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pro vyhledávání: '"Jardine, J."'
Autor:
Jardine, J. F.
The hierarchy associated to clusters in the HDBSCAN algorithm has layers, which are defined by cardinality. The layers define a layer subposet of the HDBSCAN hierarchy, which is a strong deformation retract and admits a stability analysis. That stabi
Externí odkaz:
http://arxiv.org/abs/2303.07097
Autor:
Jardine, J. F.
Local data structures are systems of neighbourhoods within data sets. Specifications of neighbourhoods can arise in multiple ways, for example, from global geometric structure (stellar charts), combinatorial structure (weighted graphs), desired compu
Externí odkaz:
http://arxiv.org/abs/2303.01415
Autor:
Jardine, J. F.
By analogy with methods of Spivak, there is a realization functor which takes a persistence diagram $Y$ in simplicial sets to an extended pseudo-metric space (or ep-metric space) $Re(Y)$. The functor $Re$ has a right adjoint, called the singular func
Externí odkaz:
http://arxiv.org/abs/2012.09026
Autor:
Jardine, J. F.
This paper displays the Healy-McInnes UMAP construction $V(X,N)$ as an iterated pushout of Vietoris-Rips objects associated to extended pseudo metric spaces (ep-metric spaces) defined by choices of neighbourhoods of the elements of a finite set $X$.
Externí odkaz:
http://arxiv.org/abs/2011.13430
Autor:
Jardine, J. F.
The hierarchy poset and branch point poset for a data set both admit a calculus of least upper bounds. A method involving upper bounds is used to show that the map of branch points associated to the inclusion of data sets is a controlled homotopy equ
Externí odkaz:
http://arxiv.org/abs/2003.06285
Autor:
Jardine, J. F.
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors), which are de
Externí odkaz:
http://arxiv.org/abs/2002.10013
Autor:
Jardine, J. F.
This paper displays complexity reduction techniques for calculations of path categories (or fundamental categories) P(K) for finite simplicial and cubical complexes K. The central technique involves identifying inclusions of complexes for which the i
Externí odkaz:
http://arxiv.org/abs/1909.08433
Autor:
Jardine, J. F.
This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a naturally defined system of groupoids. These groupoids effectively replac
Externí odkaz:
http://arxiv.org/abs/1909.08419
Autor:
Jardine, J. F.
This paper presents a model structure for natural transformations of diagrams of simplicial presheaves of a fixed shape, in which the weak equivalences are defined by analogy with pro-equivalences between pro-objects.
Comment: 2016, 19 pages
Comment: 2016, 19 pages
Externí odkaz:
http://arxiv.org/abs/1909.08429
Autor:
Jardine, J. F.
This paper presents explicit assumptions for the existence of interleaving homotopy equivalences of both Vietoris-Rips and Lesnick complexes associated to an inclusion of data sets. Consequences of these assumptions are investigated on the space leve
Externí odkaz:
http://arxiv.org/abs/1908.06323