Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of multidimensional persistent homology with respect to domain
  perturbations   Motivated by the problem of dealing with incomplete or imprecise acquisition
of data in computer vision and computer graphics, we extend results concerning
the stability of persistent homology with respect to function perturbations to
results concerning the stability with respect to domain perturbations. Domain
perturbations can be measured in a number of different ways. An important
method to compare domains is the Hausdorff distance. We show that by encoding
sets using the distance function, the multidimensional matching distance
between rank invariants of persistent homology groups is always upperly bounded
by the Hausdorff distance between sets. Moreover we prove that our construction
maintains information about the original set. Other well known methods to
compare sets are considered, such as the symmetric difference distance between
classical sets and the sup-distance between fuzzy sets. Also in these cases we
present results stating that the multidimensional matching distance between
rank invariants of persistent homology groups is upperly bounded by these
distances. An experiment showing the potential of our approach concludes the
paper.

20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio