Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Analysis of the Effective Degrees of Freedom in Genetic Algorithms   An evolution equation for a population of strings evolving under the genetic
operators: selection, mutation and crossover is derived. The corresponding
equation describing the evolution of schematas is found by performing an exact
coarse graining of this equation. In particular exact expressions for schemata
reconstruction are derived which allows for a critical appraisal of the
``building-block hypothesis'' of genetic algorithms. A further coarse-graining
is made by considering the contribution of all length-l schematas to the
evolution of population observables such as fitness growth. As a test function
for investigating the emergence of structure in the evolution the increase per
generation of the in-schemata fitness averaged over all schematas of length l,
$\Delta_l$, is introduced. In finding solutions of the evolution equations we
concentrate more on the effects of crossover, in particular we consider
crossover in the context of Kauffman Nk models with k=0,2. For k=0, with a
random initial population, in the first step of evolution the contribution from
schemata reconstruction is equal to that of schemata destruction leading to a
scale invariant situation where the contribution to fitness of schematas of
size l is independent of l. This balance is broken in the next step of
evolution leading to a situation where schematas that are either much larger or
much smaller than half the string size dominate over those with $l \approx
N/2$. The balance between block destruction and reconstruction is also broken
in a k>0 landscape. It is conjectured that the effective degrees of freedom for
such landscapes are landscape connective trees that break down into effectively
fit smaller blocks, and not the blocks themselves. Numerical simulations
confirm this ``connective tree hypothesis'' by showing that correlations drop
off with connective distance and not with intrachromosomal distance.

8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th