4 citations · 7 across the 11 of their papers we have counts for
6 papers · 1 filter
Persistent homology based goodness-of-fit tests for spatial tessellations
Christian Hirsch, Johannes Krebs, Claudia Redenbach
Motivated by the rapidly increasing relevance of virtual material design in the domain of materials science, it has become essential to assess whether topological properties of sto…
Topology-based goodness-of-fit tests for sliced spatial data
Alessandra Cipriani, Christian Hirsch, Martina Vittorietti
In materials science and many other application domains, 3D information can often only be extrapolated by taking 2D slices. In topological data analysis, persistence vineyards have…
On the consistency and asymptotic normality of multiparameter persistent Betti numbers
Magnus Bakke Botnan, Christian Hirsch
The persistent Betti numbers are used in topological data analysis to infer the scales at which topological features appear and disappear in the filtration of a topological space.…
Functional central limit theorems for persistent Betti numbers on cylindrical networks
Johannes Krebs, Christian Hirsch
We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindric…
Testing goodness of fit for point processes via topological data analysis
Christophe Ange Napoléon Biscio, Nicolas Chenavier, Christian Hirsch +1
We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate funct…
Estimation of geodesic tortuosity and constrictivity in stationary random closed sets
Matthias Neumann, Christian Hirsch, Jakub Staněk +2
We investigate the problem of estimating geodesic tortuosity and constrictivity as two structural characteristics of stationary random closed sets. They are of central importance f…