Correcting the optimally selected resampling-based error rate: A smooth analytical alternative to nested cross-validation

High-dimensional binary classification tasks, e.g. the classification of microarray samples into normal and cancer tissues, usually involve a tuning parameter adjusting the complexity of the applied method to the examined data set. By reporting the performance of the best tuning parameter value only, over-optimistic prediction errors are published. The contribution of this paper is two-fold. Firstly, we develop a new method for tuning bias correction which can be motivated by decision theoretic considerations. The method is based on the decomposition of the unconditional error rate involving the tuning procedure. Our corrected error estimator can be written as a weighted mean of the errors obtained using the different tuning parameter values. It can be interpreted as a smooth version of nested cross-validation (NCV) which is the standard approach for avoiding tuning bias. In contrast to NCV, the weighting scheme of our method guarantees intuitive bounds for the corrected error. Secondly, we suggest to use bias correction methods also to address the bias resulting from the optimal choice of the classification method among several competitors. This method selection bias is particularly relevant to prediction problems in high-dimensional data. In the absence of standards, it is common practice to try several methods successively, which can lead to an optimistic bias similar to the tuning bias. We demonstrate the performance of our method to address both types of bias based on microarray data sets and compare it to existing methods. This study confirms that our approach yields estimates competitive to NCV at a much lower computational price

Unbiased split selection for classification trees based on the Gini Index

The Gini gain is one of the most common variable selection criteria in machine learning. We derive the exact distribution of the maximally selected Gini gain in the context of binary classification using continuous predictors by means of a combinatorial approach. This distribution provides a formal support for variable selection bias in favor of variables with a high amount of missing values when the Gini gain is used as split selection criterion, and we suggest to use the resulting p-value as an unbiased split selection criterion in recursive partitioning algorithms. We demonstrate the efficiency of our novel method in simulation- and real data- studies from veterinary gynecology in the context of binary classification and continuous predictor variables with different numbers of missing values. Our method is extendible to categorical and ordinal predictor variables and to other split selection criteria such as the cross-entropy criterion

Toxicity of Pb and of Pb/Cd combination on the springtail Folsomia candida in natural soils: Reproduction, growth and bioaccumulation as indicators

The toxicity of Pb and Cd+Pb was assessed on the Collembola F. candida in two cultivated soils (SV and AU) with low organic matter (OM) content and circumneutral to basic pH, and an acid forested soil (EPC) with high OM content. Collembola reproduction and growth as well as metal content in Collembola body, in soil, exchangeable fraction and soil solutions, pH and DOC were investigated. Pb and Cd+Pb were the highest in exchangeable fraction and soil solution of the acidic soils. Soil solution pH decreased after metal spiking in every soil due to metal adsorption, which was similar for Cd and the highest in AU for Pb. With increasing Pb and Cd+Pb, the most important reproduction decrease was in EPC soil. The LOEC for reproduction after metal addition was 2400 (Pb) and 200/2400 (Cd/Pb), 1200 and 100/1200, 300 and 100/1200 μg g−1 for AU, SV and EPC, respectively. The highest and the lowest Pb toxicity was observed for EPC and AU bulk soil, respectively. The metal in Collembola increased with increasing soil concentration, except in AU, but the decreasing BFsolution with increasing concentrations indicates a limited metal transfer to Collembola or an increased metal removal. Loading high Pb concentrations decreases Cd absorption by the Collembola, but the reverse was not true. The highest Pb toxicity in EPC can be explained by pH and OM content. Because of metal complexation, OM might have a protective role but its ingestion by Collembola lead to higher toxicity. Metal bioavailability in Collembola differs from soil solution indicating that soil solution is not sufficient to evaluate toxicity in soil organisms. The toxicity as a whole decreased when metals were combined, except for Pb in AU, due to adsorption competition between Cd and Pb on clay particles and OM sites in AU and EPC soils, respectively

Determining cadmium critical concentrations in natural soils by assessing Collembola mortality, reproduction and growth

The toxicity of cadmium for the Collembola Folsomia candida was studied by determining the effects of increasing Cd concentrations on growth, survival and reproduction in three cultivated and forested soils with different pH (4.5–8.2) and organic matter content (1.6–16.5%). The Cd concentration in soil CaCl2 exchangeable fraction, in soil solution and in Collembola body was determined. At similar total soil concentrations, the Cd concentration in soil solutions strongly decreased with increasing pH. Reproduction was the most sensitive parameter. Low organic matter content was a limiting factor for reproduction. Effect of Cd on reproduction was better described by soil or body concentrations than by soil solution concentration. Values of EC50-Repro expressed on the basis of nominal soil concentration were 182, 111 and 107 μg g−1, respectively, for a carbonated cultivated soil (AU), an acid forested soil with high organic matter (EPC) and a circumneutral cultivated soil with low organic content (SV). Sensitivity to Cd was enhanced for low OM content and acidic pH. The effect of Cd on reproduction is not directly related to Cd concentration in soil solution for carbonated soil: a very low value is found for EC50-Repro (0.17) based on soil solution for the soil with the highest pH (AU; pH=8.2). Chronic toxicity cannot be predicted on the basis of soluble fractions. Critical concentrations were 8×10−5, 1.1, 0.3 μg mL−1, respectively, for AU, EPC and SV soils

Evidence of Springwater Acidification in the Vosges Mountains (North-East of France): Influence of Bedrock Buffering Capacity

Investigations on springwater acidity were carried out in the Vosges mountains (north-eastern France). Acid or poorly buffered spring and streamwaters were detected in the same area. The proportion of acid springwaters (pH < 5.6) is about 20% among 220 springs. The springwater pH on granite are equally spread between 5.0 and 6.8 whereas on sandstone a majority of springs is in the range 5.6 to 6.2. As a whole, but mainly on sandstone, from the 1960's to 1990's, the shape of the pH distributions shifts toward greater acidity. In the sandstone area, trends in pH, alkalinity, total hardness (corresponding to divalent cations), sulfate and nitrate were considered over the 30 yr period (1963-1996) in relation to the bedrock chemical composition. Kendall seasonal tau coefficients indicate that decreasing trends were significant for the first three parameters. Linear regression on the smoothed mean value revealed 18 and 90% decrease for pH and alkalinity respectively, for springwaters draining poor-base cation sandstone whereas only 8 and 30% decrease respectively, was observed on clay-enriched sandstone. On silica-enriched sandstone, alkalinity began to decrease in the early 70's as well as pH. Loss of alkalinity only occurred in the early 80's for springs draining clay enriched sandstone. This can be interpreted as a titration process by acid atmospheric inputs of the buffering capacity of weathering and exchange processes in the soils and the catchment bedrock. The nitrate presents an increasing step in the early seventies but possibly as a result of change in analytical technics and/or increase in atmospheric inputs mainly resulting from increase in fertiliser inputs in agricultural areas or in car traffic. Surprisingly no change in sulfate was noticed in any groups of springs probably as a result of the adsorption/mobilisation in the soils. These long-term trends in spring waters (1963-1996) confirmed the soil and streamwater acidification trends already mentioned in this region, in relation to acid atmospheric inputs since no climate nor forestry practice changes have been detected over the period. Moreover, in spite of acid atmospheric input reductions, no recovery can presently be detected

A Soergel-like category for complex reflection groups of rank one

We introduce analogues of Soergel bimodules for complex reflection groups of rank one. We give an explicit parametrization of the indecomposable objects of the resulting category and give a presentation of its split Grothendieck ring by generators and relations. This ring turns out to be an extension of the Hecke algebra of the reflection group $W$ and a free module of rank $|W| (|W|-1)+1$ over the base ring. We also show that it is a generically semisimple algebra if defined over the complex numbers.Comment: 24 pages. Comments welcome

Evolution and relationships of the conifer seed cone telemachus: Evidence from the triassic of antarctica

The seed cone Telemachus is known from several Triassic localities in Gondwana. New specimens from two localities in Antarctica provide additional information about the type species, Telemachus elongatus, based on details of morphology and anatomy revealed by using a modified transfer technique on the compressed plants. Seed cones of T. elongatus are up to 6.0 cm long and characterized by conspicuous, elongate bracts. A second Antarctic species, described here as Telemachus antarcticus, is segregated, based on a shorter bract and differences in cone size. Newly recognized features of the genus include the shape, size, and disposition of the ovules; vascularization of the ovuliferous complex; and scale and bract histology. As a result of this new information, it is now possible to compare Telemachus with the permineralized Middle Triassic conifer seed cone Parasciadopitys from the Central Transantarctic Mountains. The similarities between the two genera make it possible to relate organs in different preservational modes and to develop a more complete concept for this widely distributed Gondwana conifer. Placing the Telemachus plant within a phylogenetic context makes it possible to evaluate the relationship with other so-called transitional conifers, an informal group that has been interpreted as intermediate between Paleozoic and modern conifers.Fil: Escapa, Ignacio Hernán. University of Kansas; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Decombeix, Anne-Laure. University of Kansas; Estados UnidosFil: Taylor, Edith L.. University of Kansas; Estados UnidosFil: Taylor, Thomas N.. University of Kansas; Estados Unido

Secondary Growth in Vertebraria Roots from the Late Permian of Antarctica: A Change in Developmental Timing

This is the publisher's version, also available electronically from http://www.jstor.org/stable/10.1086/597784.Permineralized Vertebraria roots from the late Permian of the Central Transantarctic Mountains, Antarctica, are investigated to understand the unusual vascular anatomy of the genus. The specimens range from ∼1 mm to several centimeters in diameter and illustrate all the stages of secondary growth. Our observations confirm previous hypotheses on the development of these roots and suggest that their unique anatomy is the result of a change in developmental timing. Vertebraria is characterized by a vascular cambium that remains discontinuous through several growth seasons, leading to the formation of lacunae alternating in cross section with wedges of secondary vascular tissues. The bifacial nature of the cambium is confirmed by the presence of well‐developed secondary phloem composed of longitudinally elongated cells and uniseriate parenchymatous rays. In some of the largest specimens, a continuous vascular cylinder is formed by the differentiation of cambium from parenchymatous cells bordering the lacunae. The new specimens provide additional information on the secondary xylem anatomy and vascular connection to lateral roots

Epicormic Schoots in a Permian Gymnosperm from Antarctica

This is the publisher's version. Shared with permission, it is also available electronically from: http://dx.doi.org/10.1086/654849Two anatomically preserved gymnosperm trunks with clusters of epicormic shoots are described from the Late Permian of Antarctica. The best-preserved trunk is 14 cm long. It has a small circular parenchymatous pith and 9 cm of secondary xylem that contains at least 50 growth rings. The second specimen is slightly smaller (11 3 8 cm) and has 20 growth rings. Both specimens have pycnoxylic wood and produced more than 50 small shoots in a delimited zone on the surface of the trunk. Shoots have a wide parenchymatous pith that may be solid to septate with endarch primary xylem forming 8–10 sympodia and a small amount of secondary xylem similar to that of the parent trunk. The shoots branch and increase in number toward the outside of the trunk. Evidence based on anatomical comparisons and association at the site indicates that the specimens probably represent trunks of some glossopterid, the dominant group of seed ferns during the Permian in Gondwana. This is the first report of clusters of epicormic shoots in a Paleozoic gymnosperm. The ability to produce a large number of young shoots that were capable of developing into new branches indicates that these high-latitude trees possessed an architectural plasticity that allowed them to respond quickly to short- or longterm environmental stress