4 citations · 6 across the 9 of their papers we have counts for
9 papers
Layers and stability
J. F. Jardine
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…
Local data structures
J. F. Jardine
Local data structures are systems of neighbourhoods within data sets. Specifications of neighbourhoods can arise in multiple ways, for example, from global geometric structure (ste…
Branch points and stability
J. F. Jardine
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…
Complexity reduction for path categories
J. F. Jardine
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…
Pro-equivalences of diagrams
J. F. Jardine
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…
Galois descent criteria
J. F. Jardine
This paper gives an introduction to homotopy descent, and its applications in algebraic -theory computations for fields. On the étale site of a field, a fibrant model of a simpl…
Stable components and layers
J. F. Jardine
Component graphs are defined for arrays of sets , and in particular for arrays of path components for Vietoris-Rips complexes and Lesnick complexes. The path componen…
Fuzzy sets and presheaves
J. F. Jardine
This note presents a presheaf theoretic approach to the construction of fuzzy sets, which builds on Barr's description of fuzzy sets as sheaves of monomorphisms on a locale. A pres…
Cocycle categories
J. F. Jardine
A cocycle category H(X,Y) is defined for objects X and Y in a model category, and it is shown that the set of morphisms [X,Y] is isomorphic to the set of path components of H(X,Y)…