10,342 research outputs found
Evolutionary constraints on the complexity of genetic regulatory networks allow predictions of the total number of genetic interactions
Genetic regulatory networks (GRNs) have been widely studied, yet there is a
lack of understanding with regards to the final size and properties of these
networks, mainly due to no network currently being complete. In this study, we
analyzed the distribution of GRN structural properties across a large set of
distinct prokaryotic organisms and found a set of constrained characteristics
such as network density and number of regulators. Our results allowed us to
estimate the number of interactions that complete networks would have, a
valuable insight that could aid in the daunting task of network curation,
prediction, and validation. Using state-of-the-art statistical approaches, we
also provided new evidence to settle a previously stated controversy that
raised the possibility of complete biological networks being random and
therefore attributing the observed scale-free properties to an artifact
emerging from the sampling process during network discovery. Furthermore, we
identified a set of properties that enabled us to assess the consistency of the
connectivity distribution for various GRNs against different alternative
statistical distributions. Our results favor the hypothesis that highly
connected nodes (hubs) are not a consequence of network incompleteness.
Finally, an interaction coverage computed for the GRNs as a proxy for
completeness revealed that high-throughput based reconstructions of GRNs could
yield biased networks with a low average clustering coefficient, showing that
classical targeted discovery of interactions is still needed.Comment: 28 pages, 5 figures, 12 pages supplementary informatio
Logarithmic corrections to the Bekenstein_Hawking entropy for five-dimensional black holes and de Sitter spaces
We calculate corrections to the Bekenstein-Hawking entropy formula for the
five-dimensional topological AdS (TAdS)-black holes and topological de Sitter
(TdS) spaces due to thermal fluctuations. We can derive all thermal properties
of the TdS spaces from those of the TAdS black holes by replacing by .
Also we obtain the same correction to the Cardy-Verlinde formula for TAdS and
TdS cases including the cosmological horizon of the Schwarzschild-de Sitter
(SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and
their dynamic correspondences.Comment: 9 pages, version to appear in PL
On the Distribution of Random Geometric Graphs
Random geometric graphs (RGGs) are commonly used to model networked systems
that depend on the underlying spatial embedding. We concern ourselves with the
probability distribution of an RGG, which is crucial for studying its random
topology, properties (e.g., connectedness), or Shannon entropy as a measure of
the graph's topological uncertainty (or information content). Moreover, the
distribution is also relevant for determining average network performance or
designing protocols. However, a major impediment in deducing the graph
distribution is that it requires the joint probability distribution of the
distances between nodes randomly distributed in a bounded
domain. As no such result exists in the literature, we make progress by
obtaining the joint distribution of the distances between three nodes confined
in a disk in . This enables the calculation of the probability
distribution and entropy of a three-node graph. For arbitrary , we derive a
series of upper bounds on the graph entropy; in particular, the bound involving
the entropy of a three-node graph is tighter than the existing bound which
assumes distances are independent. Finally, we provide numerical results on
graph connectedness and the tightness of the derived entropy bounds.Comment: submitted to the IEEE International Symposium on Information Theory
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