Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accessiblility Percolation with Crossing Valleys on $n$-ary Trees   In this paper we study a variation of the accessibility percolation model,
this is also motivated by evolutionary biology and evolutionary computation.
Consider a tree whose vertices are labeled with random numbers. We study the
probability of having a monotone subsequence of a path from the root to a leaf,
where any $k$ consecutive vertices in the path contain at least one vertex of
the subsequence. An $n$-ary tree, with height $h$, is a tree whose vertices at
distance at most $h-1$ to the root have $n$ children. For the case of $n$-ary
trees, we prove that, as $h$ tends to infinity the probability of having such
subsequence: tends to 1, if $n$ grows significantly faster than
$\sqrt[k]{h/(ek)}$; and tends to 0, if $n$ grows significantly slower than
$\sqrt[k]{h/(ek)}$.

4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg