The Gauss-Green theorem in stratified groups

We lay the foundations for a theory of divergence-measure fields in noncommutative stratified nilpotent Lie groups. Such vector fields form a new family of function spaces, which generalize in a sense the $BV$ fields. They provide the most general setting to establish Gauss-Green formulas for vector fields of low regularity on sets of finite perimeter. We show several properties of divergence-measure fields in stratified groups, ultimately achieving the related Gauss-Green theorem.Comment: 69 page

A Clustering System for Dynamic Data Streams Based on Metaheuristic Optimisation

open access articleThis article presents the Optimised Stream clustering algorithm (OpStream), a novel approach to cluster dynamic data streams. The proposed system displays desirable features, such as a low number of parameters and good scalability capabilities to both high-dimensional data and numbers of clusters in the dataset, and it is based on a hybrid structure using deterministic clustering methods and stochastic optimisation approaches to optimally centre the clusters. Similar to other state-of-the-art methods available in the literature, it uses “microclusters” and other established techniques, such as density based clustering. Unlike other methods, it makes use of metaheuristic optimisation to maximise performances during the initialisation phase, which precedes the classic online phase. Experimental results show that OpStream outperforms the state-of-the-art methods in several cases, and it is always competitive against other comparison algorithms regardless of the chosen optimisation method. Three variants of OpStream, each coming with a different optimisation algorithm, are presented in this study. A thorough sensitive analysis is performed by using the best variant to point out OpStream’s robustness to noise and resiliency to parameter changes

How Demanding Should Equality of Opportunity Be, and How Much Have We Achieved?

[Excerpt] This chapter proposes tests of various notions of equality of opportunity and applies them to intergenerational income data for the United States and Britain. Agreement is widespread that equality of opportunity holds in a society if the chances that individuals have to succeed depend only on their own efforts and not on extraneous circumstances that may inhibit or expand those chances. What is contentious, however, is what constitutes effort and circumstances. Most people, we think, would say that the social connections of an individual\u27s parents would be included among circumstances: equality of opportunity is incomplete if some individuals get ahead because they have well-connected parents. This and other channels through which circumstances affect income opportunities in an intergenerational context are discussed in Section 2. Section 3 then formulates four, increasingly stringent criteria for equality of opportunity. In Section 4, we turn to an empirical implementation of these criteria to test for equality of opportunity in the United States and Britain. The results, presented in Section 5, provide only the weakest of support for equality of opportunity in the United States and no support at all in Britain. Concluding remarks are presented in Section 6

An Analysis of Students Error in Solving PISA 2012 and Its Scaffolding

Based on PISA survey in 2012, Indonesia was only placed on 64 out of 65 participating countries. The survey suggest that the students' ability of reasoning, spatial orientation, and problem solving are lower compare with other participants countries, especially in Shouth East Asia. Nevertheless, the result of PISA does not elicit clearly on the students' inability in solving PISA problem such as the location and the types of student's errors. Therefore, analyzing students' error in solving PISA problem would be essential countermeasure to help the students in solving mathematics problems and to develop scaffolding. Based on the data analysis, it is found that there are 5 types of error which is made by the subject. They consist of reading error, comprehension error, transformation error, process skill error, and encoding error. The most common mistake that subject do is encoding error with a percentage of 26%. While reading is the fewest errors made by the subjects that is only 12%. The types of given scaffolding was explaining the problem carefully and making a summary of new words and find the meaning of them, restructuring problem-solving strategies and reviewing the results of the completion of the problem

Grafting vigour is associated with DNA de-methylation in eggplant.

In horticulture, grafting is a popular technique used to combine positive traits from two different plants. This is achieved by joining the plant top part (scion) onto a rootstock which contains the stem and roots. Rootstocks can provide resistance to stress and increase plant production, but despite their wide use, the biological mechanisms driving rootstock-induced alterations of the scion phenotype remain largely unknown. Given that epigenetics plays a relevant role during distance signalling in plants, we studied the genome-wide DNA methylation changes induced in eggplant (Solanum melongena) scion using two interspecific rootstocks to increase vigour. We found that vigour was associated with a change in scion gene expression and a genome-wide hypomethylation in the CHH context. Interestingly, this hypomethylation correlated with the downregulation of younger and potentially more active long terminal repeat retrotransposable elements (LTR-TEs), suggesting that graft-induced epigenetic modifications are associated with both physiological and molecular phenotypes in grafted plants. Our results indicate that the enhanced vigour induced by heterografting in eggplant is associated with epigenetic modifications, as also observed in some heterotic hybrids