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.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Molecular evidence for the common origin of snap-traps among carnivorous plants

The snap-trap leaves of the aquatic waterwheel plant (Aldrovanda) resemble those of Venus' flytrap (Dionaea), its distribution and habit are reminiscent of bladderworts (Utricularia), but it shares many reproductive characters with sundews (Drosera). Moreover, Aldrovanda has never been included in molecular phylogenetic studies, so it has been unclear whether snap-traps evolved only once or more than once among angiosperms. Using sequences from nuclear 18S and plastid rbcL, atpB, and matK genes, we show that Aldrovanda is sister to Dionaea, and this pair is sister to Drosera. Our results indicate that snap-traps are derived from flypaper-traps and have a common ancestry among flowering plants, despite the fact that this mechanism is used by both a terrestrial species and an aquatic one. Genetic and fossil evidence for the close relationship between these unique and threatened organisms indicate that carnivory evolved from a common ancestor within this caryophyllid clade at least 65 million years ago.

The impact of genotyping error on haplotype reconstruction and frequency estimation

The choice of genotyping families vs unrelated individuals is a critical factor in any large-scale linkage disequilibrium (LD) study. The use of unrelated individuals for such studies is promising, but in contrast to family designs, unrelated samples do not facilitate detection of genotyping errors, which have been shown to be of great importance for LD and linkage studies and may be even more important in genotyping collaborations across laboratories. Here we employ some of the most commonly-used analysis methods to examine the relative accuracy of haplotype estimation using families vs unrelateds in the presence of genotyping error. The results suggest that even slight amounts of genotyping error can significantly decrease haplotype frequency and reconstruction accuracy, that the ability to detect such errors in large families is essential when the number/complexity of haplotypes is high (low LD/common alleles). In contrast, in situations of low haplotype complexity (high LD and/or many rare alleles) unrelated individuals offer such a high degree of accuracy that there is little reason for less efficient family designs. Moreover, parent-child trios, which comprise the most popular family design and the most efficient in terms of the number of founder chromosomes per genotype but which contain little information for error detection, offer little or no gain over unrelated samples in nearly all cases, and thus do not seem a useful sampling compromise between unrelated individuals and large families. The implications of these results are discussed in the context of large-scale LD mapping projects such as the proposed genome-wide haplotype map.

Patterns of resistance to angular leaf spot, anthracnose and common bacterial blight in common bean germplasm

Diseases and insect pests are major causes of low yields of common bean (Phaseolus vulgaris L.) in Latin America and Africa. Anthracnose, angular leaf spot and common bacterial blight are widespread foliar diseases of common bean that also infect pods and seeds. One thousand and eighty-two accessions from a common bean core collection from the primary centres of origin were investigated for reaction to these three diseases. Angular leaf spot and common bacterial blight were evaluated in the field at Santander de Quilichao, Colombia, and anthracnose was evaluated in a screenhouse in Popayan, Colombia. By using the 15-group level from a hierarchical clustering procedure, it was found that 7 groups were formed with mainly Andean common bean accessions (Andean gene pool), 7 groups with mainly Middle American accessions (Middle American gene pool), while 1 group contained mixed accessions. Consistent with the theory of co-evolution, it was generally observed that accessions from the Andean gene pool were resistant to Middle American pathogen isolates causing anthracnoxe, while the Middle American accessions were resistant to pathogen isolates from the Andes. Different combinations of resistance patterns were found, and breeders can use this information to select a specific group of accessions on the basis of their need.

Genetic variability in cultivated common bean beyond the two major gene pools

It is generally accepted that two major gene pools exist in cultivated common bean (Phaseolus vulgaris L.), a Middle American and an Andean one. Some evidence, based on unique phaseolin morphotypes and AFLP analysis, suggests that at least one more gene pool exists in cultivated common bean. To investigate this hypothesis, 1072 accessions from a common bean core collection from the primary centres of origin, held at CIAT, were investigated. Various agronomic and morphological attributes (14 categorical and 11 quantitative) were measured. Multivariate analyses, consisting of homogeneity analysis and clustering for categorical data, clustering and ordination techniques for quantitative data and nonlinear principal component analysis for mixed data, were undertaken. The results of most analyses supported the existence of the two major gene pools. However, the analysis of categorical data of protein types showed an additional minor gene pool. The minor gene pool is designated North Andean and includes phaseolin types CH, S and T; lectin types 312, Pr, B and K; and mostly A5, A6 and A4 types alpha-amylase inhibitor. Analysis of the combined categorical data of protein types and some plant categorical data also suggested that some other germplasm with C type phaseolin are distinguished from the major gene pools.

Tillering in grain sorghum over a wide range of population densities: Identification of a common hierarchy for tiller emergence, leaf area development and fertility

Most studies of tiller development have not related the physiological and morphological features of each calm to its subsequent fertility. This introduced problems when trying to account for the effects of tillering on yield in crop models. The objective of this study was to detect the most likely early determinants of tiller fertility in sorghum by identifying hierarchies for emergence, fertility and grain number of tillers over a wide range of assimilate availabilities. Emergence, phenology, leaf area development and dry weight partitioning were quantified weekly for individual tillers and main culms of tillering and uniculm plants grown at one of four densities, from two to 16 plants m(-2). For a given plant in any given density, the same tiller hierarchy applied for emergence of tillers, fertility of the emerged tillers and their subsequent grain number. These results were observed over a range of tiller fertility rates (from 7 to 91%), fertile tiller number per plant at maturity (from 0.2 to 4.7), and tiller contribution to grain yield (from 5 to 78%). Tiller emergence was most probably related to assimilate supply and light quality. Development, fertility and contribution to yield of a specific tiller were highly dependent on growing conditions at the time of tiller emergence, particularly via early leaf area development of the tiller, which affected its subsequent leaf area accumulation. Assimilate availability in the main culm at the time of tiller emergence was the most likely early determinant of subsequent tiller fertility in this study. (C) 2002 Annals of Botany Company.

Consensus neuropathological diagnosis of common dementia syndromes: testing and standardising the use of multiple diagnostic criteria

The aim of this study was to assess the variation between neuropathologists in the diagnosis of common dementia syndromes when multiple published protocols are applied. Fourteen out of 18 Australian neuropathologists participated in diagnosing 20 cases (16 cases of dementia, 4 age-matched controls) using consensus diagnostic methods. Diagnostic criteria, clinical synopses and slides from multiple brain regions were sent to participants who were asked for case diagnoses. Diagnostic sensitivity, specificity, predictive value, accuracy and variability were determined using percentage agreement and kappa statistics. Using CERAD criteria, there was a high inter-rater agreement for cases with probable and definite Alzheimer's disease but low agreement for cases with possible Alzheimer's disease. Braak staging and the application of criteria for dementia with Lewy bodies also resulted in high inter-rater agreement. There was poor agreement for the diagnosis of frontotemporal dementia and for identifying small vessel disease. Participants rarely diagnosed more than one disease in any case. To improve efficiency when applying multiple diagnostic criteria, several simplifications were proposed and tested on 5 of the original 210 cases. Inter-rater reliability for the diagnosis of Alzheimer's disease and dementia with Lewy bodies significantly improved. Further development of simple and accurate methods to identify small vessel lesions and diagnose frontotemporal dementia is warranted.