257 research outputs found
Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity
We introduce and study the problem Ordered Level Planarity which asks for a
planar drawing of a graph such that vertices are placed at prescribed positions
in the plane and such that every edge is realized as a y-monotone curve. This
can be interpreted as a variant of Level Planarity in which the vertices on
each level appear in a prescribed total order. We establish a complexity
dichotomy with respect to both the maximum degree and the level-width, that is,
the maximum number of vertices that share a level. Our study of Ordered Level
Planarity is motivated by connections to several other graph drawing problems.
Geodesic Planarity asks for a planar drawing of a graph such that vertices
are placed at prescribed positions in the plane and such that every edge is
realized as a polygonal path composed of line segments with two adjacent
directions from a given set of directions symmetric with respect to the
origin. Our results on Ordered Level Planarity imply -hardness for any
with even if the given graph is a matching. Katz, Krug, Rutter and
Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where
contains precisely the horizontal and vertical directions, can be solved in
polynomial time [GD'09]. Our results imply that this is incorrect unless
. Our reduction extends to settle the complexity of the Bi-Monotonicity
problem, which was proposed by Fulek, Pelsmajer, Schaefer and
\v{S}tefankovi\v{c}.
Ordered Level Planarity turns out to be a special case of T-Level Planarity,
Clustered Level Planarity and Constrained Level Planarity. Thus, our results
strengthen previous hardness results. In particular, our reduction to Clustered
Level Planarity generates instances with only two non-trivial clusters. This
answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Separation of noncommutative differential calculus on quantum Minkowski space
Noncommutative differential calculus on quantum Minkowski space is not
separated with respect to the standard generators, in the sense that partial
derivatives of functions of a single generator can depend on all other
generators. It is shown that this problem can be overcome by a separation of
variables. We study the action of the universal L-matrix, appearing in the
coproduct of partial derivatives, on generators. Powers of he resulting quantum
Minkowski algebra valued matrices are calculated. This leads to a nonlinear
coordinate transformation which essentially separates the calculus. A compact
formula for general derivatives is obtained in form of a chain rule with
partial Jackson derivatives. It is applied to the massive quantum Klein-Gordon
equation by reducing it to an ordinary q-difference equation. The rest state
solution can be expressed in terms of a product of q-exponential functions in
the separated variables.Comment: 33 page
SPD deformation of pearlitic, bainitic and martensitic steels
The deformation behavior of nearly fully pearlitic, bainitic and martensitic
steels during severe plastic deformation is summarized in this paper. Despite
their significantly different yield stresses and their microstructures, their
hardening behavior during SPD is similar. Due to the enormous hardening
capacity the SPD deformation is limited by the strength of the tool materials.
The microstructure at the obtainable limit of strain are quite similar, which
is a nanocrystalline structure in the order of 10 nm, dependent on the
obtainable strain. The nanograins are partially supersaturated with carbon and
the grain boundaries are stabilized by carbon. Another characteristic feature
is the anisotropy in grain shape which results in an anisotropy of strength,
ductility and fracture toughness. The results are important for the development
of ultra-strong materials and essential for this type of steels which are
frequently used for application where the behavior under rolling contact and
sliding contact is important
On Upward Drawings of Trees on a Given Grid
Computing a minimum-area planar straight-line drawing of a graph is known to
be NP-hard for planar graphs, even when restricted to outerplanar graphs.
However, the complexity question is open for trees. Only a few hardness results
are known for straight-line drawings of trees under various restrictions such
as edge length or slope constraints. On the other hand, there exist
polynomial-time algorithms for computing minimum-width (resp., minimum-height)
upward drawings of trees, where the height (resp., width) is unbounded.
In this paper we take a major step in understanding the complexity of the
area minimization problem for strictly-upward drawings of trees, which is one
of the most common styles for drawing rooted trees. We prove that given a
rooted tree and a grid, it is NP-hard to decide whether
admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Mixed Linear Layouts of Planar Graphs
A -stack (respectively, -queue) layout of a graph consists of a total
order of the vertices, and a partition of the edges into sets of
non-crossing (non-nested) edges with respect to the vertex ordering. In 1992,
Heath and Rosenberg conjectured that every planar graph admits a mixed
-stack -queue layout in which every edge is assigned to a stack or to a
queue that use a common vertex ordering.
We disprove this conjecture by providing a planar graph that does not have
such a mixed layout. In addition, we study mixed layouts of graph subdivisions,
and show that every planar graph has a mixed subdivision with one division
vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends
We study the following classes of beyond-planar graphs: 1-planar, IC-planar,
and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar,
and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every
edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs
of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two
pairs of crossing edges share two vertices. We study the relations of these
beyond-planar graph classes (beyond-planar graphs is a collective term for the
primary attempts to generalize the planar graphs) to right-angle crossing (RAC)
graphs that admit compact drawings on the grid with few bends. We present four
drawing algorithms that preserve the given embeddings. First, we show that
every -vertex NIC-planar graph admits a NIC-planar RAC drawing with at most
one bend per edge on a grid of size . Then, we show that
every -vertex 1-planar graph admits a 1-planar RAC drawing with at most two
bends per edge on a grid of size . Finally, we make two
known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at
most one bend per edge and for drawing IC-planar RAC graphs straight-line
Anisotropic Radial Layout for Visualizing Centrality and Structure in Graphs
This paper presents a novel method for layout of undirected graphs, where
nodes (vertices) are constrained to lie on a set of nested, simple, closed
curves. Such a layout is useful to simultaneously display the structural
centrality and vertex distance information for graphs in many domains,
including social networks. Closed curves are a more general constraint than the
previously proposed circles, and afford our method more flexibility to preserve
vertex relationships compared to existing radial layout methods. The proposed
approach modifies the multidimensional scaling (MDS) stress to include the
estimation of a vertex depth or centrality field as well as a term that
penalizes discord between structural centrality of vertices and their alignment
with this carefully estimated field. We also propose a visualization strategy
for the proposed layout and demonstrate its effectiveness using three social
network datasets.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
q-Deformed Superalgebras
The article deals with q-analogs of the three- and four-dimensional Euclidean
superalgebra and the Poincare superalgebra.Comment: 38 pages, LateX, no figures, corrected typo
Activation of Dendritic Cells through the Interleukin 1 Receptor 1 Is Critical for the Induction of Autoimmune Myocarditis
Dilated cardiomyopathy, resulting from myocarditis, is the most common cause of heart failure in young patients. We here show that interleukin (IL)-1 receptor type 1–deficient (IL-1R1−/−) mice are protected from development of autoimmune myocarditis after immunization with α-myosin-peptide(614–629). CD4+ T cells from immunized IL-1R1−/− mice proliferated poorly and failed to transfer disease after injection into naive severe combined immunodeficiency (SCID) mice. In vitro stimulation experiments suggested that the function of IL-1R1−/−CD4+ T cells was not intrinsically defect, but their activation by dendritic cells was impaired in IL-1R1−/− mice. Accordingly, production of tumor necrosis factor (TNF)-α, IL-1, IL-6, and IL-12p70 was reduced in dendritic cells lacking the IL-1 receptor type 1. In fact, injection of immature, antigen-loaded IL-1R1+/+ but not IL-1R1−/− dendritic cells into IL-1R1−/− mice fully restored disease susceptibility by rendering IL-1R1−/− CD4+ T cells pathogenic. Thus, IL-1R1 triggering is required for efficient activation of dendritic cells, which is in turn a prerequisite for induction of autoreactive CD4+ T cells and autoimmunity
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