48,812 research outputs found
Community detection for networks with unipartite and bipartite structure
Finding community structures in networks is important in network science,
technology, and applications. To date, most algorithms that aim to find
community structures only focus either on unipartite or bipartite networks. A
unipartite network consists of one set of nodes and a bipartite network
consists of two nonoverlapping sets of nodes with only links joining the nodes
in different sets. However, a third type of network exists, defined here as the
mixture network. Just like a bipartite network, a mixture network also consists
of two sets of nodes, but some nodes may simultaneously belong to two sets,
which breaks the nonoverlapping restriction of a bipartite network. The mixture
network can be considered as a general case, with unipartite and bipartite
networks viewed as its limiting cases. A mixture network can represent not only
all the unipartite and bipartite networks, but also a wide range of real-world
networks that cannot be properly represented as either unipartite or bipartite
networks in fields such as biology and social science. Based on this
observation, we first propose a probabilistic model that can find modules in
unipartite, bipartite, and mixture networks in a unified framework based on the
link community model for a unipartite undirected network [B Ball et al (2011
Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both
overlapping and nonoverlapping communities) and apply it to two real-world
networks: a southern women bipartite network and a human transcriptional
regulatory mixture network. The results suggest that our model performs well
for all three types of networks, is competitive with other algorithms for
unipartite or bipartite networks, and is applicable to real-world networks.Comment: 27 pages, 8 figures.
(http://iopscience.iop.org/1367-2630/16/9/093001
Quotients and subgroups of Baumslag-Solitar groups
We determine all generalized Baumslag-Solitar groups (finitely generated
groups acting on a tree with all stabilizers infinite cyclic) which are
quotients of a given Baumslag-Solitar group BS(m,n), and (when BS(m,n) is not
Hopfian) which of them also admit BS(m,n) as a quotient. We determine for which
values of r,s one may embed BS(r,s) into a given BS(m,n), and we characterize
finitely generated groups which embed into some BS(n,n).Comment: Final version, to appear in Journal of Group Theor
Discovery of statistical equivalence classes using computer algebra
Discrete statistical models supported on labelled event trees can be
specified using so-called interpolating polynomials which are generalizations
of generating functions. These admit a nested representation. A new algorithm
exploits the primary decomposition of monomial ideals associated with an
interpolating polynomial to quickly compute all nested representations of that
polynomial. It hereby determines an important subclass of all trees
representing the same statistical model. To illustrate this method we analyze
the full polynomial equivalence class of a staged tree representing the best
fitting model inferred from a real-world dataset.Comment: 26 pages, 9 figure
Generalizing the rotation interval to vertex maps on graphs
Graph maps that are homotopic to the identity and that permute the vertices
are studied. Given a periodic point for such a map, a {\em rotation element} is
defined in terms of the fundamental group. A number of results are proved about
the rotation elements associated to periodic points in a given edge of the
graph. Most of the results show that the existence of two periodic points with
certain rotation elements will imply an infinite family of other periodic
points with related rotation elements. These results for periodic points can be
considered as generalizations of the rotation interval for degree one maps of
the circle
- …