Combinatorial presentation of multidimensional persistent homology
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The starting point for this project is the article of Kathryn Hess [11]. In this article, a homotopic version of monadic descent is developed. In the classical setting, one constructs a category D(𝕋) of coalgebras in the Eilenberg-Moore category of ...
K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other fields of mathematics, like spaces and (not necessarily c ...
In homological algebra, to understand commutative rings R, one studies R-modules, chain complexes of R-modules and their monoids, the differential graded R-algebras. The category of R-modules has a rich structure, but too rigid to efficiently work with hom ...
Let A be a commutative noetherian ring of Krull dimension 3. We give a necessary and sufficient condition for A-projective modules of rank 2 to be free. Using this, we show that all the finitely generated projective modules over the algebraic real 3-sphere ...
In an application of the notion of twisting structures introduced by Hess and Lack, we define twisted composition products of symmetric sequences of chain complexes that are degreewise projective and finitely generated. Let Q be a cooperad and let BP be th ...
Summary: ExpressionView is an R package that provides an interactive graphical environment to explore transcription modules identified in gene expression data. A sophisticated ordering algorithm is used to present the modules with the expression in a visua ...
In this paper, we use projectivity relative to kG-modules to define groups of relatively endotrivial modules, which are obtained by replacing the notion of projectivity with that of relative projectivity in the definition of ordinary endotrivial modules. T ...
In this paper we propose a novel wearable architecture based on the popular and proven I2C protocol. Our goal is to develop a modular approach towards wearable computing in a sense that users simply attach specific modules to their garments depending on th ...
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D-Finder 2 is a new tool for deadlock detection in concurrent systems based on effective invariant computation to approximate the effects of interactions among modules. It is part of the BIP framework, which provides various tools centered on a component-b ...
Ring modules are tensegrity systems that include a single strut circuit and recently, they have been shown to be viable systems for pedestrian bridges. Furthermore, their shape can be controlled using cable actuation. This paper focuses on the deployment o ...
