Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Virtual persistence diagrams, signed measures, Wasserstein distances,
  and Banach spaces   Persistence diagrams, an important summary in topological data analysis,
consist of a set of ordered pairs, each with positive multiplicity. Persistence
diagrams are obtained via Mobius inversion and may be compared using a
one-parameter family of metrics called Wasserstein distances. In certain cases,
Mobius inversion produces sets of ordered pairs which may have negative
multiplicity. We call these virtual persistence diagrams. Divol and Lacombe
recently showed that there is a Wasserstein distance for Radon measures on the
half plane of ordered pairs that generalizes both the Wasserstein distance for
persistence diagrams and the classical Wasserstein distance from optimal
transport theory. Following this work, we define compatible Wasserstein
distances for persistence diagrams and Radon measures on arbitrary metric
spaces. We show that the 1-Wasserstein distance extends to virtual persistence
diagrams and to signed measures. In addition, we characterize the Cauchy
completion of persistence diagrams with respect to the Wasserstein distances.
We also give a universal construction of a Banach space with a 1-Wasserstein
norm. Persistence diagrams with the 1-Wasserstein distance isometrically embed
into this Banach space.

4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph