249 research outputs found
JSJ decompositions of Quadratic Baumslag-Solitar groups
Generalized Baumslag-Solitar groups are defined as fundamental groups of
graphs of groups with infinite cyclic vertex and edge groups. Forester proved
(in "On uniqueness of JSJ decompositions of finitely generated groups",
Comment. Math. Helv. 78 (2003) pp 740-751) that in most cases the defining
graphs are cyclic JSJ decompositions, in the sense of Rips and Sela. Here we
extend Forester's results to graphs of groups with vertex groups that can be
either infinite cyclic or quadratically hanging surface groups.Comment: 20 pages, 2 figures. Several corrections and improvements from
referee's report. Imprtant changes in Definition 5.1, and the proof of
Theorem 5.5 (previously 5.4). Lemma 5.4 was adde
Uncoverings on graphs and network reliability
We propose a network protocol similar to the -tree protocol of Itai and
Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we
define an {\em -uncovering-by-bases} for a connected graph to be a
collection of spanning trees for such that any -subset of
edges of is disjoint from at least one tree in , where is
some integer strictly less than the edge connectivity of . We construct
examples of these for some infinite families of graphs. Many of these infinite
families utilise factorisations or decompositions of graphs. In every case the
size of the uncovering-by-bases is no larger than the number of edges in the
graph and we conjecture that this may be true in general.Comment: 12 pages, 5 figure
Multicolored parallelisms of Hamiltonian cycles
AbstractA subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we prove that a complete graph on 2m+1 vertices K2m+1 can be properly edge-colored with 2m+1 colors in such a way that the edges of K2m+1 can be partitioned into m multicolored Hamiltonian cycles
Image patch analysis of sunspots and active regions. II. Clustering via matrix factorization
Separating active regions that are quiet from potentially eruptive ones is a
key issue in Space Weather applications. Traditional classification schemes
such as Mount Wilson and McIntosh have been effective in relating an active
region large scale magnetic configuration to its ability to produce eruptive
events. However, their qualitative nature prevents systematic studies of an
active region's evolution for example. We introduce a new clustering of active
regions that is based on the local geometry observed in Line of Sight
magnetogram and continuum images. We use a reduced-dimension representation of
an active region that is obtained by factoring the corresponding data matrix
comprised of local image patches. Two factorizations can be compared via the
definition of appropriate metrics on the resulting factors. The distances
obtained from these metrics are then used to cluster the active regions. We
find that these metrics result in natural clusterings of active regions. The
clusterings are related to large scale descriptors of an active region such as
its size, its local magnetic field distribution, and its complexity as measured
by the Mount Wilson classification scheme. We also find that including data
focused on the neutral line of an active region can result in an increased
correspondence between our clustering results and other active region
descriptors such as the Mount Wilson classifications and the value. We
provide some recommendations for which metrics, matrix factorization
techniques, and regions of interest to use to study active regions.Comment: Accepted for publication in the Journal of Space Weather and Space
Climate (SWSC). 33 pages, 12 figure
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