276 search results - page 1 / 56 » Quantifying Homology Classes |
CORR
2008
Springer
13 years 4 months ago
2008
Springer
We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we defi...
FOCM
2011
12 years 8 months ago
2011
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbatio...
BMCBI
2010
13 years 4 months ago
2010
Background: In recent years, the number of available RNA structures has rapidly grown reflecting the increased interest on RNA biology. Similarly to the studies carried out two de...
CORR
2011
Springer
12 years 8 months ago
2011
Springer
Given a function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the exten...
ESA
2010
Springer
13 years 5 months ago
2010
Springer
We define the robustness of a level set homology class of a function f : X R as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theor...