Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural Models for Evolution on Networks   Evolutionary dynamics have been traditionally studied in the context of
homogeneous populations, mainly described my the Moran process. Recently, this
approach has been generalized in \cite{LHN} by arranging individuals on the
nodes of a network. Undirected networks seem to have a smoother behavior than
directed ones, and thus it is more challenging to find suppressors/amplifiers
of selection. In this paper we present the first class of undirected graphs
which act as suppressors of selection, by achieving a fixation probability that
is at most one half of that of the complete graph, as the number of vertices
increases. Moreover, we provide some generic upper and lower bounds for the
fixation probability of general undirected graphs. As our main contribution, we
introduce the natural alternative of the model proposed in \cite{LHN}, where
all individuals interact simultaneously and the result is a compromise between
aggressive and non-aggressive individuals. That is, the behavior of the
individuals in our new model and in the model of \cite{LHN} can be interpreted
as an "aggregation" vs. an "all-or-nothing" strategy, respectively. We prove
that our new model of mutual influences admits a \emph{potential function},
which guarantees the convergence of the system for any graph topology and any
initial fitness vector of the individuals. Furthermore, we prove fast
convergence to the stable state for the case of the complete graph, as well as
we provide almost tight bounds on the limit fitness of the individuals. Apart
from being important on its own, this new evolutionary model appears to be
useful also in the abstract modeling of control mechanisms over invading
populations in networks. We demonstrate this by introducing and analyzing two
alternative control approaches, for which we bound the time needed to stabilize
to the "healthy" state of the system.

25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph