Measurement of qubits

We describe in detail the theory underpinning the measurement of density matrices of a pair of quantum two-level systems (qubits). Our particular emphasis is on qubits realized by the two polarization degrees of freedom of a pair of entangled photons generated in a down-conversion experiment; however, the discussion applies in general, regardless of the actual physical realization. Two techniques are discussed, namely, a tomographic reconstruction (in which the density matrix is linearly related to a set of measured quantities) and a maximum likelihood technique which requires numerical optimization (but has the advantage of producing density matrices that are always non-negative definite). In addition, a detailed error analysis is presented, allowing errors in quantities derived from the density matrix, such as the entropy or entanglement of formation, to be estimated. Examples based on down-conversion experiments are used to illustrate our results.

3,5-cycle decompositions

For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n -1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n-2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. (C) 1998 John Wiley & Sons, Inc.

Factorizations of the complete graph into C-5-factors and 1-factors

In this paper, we show that K-10n can be factored into alpha C-5-factors and beta 1-factors for all non-negative integers alpha and beta satisfying 2alpha + beta = 10(n) - 1.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

Quantifying the effect of stress relaxation on excavation

Stress relaxation is relevant to the design of both civil and mining excavations. While many authors refer to the adverse effect of stress relaxation on excavation stability, some present compelling empirical evidence indicating that stress relaxation does not have a significant effect. Establishing clear definitions of stress relaxation was critical to understanding and quantifying stress relaxation of the various types that have been referred to in the literature. This paper defines three types of stress relaxation – partial relaxation, full relaxation and tangential relaxation. Once clear definitions were determined, it became clear that the theoretical arguments and empirical evidence presented by various authors to support their respective cases are not contradictory; rather, the different conclusions can be attributed to different types of stress relaxation. In particular, when the minor principal stress is negative the intermediate principal stress has been identified as significantly affecting jointed rock mass behaviour. The aim of the study was to review and evaluate existing methods of quantifying the effect of stress relaxation around underground excavations and, if necessary, propose a new set of recommendations. An empirical stope stability model, that has been termed the Extended Mathews stability chart, was considered to be the most appropriate method of quantifying the effects of stress relaxation. A new set of guidelines to account for the effect of stress relaxation on excavation stability in the Extended Mathews stability chart has been proposed from a back-analysis of 55 case histories of stress relaxation.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

The use of 16s rDNA restriction fragment length polymorphism analysis for the identification of non-fermenting gram negative bacilli in a cystic fibrosis microbiology referral service

The utility of 16s rDNA restriction fragment length polymorphism (RFLP) analysis for the partial genomovar differentiation of Burkholderia cepacia complex bacterium is well documented. We compared the 16s rDNA RFLP signatures for a number of non-fermenting gram negative bacilli (NF GNB) LMG control strains and clinical isolates pertaining to the genera Burkholderia, Pseudomonas, Achromobacter (Alcaligenes), Ralstonia, Stenotrophomonas and Pandoraea. A collection of 24 control strain (LMG) and 25 clinical isolates were included in the study. Using conventional PCR, a 1.2 kbp 16s rDNA fragment was generated for each organism. Following restriction digestion and electrophoresis, each clinical isolate RFLP signature was compared to those of the control strain panel. Nineteen different RFLP signatures were detected from the 28 control strains included in the study. TwentyoneyTwenty- five of the clinical isolates could be classified by RFLP analysis into a single genus and species when compared to the patterns produced by the control strain panel. Four clinical B. pseudomallei isolates produced RFLP signatures which were indistinguishable from B. cepacia genomovars I, III and VIII. The identity of these four isolates were confirmed using B. pseudomallei specific PCR. 16s rDNA RFLP analysis can be a useful identification strategy when applied to NF GNB, particularly for those which exhibit colistin sulfate resistance. The use of this molecular based methodology has proved very useful in the setting of a CF referral laboratory particularly when utilised in conjunction with B. cepacia complex and genomovar specific PCR techniques. Species specific PCR or sequence analysis should be considered for selected isolates; especially where discrepancies between epidemiology, phenotypic and genotypic characteristics occur.

Comparison of three commercial sparse-matrix crystallization screens

Sparse-matrix sampling using commercially available crystallization screen kits has become the most popular way of determining the preliminary crystallization conditions for macromolecules. In this study, the efficiency of three commercial screening kits, Crystal Screen and Crystal Screen 2 (Hampton Research), Wizard Screens I and II (Emerald BioStructures) and Personal Structure Screens 1 and 2 (Molecular Dimensions), has been compared using a set of 19 diverse proteins. 18 proteins yielded crystals using at least one crystallization screen. Surprisingly, Crystal Screens and Personal Structure Screens showed dramatically different results, although most of the crystallization formulations are identical as listed by the manufacturers. Higher molecular weight polyethylene glycols and mixed precipitants were found to be the most effective precipitants in this study.

Acquisition of negative valence and modified attentional processing by non fear relevant stimuli

The current research examined valence and attentional processing of a priori fear relevant stimuli and investigated the extent to which these characteristics can be acquired by non fear relevant stimuli across an aversive learning episode. The first experiment compared pictures of snakes and spiders with pictures of birds and fish using affective priming, visual search and detection of a dot probe. Snakes and spiders were more negative than birds and fish as indexed by affective priming, and were preferentially attended to in the visual search task. The second experiment exposed the non fear relevant animal pictures, birds and fish, in an aversive learning episode involving an aversive shock US. Skin conductance responding was measured during acquisition. After acquisition, conditioned non fear relevant animal stimuli, CS1, and non conditioned, non fear relevant animal stimuli, CS, were compared across affective priming, visual search and dot probe tasks. During acquisition, skin conductance responses were larger during CS1 than during CS across all three response intervals. After acquisition, CS1 non fear relevant animal pictures were more negative than CS non fear relevant animal pictures as indexed by affective priming, and were preferentially attended to in a dot probe task. These studies provide evidence that negative valence and modified attentional processing can be acquired in a brief aversive learning episode.

Non-linear principal components analysis: an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia, Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore. three geographical areas with unique environmental characteristics could be identified. Copyright (c) 2005 John Wiley & Sons, Ltd.

Hydrothermal Stability of Modified Silica Membranes for Gas Separation

A new class of hybrid molecular sieve silica (MSS) membranes is developed and tested against standard and organic templated membranes. The hybrid membrane is synthesized by the standard sol-gel process, integrating a template (methyltriethoxysilane - MTES) and a C6 surfactant (triethylhexylammonium bromide) into the silica film matrix. After hydro treatment under a relative humidity of 96% for 50h, the hybrid membrane shows no changes in its gas separation capabilities or energy of mobility. The structural characteristics and integrity of the hybrid membrane are retained due to a high concentration of organophilic functional groups and alkoxides observed using 29 Si NMR. In contrast, the structural integrity of the membranes prepared with non-templated films deteriorated during the hydro treatment due to a large percentage of silanol groups (Si-OH) which react with water. The hybrid membranes underwent a decrease in the H2/CO2 selectivity of only 1% whereas for the non-templated membrane a 21% decrease was observed. The transport mechanism of the hybrid membranes is activated as permeation increased with temperature. The activation energy for the permeation of H2 is positive while negative for CO2. The H2 permeation obtained was 3x 10 -8 mol.m -2 .s -1 .Pa -1 and permselectivities for H2/CO2 and H2/N2 varied between 1-7 and 31-34, respectively.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.