how teaching beyond the second generation and language shifts presented both challenges and opportunities. Still, all parties corroborated on the pertinence of HL maintenance as facilitated by CS through ‘culture learning’ towards a strong ethnic identity and bicultural adaptation

Behaviour of non-donor specific antibodies during rapid re-synthesis of donor specific HLA antibodies after antibody incompatible renal transplantation

Background: HLA directed antibodies play an important role in acute and chronic allograft rejection. During viral infection of a patient with HLA antibodies, the HLA antibody levels may rise even though there is no new immunization with antigen. However it is not known whether the converse occurs, and whether changes on non-donor specific antibodies are associated with any outcomes following HLA antibody incompatible renal transplantation. Methods: 55 patients, 31 women and 24 men, who underwent HLAi renal transplant in our center from September 2005 to September 2010 were included in the studies. We analysed the data using two different approaches, based on; i) DSA levels and ii) rejection episode post transplant. HLA antibody levels were measured during the early post transplant period and corresponding CMV, VZV and Anti-HBs IgG antibody levels and blood group IgG, IgM and IgA antibodies were quantified. Results: Despite a significant DSA antibody rise no significant non-donor specific HLA antibody, viral or blood group antibody rise was found. In rejection episode analyses, multiple logistic regression modelling showed that change in the DSA was significantly associated with rejection (p = 0.002), even when adjusted for other antibody levels. No other antibody levels were predictive of rejection. Increase in DSA from pre treatment to a post transplant peak of 1000 was equivalent to an increased chance of rejection with an odds ratio of 1.47 (1.08, 2.00). Conclusion: In spite of increases or decreases in the DSA levels, there were no changes in the viral or the blood group antibodies in these patients. Thus the DSA rise is specific in contrast to the viral, blood group or third party antibodies post transplantation. Increases in the DSA post transplant in comparison to pre-treatment are strongly associated with occurrence of rejection

Experimental study of multiple cracks detection utilizing a probabilistic approach

This paper studies the possibility of using measured transient vibration data in the detection of multiple cracks on beams by following the Bayesian probabilistic framework. The proposed method adopts different classes of models in modelling a beam with different numbers of cracks. The number of cracks on the beam can then be identified by calculating the probability of a model class conditional on a given set of measured transient vibration data. By following the Bayesian probabilistic framework, the posterior probability density functions (PDFs) for a set of crack parameters, such as the crack locations and the corresponding extents, can be calculated. The PDFs allow engineers to quantify the uncertainties associated with the results of crack detection. The paper reports not only the theoretical developed but also the experimental verification of the proposed method

Generalized Background-Field Method

The graphical method discussed previously can be used to create new gauges not reachable by the path-integral formalism. By this means a new gauge is designed for more efficient two-loop QCD calculations. It is related to but simpler than the ordinary background-field gauge, in that even the triple-gluon vertices for internal lines contain only four terms, not the usual six. This reduction simplifies the calculation inspite of the necessity to include other vertices for compensation. Like the ordinary background-field gauge, this generalized background-field gauge also preserves gauge invariance of the external particles. As a check of the result and an illustration for the reduction in labour, an explicit calculation of the two-loop QCD $\beta$-function is carried out in this new gauge. It results in a saving of 45% of computation compared to the ordinary background-field gauge.Comment: 17 pages, Latex, 18 figures in Postscrip

Combinatorial Hopf algebras and Towers of Algebras

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras $\bigoplus_{n\ge0}A_n$ can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of algebras. We show that if a tower $\bigoplus_{n\ge0}A_n$ gives rise to graded dual Hopf algebras then we must have $\dim(A_n)=r^nn!$ where $r = \dim(A_1)$.Comment: 7 page

Continuous-Variable Spatial Entanglement for Bright Optical Beams

A light beam is said to be position squeezed if its position can be determined to an accuracy beyond the standard quantum limit. We identify the position and momentum observables for bright optical beams and show that position and momentum entanglement can be generated by interfering two position, or momentum, squeezed beams on a beam splitter. The position and momentum measurements of these beams can be performed using a homodyne detector with local oscillator of an appropriate transverse beam profile. We compare this form of spatial entanglement with split detection-based spatial entanglement.Comment: 7 pages, 3 figures, submitted to PR