On the prescribed scalar curvature problem on Sn: The degree zero case

In this Note, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere $S^n$, $n?3$. We give new existence and multiplicity results based on a new Euler–Hopf formula type. Our argument also has the advantage of extending the well known results due to Y. Li (1995) [10].     

Influence of new effective allelochemicals on the distribution of Cleome arabica L. community in nature

Abstract

New allelochemicals were identified through bio-guided fractionation from the ethyl acetate of seeds extracts, which was the most autotoxic compared to the other plant parts. Phytochemical investigation of the seeds extracts of C. arabica by spectroscopy analyses has led to identify two new dammarane type triterpenes (4 and 9), with nine known analogues (1???3, 5???8, 10 and 11), a new cucurbitane triterpene (12), acylated dehydrodiconiferyl alcohol (13), and three highly oxygenated flavonols (14?16). The most autotoxic compounds on germination and seedling growth were elucidated as dammarane type triterpenes. However, less autotoxic effect was recorded by an inhibition under 50% for most of the identified flavonoids. These results suggest that those autotoxic substances may be used as a new bio-herbicide that may contribute to manage the distribution of C. arabica in agronomic field.

     

Ensemble feature selection for high dimensional data: a new method and a comparative study

The curse of dimensionality is based on the fact that high dimensional data is often difficult to work with. A large number of features can increase the noise of the data and thus the error of a learning algorithm. Feature selection is a solution for such problems where there is a need to reduce the data dimensionality. Different feature selection algorithms may yield feature subsets that can be considered local optima in the space of feature subsets. Ensemble feature selection combines independent feature subsets and might give a better approximation to the optimal subset of features. We propose an ensemble feature selection approach based on feature selectors’ reliability assessment. It aims at providing a unique and stable feature selection without ignoring the predictive accuracy aspect. A classification algorithm is used as an evaluator to assign a confidence to features selected by ensemble members based on their associated classification performance. We compare our proposed approach to several existing techniques and to individual feature selection algorithms. Results show that our approach often improves classification performance and feature selection stability for high dimensional data sets.     

Modeling the beta distribution in short intervals

Lithuanian Mathematical Journal - We prove that any beta distribution can be simulated by means of a sequence of distributions defined via multiplicative functions in a short interval.