Model: InriaValda/scibert_base_ft
Author: InriaValda
Pipeline: text-classification
Library: transformers
Tags: transformers, tf, bert, text-classification, endpoints_compatible, region:us
Card metadata: pipeline_tag: text-classification
widget: text: Dijkstra's algorithm is an algorithm for finding the paths between nodes in a weighted graph
example_title: Djikstra, text: Proposition 1. The sum of the differential weight d on the Dowker complex D(X, Y, R) is the number of elements of Y .
example_title: Proposition, text: Proof. This follows from showing that t is order-reversing in the following way: if σ ⊆ τ, then t(σ) ≥ t(τ).
example_title: Proof 1, text: Theorem 1. Given the Dowker complex D(X, Y, R) and differential weight d, one can reconstruct R up to a bijection on Y .
example_title: Theorem, text: The Dowker complex D(X,Y,R) is a functor between an appropriately con- structed category of relations and the category of abstract simplicial complexes. We prove this fact in Theorem 3 along with a few other observations.
example_title: Basic, text: Lemma 1. Let f : X → Y be a simplicial map. For every pair of simplices σ, τ of X satisfying σ ⊆ τ, their images in Y satisfy f(σ) ⊆ f(τ).
example_title: Theorem, text: Since f is a simplicial map, then f(σ) is a simplex of Y and so is f(τ). If σ ⊆ τ, then every vertex v of σ is also a vertex of τ. By the definition of simplicial maps, f(v) is a vertex of both f(σ) and f(τ). Conversely, every vertex of f(σ) is the image of some vertex w of σ. □
example_title: Proof without keyword, text: The Dowker complex defined in Definition 2 is a covariant functor D : Rel → Asc.
example_title: th without keyword
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Created: 2023-06-28 20:19:27