4,559 research outputs found
Threshold phenomena in random graphs
In the 1950s, random graphs appeared for the first time in a result of the prolific hungarian mathematician Pál Erd\H{o}s. Since then, interest in random graph theory has only grown up until now. In its first stages, the basis of its theory were set, while they were mainly used in probability and combinatorics theory. However, with the new century and the boom of technologies like the World Wide Web, random graphs are even more important since they are extremely useful to handle problems in fields like network and communication theory. Because of this fact, nowadays random graphs are widely studied by the mathematical community around the world and new promising results have been recently achieved, showing an exciting future for this field. In this bachelor thesis, we focus our study on the threshold phenomena for graph properties within random graphs
SANA NetGO: A combinatorial approach to using Gene Ontology (GO) terms to score network alignments
Gene Ontology (GO) terms are frequently used to score alignments between
protein-protein interaction (PPI) networks. Methods exist to measure the GO
similarity between two proteins in isolation, but pairs of proteins in a
network alignment are not isolated: each pairing is implicitly dependent upon
every other pairing via the alignment itself. Current methods fail to take into
account the frequency of GO terms across the networks, and attempt to account
for common GO terms in an ad hoc fashion by imposing arbitrary rules on when to
"allow" GO terms based on their location in the GO hierarchy, rather than using
readily available frequency information in the PPI networks themselves. Here we
develop a new measure, NetGO, that naturally weighs infrequent, informative GO
terms more heavily than frequent, less informative GO terms, without requiring
arbitrary cutoffs. In particular, NetGO down-weights the score of frequent GO
terms according to their frequency in the networks being aligned. This is a
global measure applicable only to alignments, independent of pairwise GO
measures, in the same sense that the edge-based EC or S3 scores are global
measures of topological similarity independent of pairwise topological
similarities. We demonstrate the superiority of NetGO by creating alignments of
predetermined quality based on homologous pairs of nodes and show that NetGO
correlates with alignment quality much better than any existing GO-based
alignment measures. We also demonstrate that NetGO provides a measure of
taxonomic similarity between species, consistent with existing taxonomic
measures--a feature not shared with existing GO-based network alignment
measures. Finally, we re-score alignments produced by almost a dozen aligners
from a previous study and show that NetGO does a better job than existing
measures at separating good alignments from bad ones
Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path
In millimeter-wave channels, most of the received energy is carried by a few
paths. Traditional precoders sweep the angle-of-departure (AoD) and
angle-of-arrival (AoA) space with directional precoders to identify directions
with largest power. Such precoders are heuristic and lead to sub-optimal
AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao
bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the
transmitter and spatial filtering of a single path. The precoders are found by
solving a suitable convex optimization problem. We demonstrate that the
accuracy can be improved by at least a factor of two over traditional
precoders, and show that there is an optimal number of distinct precoders
beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9
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