Towards a certified computation of homology groups for digital images

International audienceIn this paper we report on a project to obtain a verified computation of homology groups of digital images. The methodology is based on program- ming and executing inside the COQ proof assistant. Though more research is needed to integrate and make efficient more processing tools, we present some examples partially computed in COQ from real biomedical images

Formalization of a normalization theorem in simplicial topology

In this paper we present a complete formalization of the Normalization Theorem, a result in Algebraic Simplicial Topology stating that there exists a homotopy equivalence between the chain complex of a simplicial set, and a smaller chain complex for the same simplicial set, called the normalized chain complex. Even if the Normalization Theorem is usually stated as a higher-order result (with a Category Theory flavor) we manage to give a first-order proof of it. To this aim it is instrumental the introduction of an algebraic data structure called simplicial polynomial. As a demonstration of the validity of our techniques we developed a formal proof in the ACL2 theorem prover.Ministerio de Ciencia e Innovación MTM2009-13842European Commission FP7 STREP project ForMath n. 24384

Distant Localities: The Rhetorical Contradictions Of Local Food Narratives

This dissertation explores the rhetorical construction of the local food movement through the narrative genre of the food exposé. On its face, local food appears to be a grassroots movement, and yet, through an analysis of the tropes used to describe and construct the movement, another story emerges – one intended for elite audiences. Using narrative critique, this project explores both the narratives of local food, as well as the deployment of that narrative into the material world and in the construction of particular identities. Ultimately, I argue that the narratives of local food give the impression that this way of eating and living is for everyone, while simultaneously entrenching an elite position that threatens the movement’s ability to forge identification with a wider audience. Thus, this dissertation highlights how considering narratives across texts reveals rhetorical inconsistencies that undermine both the rhetorical and material goals of the local food movement