Exploració per tema "Classificació AMS::55 Algebraic topology::55U Applied homological algebra and category theory"

Ara es mostren els items 1-7 de 7

    • A Cartan-Eilenberg approach to homotopical algebra 

      Pascual Gainza, Pere; Roig Martí, Agustín; Guillén Santos, Francisco; Navarro Aznar, Vicente (2008-09-01)
      Article
      Accés obert
      In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects ...

    • Colored spanning graphs for set visualization 

      Hurtado Díaz, Fernando Alfredo; Korman, Matias; Van Kreveld, Matias; Löffler, Maarten; Sacristán Adinolfi, Vera; Shioura, Akiyoshi; Silveira, Rodrigo Ignacio; Speckmann, Bettina; Tokuyama, Takeshi (2018-03)
      Article
      Accés obert
      We study an algorithmic problem that is motivated by ink minimization for sparse set visualizations. Our input is a set of points in the plane which are either blue, red, or purple. Blue points belong exclusively to the ...

    • Detection of dynamical states of neuronal networks with persistent homology tools 

      Gutiérrez Von Porat, Nils (Universitat Politècnica de Catalunya, 2021-07)
      Projecte Final de Màster Oficial
      Accés obert
      The Brunel network is a neuronal network model composed of excitatory and inhibitory leaky integrate-and-fire spiking neurons. This network is known to present four distinguished activity states, which can be mainly described ...

    • General persistence theory: on the course to multiparameter persistent homology 

      Lecha Sánchez, Manuel (Universitat Politècnica de Catalunya, 2022-10)
      Projecte Final de Màster Oficial
      Accés obert
      We explore Persistence Theory in its full generality. As a particular instance, we first discuss one parameter persistence theory, which arises from uniparametric filtrations of spaces. Although enjoying many excellent ...

    • Improving neural networks using topological data analysis 

      Ballester Bautista, Rubén (Universitat Politècnica de Catalunya, 2022-09)
      Projecte Final de Màster Oficial
      Accés obert
      Generalisation measures are metrics that indicate how well a neural network will perform in presence of unknown data. Differentiable generalisation measures with respect to the parameters of a neural network that use only ...

    • Model categories and cubical descent 

      Rubió Pons, Llorenç (2007-06-12)
      Article
      Accés obert
      We prove that the subcategory of fibrant objects of a simplicial model category is a cohomological descent category, in the sense of Guillén and Navarro, if and only if an acyclicity criterion holds.

    • Thomason cohomology of categories 

      Gálvez Carrillo, Maria Immaculada; Neumann, Frank; Tonks, Andrew (2013)
      Article
      Accés obert
      We investigate cohomology and homology theories of categories with general coefficients given by functors on simplex categories first studied by Thomason. These generalize Baues–Wirsching cohomology and homology of a small ...