13,762 research outputs found
Multi-scale Modularity in Complex Networks
We focus on the detection of communities in multi-scale networks, namely
networks made of different levels of organization and in which modules exist at
different scales. It is first shown that methods based on modularity are not
appropriate to uncover modules in empirical networks, mainly because modularity
optimization has an intrinsic bias towards partitions having a characteristic
number of modules which might not be compatible with the modular organization
of the system. We argue for the use of more flexible quality functions
incorporating a resolution parameter that allows us to reveal the natural
scales of the system. Different types of multi-resolution quality functions are
described and unified by looking at the partitioning problem from a dynamical
viewpoint. Finally, significant values of the resolution parameter are selected
by using complementary measures of robustness of the uncovered partitions. The
methods are illustrated on a benchmark and an empirical network.Comment: 8 pages, 3 figure
Dividing population genetic distance data with the software Partitioning Optimization with Restricted Growth Strings (PORGS): an application for Chinook salmon (Oncorhynchus tshawytscha), Vancouver Island, British Columbia
A new method of finding the optimal group membership and number of groupings to partition population genetic distance data is presented. The software program Partitioning Optimization with Restricted Growth Strings (PORGS), visits all possible set partitions and deems
acceptable partitions to be those that reduce mean intracluster distance. The optimal number of groups is determined with the gap statistic which compares PORGS results with a reference distribution. The PORGS method was validated by a simulated data set with a known distribution.
For efficiency, where values of n were larger, restricted growth strings (RGS) were used to bipartition populations during a nested search (bi-PORGS). Bi-PORGS was applied to a set of genetic data from 18 Chinook salmon (Oncorhynchus
tshawytscha) populations from the west coast of Vancouver Island. The optimal grouping of these populations
corresponded to four geographic locations: 1) Quatsino Sound, 2) Nootka Sound, 3) Clayoquot +Barkley sounds,
and 4) southwest Vancouver Island. However, assignment of populations to groups did not strictly reflect the geographical divisions; fish of Barkley Sound origin that had strayed into the Gold River and close genetic similarity
between transferred and donor populations meant groupings crossed geographic boundaries. Overall, stock structure determined by this partitioning method was similar to that
determined by the unweighted pair-group method with arithmetic averages (UPGMA), an agglomerative clustering algorithm
PT-Scotch: A tool for efficient parallel graph ordering
The parallel ordering of large graphs is a difficult problem, because on the
one hand minimum degree algorithms do not parallelize well, and on the other
hand the obtainment of high quality orderings with the nested dissection
algorithm requires efficient graph bipartitioning heuristics, the best
sequential implementations of which are also hard to parallelize. This paper
presents a set of algorithms, implemented in the PT-Scotch software package,
which allows one to order large graphs in parallel, yielding orderings the
quality of which is only slightly worse than the one of state-of-the-art
sequential algorithms. Our implementation uses the classical nested dissection
approach but relies on several novel features to solve the parallel graph
bipartitioning problem. Thanks to these improvements, PT-Scotch produces
consistently better orderings than ParMeTiS on large numbers of processors
An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging
This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions
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