CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

Higher Moments of Net Proton Multiplicity Distributions at RHIC

200 GeV corresponding to baryon chemical potentials (mu(B)) between 200 and 20 MeV. Our measurements of the products kappa sigma(2) and S sigma, which can be related to theoretical calculations sensitive to baryon number susceptibilities and long-range correlations, are constant as functions of collision centrality. We compare these products with results from lattice QCD and various models without a critical point and study the root s(NN) dependence of kappa sigma(2). From the measurements at the three beam energies, we find no evidence for a critical point in the QCD phase diagram for mu(B) below 200 MeV.

Barrier distributions for weakly bound systems

We discuss the use of reduced fusion cross sections in the derivation of fusion barrier distributions. We show that the elimination of static effects associated with system sizes and optical potentials obtained by the recently introduced fusion functions can be extended to barrier distributions. This can be a useful tool for systematic studies of breakup coupling effects in fusion processes.

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem. (C) 2010 Elsevier B.V. All rights reserved.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

On the use of correlated beta random variables with animal population modelling

We give reasons why demographic parameters such as survival and reproduction rates are often modelled well in stochastic population simulation using beta distributions. In practice, it is frequently expected that these parameters will be correlated, for example with survival rates for all age classes tending to be high or low in the same year. We therefore discuss a method for producing correlated beta random variables by transforming correlated normal random variables, and show how it can be applied in practice by means of a simple example. We also note how the same approach can be used to produce correlated uniform triangular, and exponential random variables. (C) 2008 Elsevier B.V. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

Determination of pore size distributions by regularization and finite element collocation

The problem of extracting pore size distributions from characterization data is solved here with particular reference to adsorption. The technique developed is based on a finite element collocation discretization of the adsorption integral, with fitting of the isotherm data by least squares using regularization. A rapid and simple technique for ensuring non-negativity of the solutions is also developed which modifies the original solution having some negativity. The technique yields stable and converged solutions, and is implemented in a package RIDFEC. The package is demonstrated to be robust, yielding results which are less sensitive to experimental error than conventional methods, with fitting errors matching the known data error. It is shown that the choice of relative or absolute error norm in the least-squares analysis is best based on the kind of error in the data. (C) 1998 Elsevier Science Ltd. All rights reserved.

X-ray computed tomography to quantify tree rooting spatial distributions

Poor root development due to constraining soil conditions could be an important factor influencing health of urban trees. Therefore, there is a need for efficient techniques to analyze the spatial distribution of tree roots. An analytical procedure for describing tree rooting patterns from X-ray computed tomography (CT) data is described and illustrated. Large irregularly shaped specimens of undisturbed sandy soil were sampled from Various positions around the base of trees using field impregnation with epoxy resin, to stabilize the cohesionless soil. Cores approximately 200 mm in diameter by 500 mm in height were extracted from these specimens. These large core samples were scanned with a medical X-ray CT device, and contiguous images of soil slices (2 mm thick) were thus produced. X-ray CT images are regarded as regularly-spaced sections through the soil although they are not actual 2D sections but matrices of voxels similar to 0.5 mm x 0.5 mm x 2 mm. The images were used to generate the equivalent of horizontal root contact maps from which three-dimensional objects, assumed to be roots, were reconstructed. The resulting connected objects were used to derive indices of the spatial organization of roots, namely: root length distribution, root length density, root growth angle distribution, root spatial distribution, and branching intensity. The successive steps of the method, from sampling to generation of indices of tree root organization, are illustrated through a case study examining rooting patterns of valuable urban trees. (C) 1999 Elsevier Science B.V. All rights reserved.

Habitat structure and egg distributions in the processionary caterpillar Ochrogaster lunifer: lessons for conservation and pest management

1. The spatial and temporal distribution of eggs laid by herbivorous insects is a crucial component of herbivore population stability, as it influences overall mortality within the population. Thus an ecologist studying populations of an endangered butterfly can do little to increase its numbers through habitat management without knowledge of its egg-laying patterns across individual host-plants under different habitat management regimes. At the other end of the spectrum, a knowledge of egg-laying behaviour can do much to control pest outbreaks by disrupting egg distributions that lead to rapid population growth. 2. The distribution of egg batches of the processionary caterpillar Ochrogaster lunifer on acacia trees was monitored in 21 habitats during 2 years in coastal Australia. The presence of egg batches on acacias was affected by host-tree 'quality' (tree size and foliar chemistry that led to increased caterpillar survival) and host-tree 'apparency' (the amount of vegetation surrounding host-trees). 3. In open homogeneous habitats, more egg batches were laid on high-quality trees, increasing potential population growth. In diverse mixed-species habitats, more egg batches were laid on low-quality highly apparent trees, reducing population growth and so reducing the potential for unstable population dynamics. The aggregation of batches on small apparent trees in diverse habitats led to outbreaks on these trees year after year, even when population levels were low, while site-wide outbreaks were rare. 4. These results predict that diverse habitats with mixed plant species should increase insect aggregation and increase population stability. In contrast, in open disturbed habitats or in regular plantations, where egg batches are more evenly distributed across high-quality hosts, populations should be more unstable, with site-wide outbreaks and extinctions being more common. 5. Mixed planting should be used on habitat regeneration sites to increase the population stability of immigrating or reintroduced insect species. Mixed planting also increases the diversity of resources, leading to higher herbivore species richness. With regard to the conservation of single species, different practices of habitat management will need to be employed depending on whether a project is concerned with methods of rapidly increasing the abundance of an endangered insect or concerned with the maintenance of a stable, established insect population that is perhaps endemic to an area. Suggestions for habitat management in these different cases are discussed. 6. Finally, intercropping can be highly effective in reducing pest outbreaks, although the economic gains of reduced pest attack may be outweighed by reduced crop yields in mixed-crop systems.

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.