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15:16, 22 October 2023 Khmccabe talk contribs created page Graphs with few cliques (←Created page with 'In graph theory, a class of graphs is said to have '''few cliques''' if every member of the class has a polynomial number of maximal cliques.<ref name=":0">Prisner, E. (1995). Graphs with Few Cliques. In Y. Alavi & A. Schwenk (Eds.), ''Graph theory, combinatorics, and algorithms: proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs'' (pp. 945–956). New York, N. Y: Wiley.</ref> Certain generally NP-hard c...') Tag: Visual edit
04:24, 14 April 2023 Khmccabe talk contribs created page Persistence barcode (←Created page with 'In topological data analysis, a '''persistence barcode''' (sometimes shortened to '''barcode''') is an algebraic invariant of a persistence module that characterizes the stability of topological features throughout a growing family of spaces. Formally, a persistence barcode consists of a multiset of intervals in the extended real line, where...') Tag: Visual edit
17:12, 9 April 2023 Khmccabe talk contribs created page Cubicity (←Created page with 'In graph theory, '''cubicity''' is a graph invariant defined to be the smallest dimension such that a graph can be realized as an intersection graph of unit cubes in Euclidean space. Cubicity was introduced by Fred S. Roberts in 1969 along with a related invariant called boxicity that considers the smallest dimension needed to represent a graph as an intersection graph of axis-parallel Hyperrec...') Tags: Visual edit Disambiguation links added
16:31, 9 April 2023 Khmccabe talk contribs created page Sphericity (graph theory) (←Created page with 'In graph theory, the '''sphericity''' of a graph is a graph invariant defined to be the smallest dimension of Euclidean space required to realize the graph as an intersection graph of unit spheres. The sphericity of a graph is a generalization of the boxicity and cubicity invariants defined by F.S. Roberts in the late 1960s.<ref>Roberts, F. S. (1969). On the boxicity and cubicity...') Tags: Visual edit Disambiguation links added
22:25, 7 April 2023 Khmccabe talk contribs created page Persistent homology group (←Created page with 'In persistent homology, a '''persistent homology group''' is a multiscale analog of a homology group that formally encodes information about the evolution of topological features across a filtration of spaces. While the ordinary homology group represents nontrivial homology classes of an individual topological space, the persistent homology group tracks only those classes that rema...') Tag: Visual edit
19:48, 7 April 2023 Khmccabe talk contribs created page Persistent Betti number (←Created page with 'In persistent homology, a '''persistent Betti number''' is a multiscale analog of a Betti number that tracks the number of topological features that persist over multiple scale parameters in a filtration. Whereas the classical <math>n^{th}</math> Betti number equals the rank of the <math>n^{th}</math> homology group, the <math>n^{th}</math> persistent Betti number is...') Tag: Visual edit
07:26, 7 April 2023 Khmccabe talk contribs created page User:Khmccabe (←Created page with 'I'm a graduate student in mathematics studying the theoretical foundations of topological data analysis. Below is a list of pages I've created. Please let me know if you have any comments or suggestions, and I apologize in advance for any errors! == Mathematics == Persistence module Offset filtration Multicover bifiltration Vietoris-Rips filtration Subdivision bifiltration Interl...') Tag: Visual edit
06:26, 7 April 2023 Khmccabe talk contribs created page Interleaving distance (←Created page with 'In topological data analysis, the '''interleaving distance''' is a method of comparing two persistence modules. The interleaving distance quantifies the level of similarity between two modules, a common object of study in topological data analysis and persistent homology. The interleaving distance was first introduced by Frédéric Chazal et al. in 2009.<ref>{{Cite journal |last=Chazal |first=Frédéric |last2=Cohen-Steiner |f...') Tag: Visual edit
03:10, 7 April 2023 Khmccabe talk contribs created page Talk:Vietoris-Rips Filtration (Notation: new section) Tag: New topic
21:23, 5 April 2023 Khmccabe talk contribs created page Vietoris-Rips Filtration (created page) Tags: Visual edit Disambiguation links added
04:43, 27 March 2023 Khmccabe talk contribs created page Subdivision bifiltration (←Created page with 'In topological data analysis, a '''subdivision bifiltration''' is a collection of filtered simplicial complexes, typically built upon a set of data points in a metric space, that captures shape and density information about the underlying data set. The subdivision bifiltration relies on a natural filtration of the barycentric subdivision of a simplicial complex by flags of m...') Tags: Visual edit Disambiguation links added
02:23, 27 February 2023 Khmccabe talk contribs created page Persistence Module (←Created page with 'A '''persistence module''' is a mathematical structure in persistent homology and topological data analysis that formally captures the persistence of topological features of an object across a range of scale parameters. A persistence module often consists of a collection of homology groups (or vector spaces if using field coefficients) corresponding to a...') Tag: Visual edit
22:08, 25 February 2023 Khmccabe talk contribs created page Multicover Bifiltration (created page) Tag: Visual edit
08:39, 25 February 2023 Khmccabe talk contribs created page Offset Filtration (←Created page with 'The offset filtration (also called the "union-of-balls"<ref>{{Cite journal |last=Adams |first=Henry |last2=Moy |first2=Michael |date=2021 |title=Topology Applied to Machine Learning: From Global to Local |url=https://www.frontiersin.org/articles/10.3389/frai.2021.668302 |journal=Frontiers in Artificial Intelligence |volume=4 |pages=2 |doi=10.3389/frai.2021.668302 |issn=2624-8212 |pmc=PMC8160457 |pmid=34056580}}</ref> or "union-of-disks"<ref>{{Cite book |las...') Tag: Visual edit
02:43, 9 July 2019 Khmccabe talk contribs created page Draft:Craig Jones (Martial Artist) (Created biography)
06:21, 8 July 2019 Khmccabe talk contribs created page Draft:John Danaher (martial artist) (←Created page with '{{AFC submission|t||ts=20190708061245|u=Khmccabe|ns=118|demo=}} {{Infobox martial art...')
06:14, 8 July 2019 Khmccabe talk contribs created page Draft:John Danaher (jiu-jitsu coach) (←Created page with '{{subst:AFC submission/draftnew}} {{Infobox martial artist | name = John D...')
03:16, 8 July 2019 User account Khmccabe talk contribs was created