64,388 research outputs found
Rings and rigidity transitions in network glasses
Three elastic phases of covalent networks, (I) floppy, (II) isostatically
rigid and (III) stressed-rigid have now been identified in glasses at specific
degrees of cross-linking (or chemical composition) both in theory and
experiments. Here we use size-increasing cluster combinatorics and constraint
counting algorithms to study analytically possible consequences of
self-organization. In the presence of small rings that can be locally I, II or
III, we obtain two transitions instead of the previously reported single
percolative transition at the mean coordination number , one from a
floppy to an isostatic rigid phase, and a second one from an isostatic to a
stressed rigid phase. The width of the intermediate phase and the
order of the phase transitions depend on the nature of medium range order
(relative ring fractions). We compare the results to the Group IV
chalcogenides, such as Ge-Se and Si-Se, for which evidence of an intermediate
phase has been obtained, and for which estimates of ring fractions can be made
from structures of high T crystalline phases.Comment: 29 pages, revtex, 7 eps figure
The Emergence of Scaling in Sequence-based Physical Models of Protein Evolution
It has recently been discovered that many biological systems, when
represented as graphs, exhibit a scale-free topology. One such system is the
set of structural relationships among protein domains. The scale-free nature of
this and other systems has previously been explained using network growth
models that, while motivated by biological processes, do not explicitly
consider the underlying physics or biology. In the present work we explore a
sequence-based model for the evolution protein structures and demonstrate that
this model is able to recapitulate the scale-free nature observed in graphs of
real protein structures. We find that this model also reproduces other
statistical feature of the protein domain graph. This represents, to our
knowledge, the first such microscopic, physics-based evolutionary model for a
scale-free network of biological importance and as such has strong implications
for our understanding of the evolution of protein structures and of other
biological networks.Comment: 20 pages (including figures), 4 figures, to be submitted to PNA
Exploring the assortativity-clustering space of a network's degree sequence
Nowadays there is a multitude of measures designed to capture different
aspects of network structure. To be able to say if the structure of certain
network is expected or not, one needs a reference model (null model). One
frequently used null model is the ensemble of graphs with the same set of
degrees as the original network. In this paper we argue that this ensemble can
be more than just a null model -- it also carries information about the
original network and factors that affect its evolution. By mapping out this
ensemble in the space of some low-level network structure -- in our case those
measured by the assortativity and clustering coefficients -- one can for
example study how close to the valid region of the parameter space the observed
networks are. Such analysis suggests which quantities are actively optimized
during the evolution of the network. We use four very different biological
networks to exemplify our method. Among other things, we find that high
clustering might be a force in the evolution of protein interaction networks.
We also find that all four networks are conspicuously robust to both random
errors and targeted attacks
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