A Lanczos-powered implementation of the Faber polynomial quantum time propagator for reaction probabilities

Complementing our recent work on subspace wavepacket propagation [Chem. Phys. Lett. 336 (2001) 149], we introduce a Lanczos-based implementation of the Faber polynomial quantum long-time propagator. The original version [J. Chem. Phys. 101 (1994) 10493] implicitly handles non-Hermitian Hamiltonians, that is, those perturbed by imaginary absorbing potentials to handle unwanted reflection effects. However, like many wavepacket propagation schemes, it encounters a bottleneck associated with dense matrix-vector multiplications. Our implementation seeks to reduce the quantity of such costly operations without sacrificing numerical accuracy. For some benchmark scattering problems, our approach compares favourably with the original. (C) 2004 Elsevier B.V. All rights reserved.

Reproductive anatomy of the strictly monogamous Capricorn silvereye Zosterops lateralis chlorocephalus

Anatomy of male and female comparable with similar-sized species that show low rates of extra-pair-paternity, hence low sperm competition.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

Quantum computing and polynomial equations over the finite field Z(2)

What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z(2). This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes, namely BQP subset of P-#P and BQP subset of PP.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

On the multicomponent polynomial solution models

The present study addresses the problem of predicting the properties of multicomponent systems from those of corresponding binary systems. Two types of multicomponent polynomial models have been analysed. A probabilistic interpretation of the parameters of the Polynomial model, which explicitly relates them with the Gibbs free energies of the generalised quasichemical reactions, is proposed. The presented treatment provides a theoretical justification for such parameters. A methodology of estimating the ternary interaction parameter from the binary ones is presented. The methodology provides a way in which the power series multicomponent models, where no projection is required, could be incorporated into the Calphad approach.

OntoRama: Browsing RDF ontologies using a hyperbolic-style browser

This paper presents a Java-based hyperbolic-style browser designed to render RDF files as structured ontological maps. The program was motivated by the need to browse the content of a web-accessible ontology server: WEB KB-2. The ontology server contains descriptions of over 74,500 object types derived from the WordNet 1.7 lexical database and can be accessed using RDF syntax. Such a structure creates complications for hyperbolic-style displays. In WEB KB-2 there are 140 stable ontology link types and a hyperbolic display needs to filter and iconify the view so different link relations can be distinguished in multi-link views. Our browsing tool, OntoRama, is therefore motivated by two possibly interfering aims: the first to display up to 10 times the number of nodes in a hyperbolic-style view than using a conventional graphics display; secondly, to render the ontology with multiple links comprehensible in that view.