Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diversities and the Generalized Circumradius   The generalized circumradius} of a set of points $A \subseteq \mathbb{R}^d$
with respect to a convex body $K$ equals the minimum value of $\lambda \geq 0$
such that $A$ is contained in a translate of $\lambda K$. Each choice of $K$
gives a different function on the set of bounded subsets of $\mathbb{R}^d$; we
characterize which functions can arise in this way. Our characterization draws
on the theory of diversities, a recently introduced generalization of metrics
from functions on pairs to functions on finite subsets. We additionally
investigate functions which arise by restricting the generalised circumradius
to a finite subset of $\mathbb{R}^d$. We obtain elegant characterizations in
the case that $K$ is a simplex or parallelotope.

12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex