Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kinetic Transition Networks for the Thomson Problem and Smale's 7th
  Problem   The Thomson Problem, arrangement of identical charges on the surface of a
sphere, has found many applications in physics, chemistry and biology. Here we
show that the energy landscape of the Thomson Problem for $N$ particles with
$N=132, 135, 138, 141, 144, 147$ and $150$ is single funnelled, characteristic
of a structure-seeking organisation where the global minimum is easily
accessible. Algorithmically constructing starting points close to the global
minimum of such a potential with spherical constraints is one of Smale's 18
unsolved problems in mathematics for the 21st century because it is important
in the solution of univariate and bivariate random polynomial equations. By
analysing the kinetic transition networks, we show that a randomly chosen
minimum is in fact always `close' to the global minimum in terms of the number
of transition states that separate them, a characteristic of small world
networks.

30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom