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Umap: Uniform manifold approximation and projection for dimension reduction
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning
technique for dimension reduction. UMAP is constructed from a theoretical framework based …
technique for dimension reduction. UMAP is constructed from a theoretical framework based …
Enhancing cluster analysis via topological manifold learning
We discuss topological aspects of cluster analysis and show that inferring the topological
structure of a dataset before clustering it can considerably enhance cluster detection: we …
structure of a dataset before clustering it can considerably enhance cluster detection: we …
[ספר][B] A simplicial approach to stratified homotopy theory
SJ Nand-Lal - 2019 - search.proquest.com
This thesis provides a framework to study the homotopy theory of stratified spaces, in a way
that is compatible with previous approaches. In particular our approach will be closely …
that is compatible with previous approaches. In particular our approach will be closely …
Associative -categories
We define novel fully combinatorial models of higher categories. Our definitions are based
on a connection of higher categories to" directed spaces". Directed spaces are locally …
on a connection of higher categories to" directed spaces". Directed spaces are locally …
Homotopy type theory for sewn quilts
This paper introduces PieceWork, an imperative programming language for the construction
of designs for sewn quilts, whose semantics are inspired by Homotopy Type Theory. The …
of designs for sewn quilts, whose semantics are inspired by Homotopy Type Theory. The …
Semi-simplicial set models for distributed knowledge
In recent years, a new class of models for multi-agent epistemic logic has emerged, based
on simplicial complexes. Since then, many variants of these simplicial models have been …
on simplicial complexes. Since then, many variants of these simplicial models have been …
On the∞ ∞‐topos semantics of homotopy type theory
Many introductions to homotopy type theory and the univalence axiom gloss over the
semantics of this new formal system in traditional set‐based foundations. This expository …
semantics of this new formal system in traditional set‐based foundations. This expository …
Homotopy coherent structures
Naturally occurring diagrams in algebraic topology are commutative up to homotopy, but not
on the nose. It was quickly realized that very little can be done with this information …
on the nose. It was quickly realized that very little can be done with this information …
Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets
Simplicial sets generalise many categories of graphs. In this paper, we give a complete
characterisation of the Lawvere-Tierney topologies on (semi-) simplicial sets, on bicolored …
characterisation of the Lawvere-Tierney topologies on (semi-) simplicial sets, on bicolored …
[PDF][PDF] A model structure for quasi-categories
Quasi-categories live at the intersection of homotopy theory with category theory. In
particular, they serve as a model for (∞, 1)-categories, that is, weak higher categories with n …
particular, they serve as a model for (∞, 1)-categories, that is, weak higher categories with n …