17,297 research outputs found
Evolutionary Dynamics and Optimization: Neutral Networks as Model-Landscapes for RNA Secondary-Structure Folding-Landscapes
We view the folding of RNA-sequences as a map that assigns a pattern of base
pairings to each sequence, known as secondary structure. These preimages can be
constructed as random graphs (i.e. the neutral networks associated to the
structure ). By interpreting the secondary structure as biological
information we can formulate the so called Error Threshold of Shapes as an
extension of Eigen's et al. concept of an error threshold in the single peak
landscape. Analogue to the approach of Derrida & Peliti for a of the population
on the neutral network. On the one hand this model of a single shape landscape
allows the derivation of analytical results, on the other hand the concept
gives rise to study various scenarios by means of simulations, e.g. the
interaction of two different networks. It turns out that the intersection of
two sets of compatible sequences (with respect to the pair of secondary
structures) plays a key role in the search for ''fitter'' secondary structures.Comment: 20 pages, uuencoded compressed postscript-file, Proc. of ECAL '95
conference, to appear., email: chris @ imb-jena.d
Adaptive Complex Contagions and Threshold Dynamical Systems
A broad range of nonlinear processes over networks are governed by threshold
dynamics. So far, existing mathematical theory characterizing the behavior of
such systems has largely been concerned with the case where the thresholds are
static. In this paper we extend current theory of finite dynamical systems to
cover dynamic thresholds. Three classes of parallel and sequential dynamic
threshold systems are introduced and analyzed. Our main result, which is a
complete characterization of their attractor structures, show that sequential
systems may only have fixed points as limit sets whereas parallel systems may
only have period orbits of size at most two as limit sets. The attractor states
are characterized for general graphs and enumerated in the special case of
paths and cycle graphs; a computational algorithm is outlined for determining
the number of fixed points over a tree. We expect our results to be relevant
for modeling a broad class of biological, behavioral and socio-technical
systems where adaptive behavior is central.Comment: Submitted for publicatio
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