Determining the effect of asymmetric data on the variogram. I. Underlying asymmetry

Matheron's usual variogram estimator can result in unreliable variograms when data are strongly asymmetric or skewed. Asymmetry in a distribution can arise from a long tail of values in the underlying process or from outliers that belong to another population that contaminate the primary process. This paper examines the effects of underlying asymmetry on the variogram and on the accuracy of prediction, and the second one examines the effects arising from outliers. Standard geostatistical texts suggest ways of dealing with underlying asymmetry; however, this is based on informed intuition rather than detailed investigation. To determine whether the methods generally used to deal with underlying asymmetry are appropriate, the effects of different coefficients of skewness on the shape of the experimental variogram and on the model parameters were investigated. Simulated annealing was used to create normally distributed random fields of different size from variograms with different nugget:sill ratios. These data were then modified to give different degrees of asymmetry and the experimental variogram was computed in each case. The effects of standard data transformations on the form of the variogram were also investigated. Cross-validation was used to assess quantitatively the performance of the different variogram models for kriging. The results showed that the shape of the variogram was affected by the degree of asymmetry, and that the effect increased as the size of data set decreased. Transformations of the data were more effective in reducing the skewness coefficient in the larger sets of data. Cross-validation confirmed that variogram models from transformed data were more suitable for kriging than were those from the raw asymmetric data. The results of this study have implications for the 'standard best practice' in dealing with asymmetry in data for geostatistical analyses. (C) 2007 Elsevier Ltd. All rights reserved.

Determining the effect of asymmetric data on the variogram. II. Outliers

Asymmetry in a distribution can arise from a long tail of values in the underlying process or from outliers that belong to another population that contaminate the primary process. The first paper of this series examined the effects of the former on the variogram and this paper examines the effects of asymmetry arising from outliers. Simulated annealing was used to create normally distributed random fields of different size that are realizations of known processes described by variograms with different nugget:sill ratios. These primary data sets were then contaminated with randomly located and spatially aggregated outliers from a secondary process to produce different degrees of asymmetry. Experimental variograms were computed from these data by Matheron's estimator and by three robust estimators. The effects of standard data transformations on the coefficient of skewness and on the variogram were also investigated. Cross-validation was used to assess the performance of models fitted to experimental variograms computed from a range of data contaminated by outliers for kriging. The results showed that where skewness was caused by outliers the variograms retained their general shape, but showed an increase in the nugget and sill variances and nugget:sill ratios. This effect was only slightly more for the smallest data set than for the two larger data sets and there was little difference between the results for the latter. Overall, the effect of size of data set was small for all analyses. The nugget:sill ratio showed a consistent decrease after transformation to both square roots and logarithms; the decrease was generally larger for the latter, however. Aggregated outliers had different effects on the variogram shape from those that were randomly located, and this also depended on whether they were aggregated near to the edge or the centre of the field. The results of cross-validation showed that the robust estimators and the removal of outliers were the most effective ways of dealing with outliers for variogram estimation and kriging. (C) 2007 Elsevier Ltd. All rights reserved.

Fast training of self organizing maps for the visual exploration of molecular compounds

Visual exploration of scientific data in life science area is a growing research field due to the large amount of available data. The Kohonen’s Self Organizing Map (SOM) is a widely used tool for visualization of multidimensional data. In this paper we present a fast learning algorithm for SOMs that uses a simulated annealing method to adapt the learning parameters. The algorithm has been adopted in a data analysis framework for the generation of similarity maps. Such maps provide an effective tool for the visual exploration of large and multi-dimensional input spaces. The approach has been applied to data generated during the High Throughput Screening of molecular compounds; the generated maps allow a visual exploration of molecules with similar topological properties. The experimental analysis on real world data from the National Cancer Institute shows the speed up of the proposed SOM training process in comparison to a traditional approach. The resulting visual landscape groups molecules with similar chemical properties in densely connected regions.

Spin spaces and positive decomposition of linear maps on ordered Banach spaces

Spin factors and generalizations are used to revisit positive generation of B(E, F), where E and F are ordered Banach spaces. Interior points of B(E, F)+ are discussed and in many cases it is seen that positive generation of B(E, F) is controlled by spin structure in F when F is a JBW-algebra.

The synthesis of chiral N-heterocyclic carbene–borane and –diorganoborane complexes and their use in the asymmetric reduction of ketones

Chiral N-heterocyclic carbene–borane complexes have been synthesised, and have been shown to reduce ketones with Lewis acid promotion. Chiral N-heterocyclic carbene–borane and –diorganoborane complexes can reduce ketones with enantioselectivities up to 75% and 85% ee, respectively.

Conservation strategy maps: a tool to facilitate biodiversity action planning illustrated using the heath fritillary butterfly

1. The UK Biodiversity Action Plan (UKBAP) identifies invertebrate species in danger of national extinction. For many of these species, targets for recovery specify the number of populations that should exist by a specific future date but offer no procedure to plan strategically to achieve the target for any species. 2. Here we describe techniques based upon geographic information systems (GIS) that produce conservation strategy maps (CSM) to assist with achieving recovery targets based on all available and relevant information. 3. The heath fritillary Mellicta athalia is a UKBAP species used here to illustrate the use of CSM. A phase 1 habitat survey was used to identify habitat polygons across the county of Kent, UK. These were systematically filtered using relevant habitat, botanical and autecological data to identify seven types of polygon, including those with extant colonies or in the vicinity of extant colonies, areas managed for conservation but without colonies, and polygons that had the appropriate habitat structure and may therefore be suitable for reintroduction. 4. Five clusters of polygons of interest were found across the study area. The CSM of two of them are illustrated here: the Blean Wood complex, which contains the existing colonies of heath fritillary in Kent, and the Orlestone Forest complex, which offers opportunities for reintroduction. 5. Synthesis and applications. Although the CSM concept is illustrated here for the UK, we suggest that CSM could be part of species conservation programmes throughout the world. CSM are dynamic and should be stored in electronic format, preferably on the world-wide web, so that they can be easily viewed and updated. CSM can be used to illustrate opportunities and to develop strategies with scientists and non-scientists, enabling the engagement of all communities in a conservation programme. CSM for different years can be presented to illustrate the progress of a plan or to provide continuous feedback on how a field scenario develops.

Total synthesis of (+/-) maculalactone A, maculalactone B and maculalactone C and the determination of the absolute configuration of natural (+) maculalactone A by asymmetric synthesis

Maculalactones A, B and C from the marine cyanobacterium Kyrtuthrix maculans are amongst the only compounds based on the tribenzylbutyrolactone skeleton known in nature and (+) maculalactone A from the natural source possesses significant biological activity against various marine herbivores and marine settlers. We now report a concise synthesis of racemic maculalactone A in five steps from inexpensive starting materials. Maculalactones B and C were synthesized by a minor modification to this procedure, and the synthetic design also permitted an asymmetric synthesis of maculalactone A to be achieved in around 85% ee. The (+) and (-) enantiomers of maculalactone A were assigned, respectively, to the S and R configurations on the basis of the chiral selectivity expected for catecholborane reduction of an unsymmetrical ketone in the presence of Corey's oxazoborolidine catalyst. Surprisingly, it appeared that natural (+) maculalactone A was biosynthesized in K. maculans in a partially racemic form, comprising ca. 90-95% of the (S) enantiomer and 5-10% of its (R) enantiomer. Coincidentally therefore, the percentage enantiomeric excess of the product obtained from asymmetric synthesis almost exactly matched that found in nature. (C) 2004 Elsevier Ltd. All rights reserved.

Asymmetric synthesis of (1R,2S,3R)-3-methylcispentacin and (1S,2S,3R)-3-methyltranspentacin by kinetic resolution of tert-butyl (+/-)-3-methylcyclopentene-1-carboxylate

Conjugate addition of lithium dibenzylamide to tert-butyl (+/-)-3-methylcyclopentene-1-carboxylate occurs with high levels of stereocontrol, with preferential addition of lithium dibenzylamide to the face of the cyclic alpha,beta-unsaturated acceptor anti- to the 3-methyl substituent. High levels of enantiorecognition are observed between tert-butyl (+/-)-3-methylcyclopentene-1-carboxylate and an excess of lithium (+/-)-N-benzyl-N-alpha-methylbenzylamide (10 eq.) (E > 140) in their mutual kinetic resolution, while the kinetic resolution of tert-butyl (+/-)-3-methylcyclopentene-1-carboxylate with lithium (S)-N-benzyl-N-alpha-methylbenzylamide proceeds to give, at 51% conversion, tert-butyl (1R, 2S, 3R,alphaS)-3-methyl-2-N-benzyl-N-alpha-methylbenzylaminocyclopentane-1-c arboxylate consistent with E > 130, and in 39% yield and 99 +/- 0.5% de after purification. Subsequent deprotection by hydrogenolysis and ester hydrolysis gives (1R, 2S, 3R)-3-methylcispentacin in > 98% de and 98 +/- 1% ee. Selective epimerisation of tert-butyl (1R, 2S, 3R, alphaS)-3-methyl-2-N- benzyl-N-alpha-methylbenzylaminocyclopentane-1-carboxylate by treatment with (KOBu)-Bu-t in (BuOH)-Bu-t gives tert-butyl (1S, 2S, 3R, alphaS)-3-methyl-2-N-benzyl-N-alpha-methylbenzylaminocyclopentane-1-carb oxylate in quantitative yield and in > 98% de, with subsequent deprotection by hydrogenolysis and ester hydrolysis giving (1S, 2S, 3R)-3-methyltranspentacin hydrochloride in > 98% de and 97 +/- 1% ee.

Stereodivergent approach to the asymmetric synthesis of bacillariolides: A formal synthesis of ent-bacillariolide II

Asymmetric synthesis of densely functionalized bicyclic frameworks for entry into bacillariolides I/III and ent-bacillariolide II is reported. The key features are ring-closing metathesis of a pair of diastereomerically related dienes obtained through a stereodivergent route from a R-(+)-glyceraldehyde derivative, transformation of a nonstereoselective cyclopentene ester enolate alkylation process to a completely stereoselective one through alkylation of a bulky ester enolate with a bulky electrophile, and a remote silyloxymethyl group directed epoxidation.