In topology, the Vietoris–Rips complex, also called the Vietoris complex or Rips complex, is a way of forming a topological space from distances in a...

analysis, the Vietoris–Rips filtration (sometimes shortened to "Rips filtration") is the collection of nested Vietoris–Rips complexes on a metric space...

topological space) Vietoris homology (see homology theory) Mayer–Vietoris sequence Vietoris–Begle mapping theorem Vietoris–Rips complex Vietoris remained scientifically...

Čech complex is a subcomplex of the Vietoris–Rips complex. While the Čech complex is more computationally expensive than the Vietoris–Rips complex, since...

chessboard complex forms a pseudo-manifold. The Vietoris–Rips complex of a set of points in a metric space is a special case of a clique complex, formed...

sequence of Vietoris–Rips complexes known as the Vietoris–Rips filtration. Formally, consider a real-valued function on a simplicial complex f : K → R {\displaystyle...

Eliyahu Rips, Doron Witztum, Yoav Rosenberg, and Michael Drosnin, for their work on Bible codes. Rips, E. "Group actions on R-trees". Preprint. Rips, E. (1982)...

the poset P. 5. Let M be a metric space and δ a real number. The Vietoris–Rips complex is an ASC whose faces are the finite subsets of M with diameter...

issue that arises in computation is the choice of complex. The Čech complex and the Vietoris–Rips complex are most natural at first glance; however, their...

known as the Vietoris–Rips (or simply "Rips") filtration on X {\displaystyle X} , commonly denoted Rips ( X ) {\displaystyle {\text{Rips}}(X)} or R (...

the union of balls is also known as the Čech complex, which is a subcomplex of the Vietoris-Rips complex. Therefore the offset filtration is weakly equivalent...

Beta skeleton Choudhary, Aruni (2017), Approximation algorithms for Vietoris-Rips and Čech filtrations (Thesis), Universität des Saarlandes, doi:10.22028/D291-26959...

simplicial complexes, Čech complexes and Vietoris–Rips complex, homotopy equivalence of topological spaces to their nerves, filtrations of complexes, and the...

graph, the contact graph of (not necessarily unit-sized) disks Vietoris–Rips complex, a generalization of the unit disk graph that constructs higher-order...

Dionysus 2. Retrieved 9 December 2021. Morozov, Dmitriy (2019). "Vietoris–Rips Complexes". Dionysus 2. Retrieved 9 December 2021. Mandal, Sayan (2020)....

the 1970s. In particular, Sheehy applied the construction to both the Vietoris-Rips and Čech filtrations, two common objects in the field of topological...

Metro–Goldwyn–Mayer (or MGM). Walther Mayer and Leopold Vietoris, Austrian mathematicians – Mayer–Vietoris axiom, Mayer–Vietoris theorem. Thabo Mbeki, South-African president...