Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new construction for sublevel set persistence   We construct a filtered simplicial complex $(X_L,f_L)$ associated to a subset
$X\subset \mathbb{R}^d$, a function $f:X\rightarrow \mathbb{R}$ with compactly
supported sublevel sets, and a collection of landmark points $L\subset
\mathbb{R}^d$. The persistence values $f_L(\Delta)$ are defined as the
minimizing values of a family of constrained optimization problems, whose
domains are certain higher order Voronoi cells associated to $L$. We prove that
$H_k^{a,b}(X_L)\cong H^{a,b}_k(X)$ provided that $f$ is the restriction of a
smooth function, the landmarks are sufficiently dense, and $a<b$ are generic,
and we show that the construction produces desirable results in some examples.

37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an