Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Calculation of product state distributions from resonance decay via Lanczos subspace filter diagonalization: Application to HO2

Resonance phenomena associated with the unimolecular dissociation of HO2 have been investigated quantum-mechanically by the Lanczos homogeneous filter diagonalization (LHFD) method. The calculated resonance energies, rates (widths), and product state distributions are compared to results from an autocorrelation function-based filter diagonalization (ACFFD) method. For calculating resonance wave functions via ACFFD, an analytical expression for the expansion coefficients of the modified Chebyshev polynomials is introduced. Both dissociation rates and product state distributions of O-2 show strong fluctuations, indicating the dissociation of HO2 is essentially irregular. (C) 2001 American Institute of Physics.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

For Markov processes on the positive integers with the origin as an absorbing state, Ferrari, Kesten, Martinez and Picco studied the existence of quasi-stationary and limiting conditional distributions by characterizing quasi-stationary distributions as fixed points of a transformation Phi on the space of probability distributions on {1, 2,.. }. In the case of a birth-death process, the components of Phi(nu) can be written down explicitly for any given distribution nu. Using this explicit representation, we will show that Phi preserves likelihood ratio ordering between distributions. A conjecture of Kryscio and Lefevre concerning the quasi-stationary distribution of the SIS logistic epidemic follows as a corollary.

Australian microhylid frogs (Cophixalus and Austrochaperina): phylogeny, taxonomy, calls, distributions and breeding biology

Despite a considerable surge in herpetological research in Australia over the last couple of decades the Australian microhylid frogs (Cophixalus and Austrochaperina) remain relatively poorly known. Herein I present the results of extensive fieldwork and molecular, morphological and call analysis with the aim of resolving taxonomy, call variation and distributions, and increasing our understanding of breeding biology. Analysis of 943 base pairs of mitochondrial 16S rRNA and 12S rRNA provides a well supported phylogeny that is largely consistent with current taxonomy. Levels of divergence between species are substantial and significant phylogeographic structuring is evident in C. ornatus, C. neglectus and C. aenigma, sp. nov. The description of C. concinnus was based on a mixed collection of two species from Thornton Peak and a new species is described to resolve this. C. aenigma, sp. nov., is described from high-elevation (>750 m) rainforest across the Carbine, Thornton, Finnigan and Bakers Blue Mountain uplands, north-east Queensland. C. concinnus is redescribed as a highly distinct species restricted to rainforest and boulder fields at the summit of Thornton Peak (>1100 m). Despite protection in Daintree National Park in the Wet Tropics World Heritage Area, predictions of the impact of global warming suggest C. concinnus to be of very high conservation concern ( Critically Endangered, IUCN criteria). The mating call of two species ( C. mcdonaldi and C. exiguus) is described for the first time and high levels of call variation within C. ornatus, C. neglectus, C. hosmeri, C. aenigma and Austrochaperina fryi are presented. Such variation is often attributable to genetically divergent lineages, altitudinal variation and courtship; however, in some instances ( particularly within C. hosmeri) the source or function of highly distinct calls at a site remains obscure. Molecular, morphological and call analyses allow the clarification of species distributions, especially in the northern mountains of the Wet Tropics. Notes are presented on the breeding biology of C. aenigma, C. bombiens, C. concinnus, C. exiguus, C. infacetus, C. mcdonaldi, C. monticola, C. neglectus, C. ornatus and C. saxatilis, which are largely consistent with previous accounts: small terrestrial clutches usually attended by a male. Courtship behaviour in C. ornatus is described and the first records of multiple clutching in Australian microhylids are presented (for C. ornatus and C. infacetus).

Application of density functional theory to capillary phenomena in cylindrical mesopores with radial and longitudinal density distributions

In this paper, we applied a version of the nonlocal density functional theory (NLDFT) accounting radial and longitudinal density distributions to study the adsorption and desorption of argon in finite as well as infinite cylindrical nanopores at 87.3 K. Features that have not been observed before with one-dimensional NLDFT are observed in the analysis of an inhomogeneous fluid along the axis of a finite cylindrical pore using the two-dimensional version of the NLDFT. The phase transition in pore is not strictly vapor-liquid transition as assumed and observed in the conventional version, but rather it exhibits a much elaborated feature with phase transition being complicated by the formation of solid phase. Depending on the pore size, there are more than one phase transition in the adsorption-desorption isotherm. The solid formation in finite pore has been found to be initiated by the presence of the meniscus. Details of the analysis of the extended version of NLDFT will be discussed in the paper. (C) 2004 American Institute of Physics.

Comparison of the distributions of classical and adaptively aligned EEG power spectra

The distributions of eyes-closed resting electroencephalography (EEG) power spectra and their residuals were described and compared using classically averaged and adaptively aligned averaged spectra. Four minutes of eyes-closed resting EEG was available from 69 participants. Spectra were calculated with 0.5-Hz resolution and were analyzed at this level. It was shown that power in the individual 0.5 Hz frequency bins can be considered normally distributed when as few as three or four 2-second epochs of EEG are used in the average. A similar result holds for the residuals. Power at the peak Alpha frequency has quite different statistical behaviour to power at other frequencies and it is considered that power at peak Alpha represents a relatively individuated process that is best measured through aligned averaging. Previous analyses of contrasts in upper and lower alpha bands may be explained in terms of the variability or distribution of the peak Alpha frequency itself.

Using distributions as statistical evidence in well-structured and ill-structured problems

Research has suggested that understanding in well-structured settings often does not transfer to the everyday, less-structured problems encountered outside of school. Little is known, beyond anecdotal evidence, about how teachers' consideration of distributions as evidence in well-structured settings compares with their use in ill-structured problem contexts. A qualitative study of preservice secondary teachers examined their use of distributions as evidence in four tasks of varying complexity and ill-structuredness. Results suggest that teachers' incorporation of distributions in well-structured settings does not imply that they will be incorporated in less structured problems (and vice-versa). Implications for research and teaching are discussed.