Simultaneous interval regression for K-nearest neighbor

International audienceIn some regression problems, it may be more reasonable to predict intervals rather than precise values. We are interested in finding intervals which simultaneously for all input instances x ∈X contain a β proportion of the response values. We name this problem simultaneous interval regression. This is similar to simultaneous tolerance intervals for regression with a high confidence level γ ≈ 1 and several authors have already treated this problem for linear regression. Such intervals could be seen as a form of confidence envelop for the prediction variable given any value of predictor variables in their domain. Tolerance intervals and simultaneous tolerance intervals have not yet been treated for the K-nearest neighbor (KNN) regression method. The goal of this paper is to consider the simultaneous interval regression problem for KNN and this is done without the homoscedasticity assumption. In this scope, we propose a new interval regression method based on KNN which takes advantage of tolerance intervals in order to choose, for each instance, the value of the hyper-parameter K which will be a good trade-off between the precision and the uncertainty due to the limited sample size of the neighborhood around each instance. In the experiment part, our proposed interval construction method is compared with a more conventional interval approximation method on six benchmark regression data sets

Certain subclasses of multivalent functions defined by new multiplier transformations

In the present paper the new multiplier transformations \mathrm{{\mathcal{J}% }}_{p}^{\delta }(\lambda ,\mu ,l) (\delta ,l\geq 0,\;\lambda \geq \mu \geq 0;\;p\in \mathrm{% }%\mathbb{N} )} of multivalent functions is defined. Making use of the operator $\mathrm{{\mathcal{J}}}_{p}^{\delta }(\lambda ,\mu ,l),$ two new subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$\textbf{\ }of multivalent analytic functions are introduced and investigated in the open unit disk. Some interesting relations and characteristics such as inclusion relationships, neighborhoods, partial sums, some applications of fractional calculus and quasi-convolution properties of functions belonging to each of these subclasses $\mathcal{P}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ and $\widetilde{\mathcal{P}}_{\lambda ,\mu ,l}^{\delta }(A,B;\sigma ,p)$ are investigated. Relevant connections of the definitions and results presented in this paper with those obtained in several earlier works on the subject are also pointed out

Female chromosome X mosaicism is age-related and preferentially affects the inactivated X chromosome

To investigate large structural clonal mosaicism of chromosome X, we analysed the SNP microarray intensity data of 38,303 women from cancer genome-wide association studies (20,878 cases and 17,425 controls) and detected 124 mosaic X events42Mb in 97 (0.25%) women. Here we show rates for X-chromosome mosaicism are four times higher than mean autosomal rates; X mosaic events more often include the entire chromosome and participants with X events more likely harbour autosomal mosaic events. X mosaicism frequency increases with age (0.11% in 50-year olds; 0.45% in 75-year olds), as reported for Y and autosomes. Methylation array analyses of 33 women with X mosaicism indicate events preferentially involve the inactive X chromosome. Our results provide further evidence that the sex chromosomes undergo mosaic events more frequently than autosomes, which could have implications for understanding the underlying mechanisms of mosaic events and their possible contribution to risk for chronic diseases

Detectable clonal mosaicism and its relationship to aging and cancer

In an analysis of 31,717 cancer cases and 26,136 cancer-free controls from 13 genome-wide association studies, we observed large chromosomal abnormalities in a subset of clones in DNA obtained from blood or buccal samples. We observed mosaic abnormalities, either aneuploidy or copy-neutral loss of heterozygosity, of >2 Mb in size in autosomes of 517 individuals (0.89%), with abnormal cell proportions of between 7% and 95%. In cancer-free individuals, frequency increased with age, from 0.23% under 50 years to 1.91% between 75 and 79 years (P = 4.8 × 10(-8)). Mosaic abnormalities were more frequent in individuals with solid tumors (0.97% versus 0.74% in cancer-free individuals; odds ratio (OR) = 1.25; P = 0.016), with stronger association with cases who had DNA collected before diagnosis or treatment (OR = 1.45; P = 0.0005). Detectable mosaicism was also more common in individuals for whom DNA was collected at least 1 year before diagnosis with leukemia compared to cancer-free individuals (OR = 35.4; P = 3.8 × 10(-11)). These findings underscore the time-dependent nature of somatic events in the etiology of cancer and potentially other late-onset diseases

Culture and grief: Ethnographic perspectives on ritual, relationships and remembering

This introduction to the special issue on Anthropology and grief explores the contributions of an ethnographic approach to the interdisciplinary study of grief. After a brief overview of previous anthropological research, we identify key themes emerging from this global collection of case studies: the benefits of long-term fieldwork in nuancing the complexity of grief and complicating cultural narratives that surround it; the ways in which emotional aspects of grief are shaped by cultural norms and by the manner of death; and the relationships between the living and dead, including ontologies of the dead and culturally sanctioned forms of remembering and forgetting.SCOPUS: ar.jDecretOANoAutActifinfo:eu-repo/semantics/publishe

Division polynomials and canonical local heights on hyperelliptic Jacobians

We generalize the division polynomials of elliptic curves to hyperelliptic Jacobians over the complex numbers. We construct them by using the hyperelliptic sigma function. Using the division polynomial, we describe a condition that a point on the Jacobian is a torsion point. We prove several properties of the division polynomials such as determinantal expressions and recurrence formulas. We also study relations among the sigma function, the division polynomials, and the canonical local height functions