Umap: Uniform manifold approximation and projection for dimension reduction

L McInnes, J Healy, J Melville - arxiv preprint arxiv:1802.03426, 2018‏ - arxiv.org
UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning
technique for dimension reduction. UMAP is constructed from a theoretical framework based …

Enhancing cluster analysis via topological manifold learning

M Herrmann, D Kazempour, F Scheipl… - Data Mining and …, 2024‏ - Springer
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 …

[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 …

Associative -categories

C Dorn - arxiv preprint arxiv:1812.10586, 2018‏ - arxiv.org
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 …

Homotopy type theory for sewn quilts

C Clark, R Bohrer - Proceedings of the 11th ACM SIGPLAN International …, 2023‏ - dl.acm.org
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 …

Semi-simplicial set models for distributed knowledge

É Goubault, R Kniazev, J Ledent… - 2023 38th Annual …, 2023‏ - ieeexplore.ieee.org
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 the∞ ∞‐topos semantics of homotopy type theory

E Riehl - Bulletin of the London Mathematical Society, 2024‏ - Wiley Online Library
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 …

Homotopy coherent structures

E Riehl - arxiv preprint arxiv:1801.07404, 2018‏ - arxiv.org
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 …

Characterisation of Lawvere-Tierney Topologies on Simplicial Sets, Bicolored Graphs, and Fuzzy Sets

A Rosset, HH Hansen, J Endrullis - arxiv preprint arxiv:2407.04535, 2024‏ - arxiv.org
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 …

[PDF][PDF] A model structure for quasi-categories

E Riehl - Preprint available at http://www. math. harvard …, 2008‏ - people.math.rochester.edu
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 …