Linguistic prejudice and discrimination in Brazilian Portuguese and beyond : suggestions and recommendations

In this article we make a distinction between the prejudice and discrimination towards (a) different languages and their speakers and (b) different non-standard varieties of the same language and their speakers, and argue that while the discrimination and prejudice towards (a) have been denounced by international institutions and both national and international laws are in place to guarantee the rights of speakers of different languages, the same protection has not been afforded to speakers of non-standard varieties of a language. We examine a specific case of this type of linguistic prejudice in Brazil. We discuss the effectiveness of efforts of linguists to combat linguistic prejudice based on the principle of error correction (Labov 1982) and, drawing on work by Cameron (2012) and Bourdieu (1986), suggest that linguistic prejudice cannot be disentangled from other types of prejudice and that linguists need to have a much deeper understanding of and engagement with the values attached to linguistic forms. We conclude with a number of suggestions and recommendations in order to effectively combat linguistic prejudice

Persistence modules, shape description, and completeness

Persistence modules are algebraic constructs that can be used to describe the shape of an object starting from a geometric representation of it. As shape descriptors, persistence modules are not complete, that is they may not distinguish non-equivalent shapes. In this paper we show that one reason for this is that homomorphisms between persistence modules forget the geometric nature of the problem. Therefore we introduce geometric homomorphisms between persistence modules, and show that in some cases they perform better. A combinatorial structure, the $H_0$-tree, is shown to be an invariant for geometric isomorphism classes in the case of persistence modules obtained through the 0th persistent homology functor

Graphic-based concept retrieval

Two ways of expressing concepts in the context of image retrieval are presented. One, Keypics, is on the side of an image owner, who wants the image itself to be found on the Web; the second, Trittico, is on the side of the image searcher. Both are based on the paradigm of human intermediation for overcoming the semantic gap. Both require tools capable of qualitative analysis, and have been experimented by using persistent homology

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr