Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Maximum Likelihood Estimation of Mixture Densities for Binned and Truncated Multivariate Data

Binning and truncation of data are common in data analysis and machine learning. This paper addresses the problem of fitting mixture densities to multivariate binned and truncated data. The EM approach proposed by McLachlan and Jones (Biometrics, 44: 2, 571-578, 1988) for the univariate case is generalized to multivariate measurements. The multivariate solution requires the evaluation of multidimensional integrals over each bin at each iteration of the EM procedure. Naive implementation of the procedure can lead to computationally inefficient results. To reduce the computational cost a number of straightforward numerical techniques are proposed. Results on simulated data indicate that the proposed methods can achieve significant computational gains with no loss in the accuracy of the final parameter estimates. Furthermore, experimental results suggest that with a sufficient number of bins and data points it is possible to estimate the true underlying density almost as well as if the data were not binned. The paper concludes with a brief description of an application of this approach to diagnosis of iron deficiency anemia, in the context of binned and truncated bivariate measurements of volume and hemoglobin concentration from an individual's red blood cells.

Reply to comment on `Integrable Kondo impurity in one-dimensional q-deformed t - J models

This is a reply to the comment by P Schlottmann and A A Zvyagin.

Estimating Two-Stage Models for Genetic Influences on Alcohol, Tobacco or Drug Use Initiation and Dependence Vulnerability in Twin and Family Data

Genetic research on risk of alcohol, tobacco or drug dependence must make allowance for the partial overlap of risk-factors for initiation of use, and risk-factors for dependence or other outcomes in users. Except in the extreme cases where genetic and environmental risk-factors for initiation and dependence overlap completely or are uncorrelated, there is no consensus about how best to estimate the magnitude of genetic or environmental correlations between Initiation and Dependence in twin and family data. We explore by computer simulation the biases to estimates of genetic and environmental parameters caused by model misspecification when Initiation can only be defined as a binary variable. For plausible simulated parameter values, the two-stage genetic models that we consider yield estimates of genetic and environmental variances for Dependence that, although biased, are not very discrepant from the true values. However, estimates of genetic (or environmental) correlations between Initiation and Dependence may be seriously biased, and may differ markedly under different two-stage models. Such estimates may have little credibility unless external data favor selection of one particular model. These problems can be avoided if Initiation can be assessed as a multiple-category variable (e.g. never versus early-onset versus later onset user), with at least two categories measurable in users at risk for dependence. Under these conditions, under certain distributional assumptions., recovery of simulated genetic and environmental correlations becomes possible, Illustrative application of the model to Australian twin data on smoking confirmed substantial heritability of smoking persistence (42%) with minimal overlap with genetic influences on initiation.

Loss of p16 expression is associated with histological features of melanoma invasion

While mutations of CDKN2A are associated with melanoma predisposition, the precise role of its gene product p16 in the development of sporadic melanoma is less clearly understood. We sought to determine the prevalence of p16 expression using immunohistochemical analysis in a population-based sample of melanoma tumours, and also to identify histological, phenotypic and environmental factors associated with the presence or absence of p16 expression. We conducted face-to-face interviews with 108 patients newly diagnosed with melanoma to ascertain their history of sun exposure, and recorded various phenotypic parameters. Paraffin sections of tumours from these patients were stained with an anti-p16 monoclonal antibody following antigen retrieval. Overall, 52 (48%) tumours expressed p16; nodular melanomas had significantly lower levels of p16 immunoreactivity than superficial spreading melanomas (P = 0.015). While no association was found between p16 expression and host phenotype, loss of p16 staining was associated with thicker lesions (p = 0.084) and a high mitotic index (P = 0.013). Taken together, these findings are consistent with loss of p16 being a late event in the progression of sporadic primary melanomas, being associated with tumours of a more aggressive nature. (C) 2002 Lippincott Williams Wilkins.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

Selective loss of expression of glutamate GluR2/R3 receptor subunits in cerebellar tissue from a patient with olivopontocerebellar atrophy

Expression of the mRNAs encoding the astrocytic (EAAT1, EAAT2) and neuronal (EAAT3, EAAT4) excitatory amino acid transporters and the AMPA-type glutamate receptor subunits GluR2 and GluR3 was investigated in postmortem cerebellar extracts from a patient with olivopontocerebellar atrophy (OPCA) and in material from three age-matched controls. Decreased expression in the steady state level of EAAT4 mRNA in the OPCA sample was correlated with the selective loss of Purkinje cells. Neuropathological evaluation revealed reactive gliosis and concomitantly increased expression of the mRNA encoding astrocytic glial fibrillary acidic protein (GFAP). Expression of the mRNAs encoding the AMPA receptor subunits GluR2 and GluR3 subunits was found to be decreased in OPCA suggesting that excitotoxic mechanism could play a role in the pathogenesis of the selective neuronal cell death in this disorder.

Reconciling paleodistribution models and comparative phylogeography in the Wet Tropics rainforest land snail Gnarosophia bellendenkerensis (Brazier 1875)

Comparative phylogeography has proved useful for investigating biological responses to past climate change and is strongest when combined with extrinsic hypotheses derived from the fossil record or geology. However, the rarity of species with sufficient, spatially explicit fossil evidence restricts the application of this method. Here, we develop an alternative approach in which spatial models of predicted species distributions under serial paleoclimates are compared with a molecular phylogeography, in this case for a snail endemic to the rainforests of North Queensland, Australia. We also compare the phylogeography of the snail to those from several endemic vertebrates and use consilience across all of these approaches to enhance biogeographical inference for this rainforest fauna. The snail mtDNA phylogeography is consistent with predictions from paleoclimate modeling in relation to the location and size of climatic refugia through the late Pleistocene-Holocene and broad patterns of extinction and recolonization. There is general agreement between quantitative estimates of population expansion from sequence data (using likelihood and coalescent methods) vs. distributional modeling. The snail phylogeography represents a composite of both common and idiosyncratic patterns seen among vertebrates, reflecting the geographically finer scale of persistence and subdivision in the snail. In general, this multifaceted approach, combining spatially explicit paleoclimatological models and comparative phylogeography, provides a powerful approach to locating historical refugia and understanding species' responses to them.

Disease, habitat fragmentation and conservation

Habitat loss and the resultant fragmentation of remaining habitat is the primary cause of loss of biological diversity. How do these processes affect the dynamics of parasites and pathogens? Hess has provided some important insights into this problem using metapopulation models for pathogens that exhibit 'S-I' dynamics; for example, pathogens such as rabies in which the host population may be divided into susceptible and infected individuals. A major assumption of Hess's models is that infected patches become extinct, rather than recovering and becoming resistant to future infections. In this paper, we build upon this framework in two different ways: first, we examine the consequences of including patches that are resistant to infection; second, we examine the consequences of including a second species of host that can act as a reservoir for the pathogen. Both of these effects are likely to be important from a conservation perspective. The results of both sets of analysis indicate that the benefits of corridors and other connections that allow species to disperse through the landscape far outweigh the possible risks of increased pathogen transmission. Even in the commonest case, where harmful pathogens are maintained by a common reservoir host, increased landscape connectance still allows greater coexistence and persistence of a threatened or endangered host.

Reciprocal relationship between methylation status and loss of heterozygosity at the p14 (ARF) locus in Australian and South African hepatocellular carcinomas

Chromosome 9p21, a locus comprising the tumor suppressor genes (TSG) p16(INK4) (a) and p14(ARF) , is a common region of loss of heterozygosity (LOH) in hepatocellular carcinoma (HCC). p14(ARF) shares exon 2 with p16 in a different reading frame. p14 binds to MDM2 resulting in a stabilization of functional p53 . This study examined the roles of p14, p16 and p53 in hepatocarcinogenesis, in 37 Australian and 24 South African patients. LOH at 9p21 and 17p13.1, p14 and p16 mutation analysis, p14 and p16 promoter methylation and p14, p16 and p53 protein expression was examined. LOH at 9p21 was detected more frequently in South African HCC (P = 0.04). Comparable rates of p53 LOH were observed in Australian and South African HCC (10/22, 45%vs 13/22, 59%, respectively). Hypermethylation of the p14 promoter was more prevalent in Australian HCC than in South African HCC (17/37, 46%vs 7/24, 29%, respectively). In Australian HCC the prevalence of p14 methylation increased with age (P = 0.03). p16 promoter methylation was observed in 12/37 (32%) and 6/24 (25%) in Australian and South African HCC, respectively. Loss of p16 protein expression was detected in 14/36 Australian HCC whereas p53 protein expression was detected in 9/36. Significantly, a reciprocal relationship between 9p21 LOH and p14 promoter hypermethylation was observed (P less than or equal to0.05 ). No significant association between p14 and p53 was seen in this study. The reciprocal relationship identified indicates different pathways of tumorigenesis and likely reflects different etiologies of HCC in the two countries. (C) 2002 Blackwell Science Asia Pty Ltd.

Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).

Mapping glider habitat in dry eucalypt forests for Montreal Process indicator 1.1: Fragmentation of forest types

Accurate habitat mapping is critical to landscape ecological studies such as required for developing and testing Montreal Process indicator 1.1e, fragmentation of forest types. This task poses a major challenge to remote sensing, especially in mixedspecies, variable-age forests such as dry eucalypt forests of subtropical eastern Australia. In this paper, we apply an innovative approach that uses a small section of one-metre resolution airborne data to calibrate a moderate spatial resolution model (30 m resolution; scale 1:50 000) based on Landsat Thematic Mapper data to estimate canopy structural properties in St Marys State Forest, near Maryborough, south-eastern Queensland. The approach applies an image-processing model that assumes each image pixel is significantly larger than individual tree crowns and gaps to estimate crown-cover percentage, stem density and mean crown diameter. These parameters were classified into three discrete habitat classes to match the ecology of four exudivorous arboreal species (yellowbellied glider Petaurus australis, sugar glider P. breviceps, squirrel glider P. norfolcensis , and feathertail glider Acrobates pygmaeus), and one folivorous arboreal marsupial, the greater glider Petauroides volans. These species were targeted due to the known ecological preference for old trees with hollows, and differences in their home range requirements. The overall mapping accuracy, visually assessed against transects (n = 93) interpreted from a digital orthophoto and validated in the field, was 79% (KHAT statistic = 0.72). The KHAT statistic serves as an indicator of the extent that the percentage correct values of the error matrix are due to ‘true’ agreement verses ‘chance’ agreement. This means that we are able to reliably report on the effect of habitat loss on target species, especially those with a large home range size (e.g. yellow-bellied glider). However, the classified habitat map failed to accurately capture the spatial patterning (e.g. patch size and shape) of stands with a trace or sub-dominance of senescent trees. This outcome makes the reporting of the effects of habitat fragmentation more problematic, especially for species with a small home range size (e.g. feathertail glider). With further model refinement and validation, however, this moderateresolution approach offers an important, cost eff e c t i v e advancement in mapping the age of dry eucalypt forests in the region.