Contingent kernel density estimation

Kernel density estimation is a widely used method for estimating a distribution based on a sample of points drawn from that distribution. Generally, in practice some form of error contaminates the sample of observed points. Such error can be the result of imprecise measurements or observation bias. Often this error is negligible and may be disregarded in analysis. In cases where the error is non-negligible, estimation methods should be adjusted to reduce resulting bias. Several modifications of kernel density estimation have been developed to address specific forms of errors. One form of error that has not yet been addressed is the case where observations are nominally placed at the centers of areas from which the points are assumed to have been drawn, where these areas are of varying sizes. In this scenario, the bias arises because the size of the error can vary among points and some subset of points can be known to have smaller error than another subset or the form of the error may change among points. This paper proposes a "contingent kernel density estimation" technique to address this form of error. This new technique adjusts the standard kernel on a point-by-point basis in an adaptive response to changing structure and magnitude of error. In this paper, equations for our contingent kernel technique are derived, the technique is validated using numerical simulations, and an example using the geographic locations of social networking users is worked to demonstrate the utility of the method.     

Multiclass molecular cancer classification by kernel subspace methods with effective kernel parameter selection

Microarray techniques provide new insights into molecular classification of cancer types, which is critical for cancer treatments and diagnosis. Recently, an increasing number of supervised machine learning methods have been applied to cancer classification problems using gene expression data. Support vector machines (SVMs), in particular, have become one of the most effective and leading methods. However, there exist few studies on the application of other kernel methods in the literature. We apply a kernel subspace (KS) method to multiclass cancer classification problems, and assess its validity by comparing it with multiclass SVMs. Our comparative study using seven multiclass cancer datasets demonstrates that the KS method has high performance that is comparable to multiclass SVMs. Furthermore, we propose an effective criterion for kernel parameter selection, which is shown to be useful for the computation of the KS method.     

Estrone in Olea europaea kernel

The estrogen of the olive kernel and of commercial oils has been investigated. A crystalline estrone has been isolated from olive kernel. An estrogen ester has been assayed in olive oil and a free estrone in corn oil.     

Control of kernel weight and kernel water relations by post-flowering source-sink ratio in maize

The maize (Zea mays L.) kernel undergoes large changes in water content during its development. Whether such changes regulate the pattern of kernel development or are simply a consequence of it has not yet been established because other factors, such as assimilate supply, can also affect the rate and duration of kernel growth. This study was conducted to determine whether variation in kernel weight (KW) in response to source-sink treatments is mediated by a change in kernel water relations. Two hybrids were sown at three stand densities (one, eight and 18 plants m-2), and kernel numbers were restricted to control the post-flowering source-sink ratio within each stand density. Kernel development and water relations [water content, water potential (psiw), osmotic potential (psis) and turgor] were monitored throughout grain filling. Final KW varied from 253 to 372 mg per kernel in response to source-sink treatments. For both genotypes, variation in KW was a result of a change in kernel growth rate (r2 = 0.91; P < 0.001) and not in the duration of kernel filling. Final KW was closely correlated with maximum kernel water content (r2 = 0.94; P < 0.001) achieved during rapid dry matter accumulation. However, variation in KW was not reflected in kernel water status parameters (psiw, psis or turgor), which remained fairly stable across treatments. These results indicate that maximum water content provides an easily quantifiable measure of kernel sink capacity in maize. Kernel water status parameters may affect the duration of grain filling, but have no discernible impact on kernel growth rate.     

α-Galactosidase from coconut kernel

The properties of two forms, A and B, of (α-galactosidase from coconut kernel are described. They are interconvertible and in the absence of KCl the lower MW form, B, is favoured. When B is mixed with KCl and an enzymatically inactive protein fraction, C, from the kernel, there is almost complete conversion to A.     

Peanut-pod mycoflora and kernel infection

Summary The mycoflora in soil clinging to dry pods of peanuts of the Spanish variety Argentine was sampled in 2 experiments by serially washing pods for increasing periods in changes of sterile water. Of the 9 principal fungi found,Aspergillus niger, A. flavus, A. terreus, Rhizopus spp. andSclerotium bataticola were present initially in relatively small numbers and decreased rapidly in subsequent dilutions. This decrease paralleled a decrease in weight of suspended material and in percentage of soil and organic particles greater than 0.016 mm in size.Penicillium funiculosum, P. rubrum, P. citrinum, andFusarium spp. were found in large numbers and increased or slowly decreased in numbers in subsequent dilutions. In some instances variations in numbers followed trends of percentages of soil and organic particles less than 0.016 mm in size.When dry pods with this known mycoflora were allowed to hydrate over a 6-day period at 26°, 32°, or 38°C, there was extensive pod penetration and kernel infection byA. niger, A. flavus, S. bataticola andRhizopus spp. but not by other fungi. The degree ofA. flavus andA. niger infection increased with increasing temperatures.Approved by the Director as Journal Series Paper No. 135.     

Reduced multiple empirical kernel learning machine

Multiple kernel learning (MKL) is demonstrated to be flexible and effective in depicting heterogeneous data sources since MKL can introduce multiple kernels rather than a single fixed kernel into applications. However, MKL would get a high time and space complexity in contrast to single kernel learning, which is not expected in real-world applications. Meanwhile, it is known that the kernel mapping ways of MKL generally have two forms including implicit kernel mapping and empirical kernel mapping (EKM), where the latter is less attracted. In this paper, we focus on the MKL with the EKM, and propose a reduced multiple empirical kernel learning machine named RMEKLM for short. To the best of our knowledge, it is the first to reduce both time and space complexity of the MKL with EKM. Different from the existing MKL, the proposed RMEKLM adopts the Gauss Elimination technique to extract a set of feature vectors, which is validated that doing so does not lose much information of the original feature space. Then RMEKLM adopts the extracted feature vectors to span a reduced orthonormal subspace of the feature space, which is visualized in terms of the geometry structure. It can be demonstrated that the spanned subspace is isomorphic to the original feature space, which means that the dot product of two vectors in the original feature space is equal to that of the two corresponding vectors in the generated orthonormal subspace. More importantly, the proposed RMEKLM brings a simpler computation and meanwhile needs a less storage space, especially in the processing of testing. Finally, the experimental results show that RMEKLM owns a much efficient and effective performance in terms of both complexity and classification. The contributions of this paper can be given as follows: (1) by mapping the input space into an orthonormal subspace, the geometry of the generated subspace is visualized; (2) this paper first reduces both the time and space complexity of the EKM-based MKL; (3) this paper adopts the Gauss Elimination, one of the on-the-shelf techniques, to generate a basis of the original feature space, which is stable and efficient.     

Tissue-specific zein synthesis in maize kernel

Zein may account for as much as 10% of the total protein in the mature embryo of maize inbred W64A. This protein exhibited an electrophoretic pattern on SDS gels similar to that of the endosperm. Like the endosperm system, the synthesis of zein components in the embryo was controlled by the opaque-2 and floury-2 mutations. However, unlike zein synthesis in the endosperm, zein synthesis in the embryo could not be increased by nitrogen fertilizer. Variations in amino acid composition were observed between the zein components of the embryo and those of the endosperm.     

On identification of separable kernel systems

An identification procedure for special separable kernel systems is presented. The suitable definition of adequateness of a signal leads to a systematic treatment of the choice of inputs for identification.This work was supported by the Stiftung Volkswagenwerk grant number II/35 111. Prof. Dr.-Ing. W. v. Seelen was in charge of the project     

Extracting glycan motifs using a biochemicallyweighted kernel

Carbohydrates, or glycans, are one of the most abundant and structurally diverse biopolymers constitute the third major class of biomolecules, following DNA and proteins. However, the study of carbohydrate sugar chains has lagged behind compared to that of DNA and proteins, mainly due to their inherent structural complexity. However, their analysis is important because they serve various important roles in biological processes, including signaling transduction and cellular recognition. In order to glean some light into glycan function based on carbohydrate structure, kernel methods have been developed in the past, in particular to extract potential glycan biomarkers by classifying glycan structures found in different tissue samples. The recently developed weighted qgram method (LK-method) exhibits good performance on glycan structure classification while having limitations in feature selection. That is, it was unable to extract biologically meaningful features from the data. Therefore, we propose a biochemicallyweighted tree kernel (BioLK-method) which is based on a glycan similarity matrix and also incorporates biochemical information of individual q-grams in constructing the kernel matrix. We further applied our new method for the classification and recognition of motifs on publicly available glycan data. Our novel tree kernel (BioLK-method) using a Support Vector Machine (SVM) is capable of detecting biologically important motifs accurately while LK-method failed to do so. It was tested on three glycan data sets from the Consortium for Functional Glycomics (CFG) and Kyoto Encyclopedia of Genes and Genomes (KEGG) GLYCAN and showed that the results are consistent with the literature. The newly developed BioLK-method also maintains comparable classification performance with the LK-method. Our results obtained here indicate that the incorporation of biochemical information of q-grams further shows the flexibility and capability of the novel kernel in feature extraction, which may aid in the prediction of glycan biomarkers.     

Ligand-based virtual screening using binary kernel discrimination

This paper discusses the use of a machine-learning technique called binary kernel discrimination (BKD) for virtual screening in drug- and pesticide-discovery programmes. BKD is compared with several other ligand-based tools for virtual screening in databases of 2D structures represented by fragment bit-strings, and is shown to provide an effective, and reasonably efficient, way of prioritising compounds for biological screening.     

Sparse kernel methods for high-dimensional survival data

Sparse kernel methods like support vector machines (SVM) have been applied with great success to classification and (standard) regression settings. Existing support vector classification and regression techniques however are not suitable for partly censored survival data, which are typically analysed using Cox's proportional hazards model. As the partial likelihood of the proportional hazards model only depends on the covariates through inner products, it can be 'kernelized'. The kernelized proportional hazards model however yields a solution that is dense, i.e. the solution depends on all observations. One of the key features of an SVM is that it yields a sparse solution, depending only on a small fraction of the training data. We propose two methods. One is based on a geometric idea, where-akin to support vector classification-the margin between the failed observation and the observations currently at risk is maximised. The other approach is based on obtaining a sparse model by adding observations one after another akin to the Import Vector Machine (IVM). Data examples studied suggest that both methods can outperform competing approaches. AVAILABILITY: Software is available under the GNU Public License as an R package and can be obtained from the first author's website http://www.maths.bris.ac.uk/~maxle/software.html.