7,409 research outputs found
Modularity and community structure in networks
Many networks of interest in the sciences, including a variety of social and
biological networks, are found to divide naturally into communities or modules.
The problem of detecting and characterizing this community structure has
attracted considerable recent attention. One of the most sensitive detection
methods is optimization of the quality function known as "modularity" over the
possible divisions of a network, but direct application of this method using,
for instance, simulated annealing is computationally costly. Here we show that
the modularity can be reformulated in terms of the eigenvectors of a new
characteristic matrix for the network, which we call the modularity matrix, and
that this reformulation leads to a spectral algorithm for community detection
that returns results of better quality than competing methods in noticeably
shorter running times. We demonstrate the algorithm with applications to
several network data sets.Comment: 7 pages, 3 figure
Fast Algorithm for Finding Maximum Distance with Space Subdivision in E2
Finding an exact maximum distance of two points in the given set is a
fundamental computational problem which is solved in many applications. This
paper presents a fast, simple to implement and robust algorithm for finding
this maximum distance of two points in E2. This algorithm is based on a polar
subdivision followed by division of remaining points into uniform grid. The
main idea of the algorithm is to eliminate as many input points as possible
before finding the maximum distance. The proposed algorithm gives the
significant speed up compared to the standard algorithm
Faster ASV decomposition for orthogonal polyhedra using the Extreme Vertices Model (EVM)
The alternating sum of volumes (ASV) decomposition is a widely used
technique for converting a B-Rep into a CSG model. The obtained CSG
tree has convex primitives at its leaf nodes, while the contents of
its internal nodes alternate between the set union and difference
operators.
This work first shows that the obtained CSG tree T can also be
expressed as the regularized Exclusive-OR operation among all the
convex primitives at the leaf nodes of T, regardless the structure and
internal nodes of T. This is an important result in the case in which
EVM represented orthogonal polyhedra are used because in this model
the Exclusive-OR operation runs much faster than set union and
difference operations. Therefore this work applies this result to EVM
represented orthogonal polyhedra. It also presents experimental
results that corroborate the theoretical results and includes some
practical uses for the ASV decomposition of orthogonal polyhedra.Postprint (published version
Finding all equilibria in games of strategic complements
I present a simple and fast algorithm that finds all the pure-strategy Nash equilibria in games with strategic complementarities. This is the first non-trivial algorithm for finding all pure-strategy Nash equilibria
TT2NE: A novel algorithm to predict RNA secondary structures with pseudoknots
We present TT2NE, a new algorithm to predict RNA secondary structures with
pseudoknots. The method is based on a classification of RNA structures
according to their topological genus. TT2NE guarantees to find the minimum free
energy structure irrespectively of pseudoknot topology. This unique proficiency
is obtained at the expense of the maximum length of sequence that can be
treated but comparison with state-of-the-art algorithms shows that TT2NE is a
very powerful tool within its limits. Analysis of TT2NE's wrong predictions
sheds light on the need to study how sterical constraints limit the range of
pseudoknotted structures that can be formed from a given sequence. An
implementation of TT2NE on a public server can be found at
http://ipht.cea.fr/rna/tt2ne.php
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