Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

Hemichordates and deuterostome evolution: robust molecular phylogenetic support for a hemichordate plus echinoderm clade

Hemichordates were traditionally allied to the chordates, but recent molecular analyses have suggested that hemichordates are a sister group to the echinoderms, a relationship that has important consequences for the interpretation of the evolution of deuterostome body plans. However, the molecular phylogenetic analyses to date have not provided robust support for the hemichordate + echinoderm clade. We use a maximum likelihood framework, including the parametric bootstrap, to reanalyze DNA data from complete mitochondrial genomes and nuclear 18S rRNA. This approach provides the first statistically significant support for the hemichordate + echinoderm clade from molecular data. This grouping implies that the ancestral deuterostome had features that included an adult with a pharynx and a dorsal nerve cord and an indirectly developing dipleurula-like larva.

The HI Parkes All Sky Survey: southern observations, calibration and robust imaging

The acquisition of HI Parkes All Shy Survey (HIPASS) southern sky data commenced at the Australia Telescope National Facility's Parkes 64-m telescope in 1997 February, and was completed in 2000 March. HIPASS is the deepest HI survey yet of the sky south of declination +2 degrees, and is sensitive to emission out to 170 h(75)(-1) Mpc. The characteristic root mean square noise in the survey images is 13.3 mJy. This paper describes the survey observations, which comprise 23 020 eight-degree scans of 9-min duration, and details the techniques used to calibrate and image the data. The processing algorithms are successfully designed to be statistically robust to the presence of interference signals, and are particular to imaging point (or nearly point) sources. Specifically, a major improvement in image quality is obtained by designing a median-gridding algorithm which uses the median estimator in place of the mean estimator.

True measures of GDP and convergence

Widely used ''purchasing power parity'' comparisons of per capita GDP are not true quantity indexes and are subject to systematic substitution bins. This bias may distort measurement of convergence and divergence. Extending Varian's nonparametric construction of a true index gives the set of true indexes, including the new Ideal Afriat Index. These indexes are utility-consistent and independent of arbitrary reference price vectors. We establish bounds on the dispersion of true multilateral indexes, hence bounds on convergence. International price indexes understate both true GDP dispersion and, where prices are converging over time, the rate of true quantity convergence.

Robust algorithms for solving stochastic partial differential equations

A robust semi-implicit central partial difference algorithm for the numerical solution of coupled stochastic parabolic partial differential equations (PDEs) is described. This can be used for calculating correlation functions of systems of interacting stochastic fields. Such field equations can arise in the description of Hamiltonian and open systems in the physics of nonlinear processes, and may include multiplicative noise sources. The algorithm can be used for studying the properties of nonlinear quantum or classical field theories. The general approach is outlined and applied to a specific example, namely the quantum statistical fluctuations of ultra-short optical pulses in chi((2)) parametric waveguides. This example uses a non-diagonal coherent state representation, and correctly predicts the sub-shot noise level spectral fluctuations observed in homodyne detection measurements. It is expected that the methods used wilt be applicable for higher-order correlation functions and other physical problems as well. A stochastic differencing technique for reducing sampling errors is also introduced. This involves solving nonlinear stochastic parabolic PDEs in combination with a reference process, which uses the Wigner representation in the example presented here. A computer implementation on MIMD parallel architectures is discussed. (C) 1997 Academic Press.

Robust parameter settings of evolutionary algorithms for the optimisation of agricultural systems models

Numerical optimisation methods are being more commonly applied to agricultural systems models, to identify the most profitable management strategies. The available optimisation algorithms are reviewed and compared, with literature and our studies identifying evolutionary algorithms (including genetic algorithms) as superior in this regard to simulated annealing, tabu search, hill-climbing, and direct-search methods. Results of a complex beef property optimisation, using a real-value genetic algorithm, are presented. The relative contributions of the range of operational options and parameters of this method are discussed, and general recommendations listed to assist practitioners applying evolutionary algorithms to the solution of agricultural systems. (C) 2001 Elsevier Science Ltd. All rights reserved.

Differential inclusions and robust control theory

Uncontrolled systems (x) over dot is an element of Ax, where A is a non-empty compact set of matrices, and controlled systems (x) over dot is an element of Ax + Bu are considered. Higher-order systems 0 is an element of Px - Du, where and are sets of differential polynomials, are also studied. It is shown that, under natural conditions commonly occurring in robust control theory, with some mild additional restrictions, asymptotic stability of differential inclusions is guaranteed. The main results are variants of small-gain theorems and the principal technique used is the Krasnosel'skii-Pokrovskii principle of absence of bounded solutions.

Atom lasers, coherent states, and coherence II. Maximally robust ensembles of pure states

As discussed in the preceding paper [Wiseman and Vaccaro, preceding paper, Phys. Rev. A 65, 043605 (2002)], the stationary state of an optical or atom laser far above threshold is a mixture of coherent field states with random phase, or, equivalently, a Poissonian mixture of number states. We are interested in which, if either, of these descriptions of rho(ss) as a stationary ensemble of pure states, is more natural. In the preceding paper we concentrated upon the question of whether descriptions such as these are physically realizable (PR). In this paper we investigate another relevant aspect of these ensembles, their robustness. A robust ensemble is one for which the pure states that comprise it survive relatively unchanged for a long time under the system evolution. We determine numerically the most robust ensembles as a function of the parameters in the laser model: the self-energy chi of the bosons in the laser mode, and the excess phase noise nu. We find that these most robust ensembles are PR ensembles, or similar to PR ensembles, for all values of these parameters. In the ideal laser limit (nu=chi=0), the most robust states are coherent states. As the phase noise or phase dispersion is increased through nu or the self-interaction of the bosons chi, respectively, the most robust states become more and more amplitude squeezed. We find scaling laws for these states, and give analytical derivations for them. As the phase diffusion or dispersion becomes so large that the laser output is no longer quantum coherent, the most robust states become so squeezed that they cease to have a well-defined coherent amplitude. That is, the quantum coherence of the laser output is manifest in the most robust PR ensemble being an ensemble of states with a well-defined coherent amplitude. This lends support to our approach of regarding robust PR ensembles as the most natural description of the state of the laser mode. It also has interesting implications for atom lasers in particular, for which phase dispersion due to self-interactions is expected to be large.

Ductile fabrics in the zone of active oblique convergence near the Alpine Fault, New Zealand: identifying the neotectonic overprint

The mid-crustal Alpine Schist in central Southern Alps, New Zealand has been exhumed during the past similar to3 m.y. on the hanging wall of the oblique-slip Alpine Fault. These rocks underwent ductile deformation during their passage through the similar to 150-km-wide Pacific-Australia plate boundary zone. Likely to be Cretaceous in age, peak metamorphism predates the largely Pliocene and younger oblique convergence that continues to uplift the Southern Alps today. Late Cenozoic ductile deformation constructively reinforced a pre-existing fabric that was well oriented to accommodate a dextral-transpressive overprint. Quartz microstructures below a recently exhumed brittle-ductile transition zone reflect a late Cenozoic increment of ductile strain that was distributed across deeper levels of the Pacific Plate. Deformation was transpressive, including a dextral-normal shear component that bends and rotates a delaminated panel of Pacific Plate crust onto the oblique footwall ramp of the Alpine Fault. Progressive ductile shear in mylonites at the base of the Pacific Plate overprints earlier fabrics in a dextral-reverse sense, a deformation that accompanies translation of the schists up the Alpine Fault. Ductile shear along that structure affects not only the 12-km-thick section of Alpine mylonites, but is distributed across several kilometres of overlying nonmylonitic rocks. (C) 2001 Elsevier Science Ltd. All rights reserved.

Robust model-order reduction of complex biological processes

This paper addresses robust model-order reduction of a high dimensional nonlinear partial differential equation (PDE) model of a complex biological process. Based on a nonlinear, distributed parameter model of the same process which was validated against experimental data of an existing, pilot-scale BNR activated sludge plant, we developed a state-space model with 154 state variables in this work. A general algorithm for robustly reducing the nonlinear PDE model is presented and based on an investigation of five state-of-the-art model-order reduction techniques, we are able to reduce the original model to a model with only 30 states without incurring pronounced modelling errors. The Singular perturbation approximation balanced truncating technique is found to give the lowest modelling errors in low frequency ranges and hence is deemed most suitable for controller design and other real-time applications. (C) 2002 Elsevier Science Ltd. All rights reserved.

Sorting and convergence of primary olfactory axons are independent of the olfactory bulb

Primary olfactory axons expressing the same odorant receptor gene sort out and converge to fixed sites in the olfactory bulb. We examined the guidance of axons expressing the P2 odorant receptor when they were challenged with different cellular environments in vivo. In the mutant extratoes mouse, the olfactory bulb is lacking and is replaced by a fibrocellular mass. In these animals, primary olfactory axons form glomerular-like loci despite the absence of normal postsynaptic targets. P2 axons are able to sort out from other axons in this fibrocellular mass and converge to form loci of like axons. The sites of these loci along mediolateral and ventrodorsal axes were highly variable. Similar convergence was observed for larger subpopulations of axons expressing the same cell surface carbohydrates. The sorting out and convergence of like axons also occurred during regeneration following bulbectomy. Olfactory axon behaviour in these models demonstrates that sorting and convergence of axons are independent of the target, which instead provides distinct topographic cues for guidance. (C) 2003 Wiley-Liss, Inc.