46,896 research outputs found
Graph classes and forbidden patterns on three vertices
This paper deals with graph classes characterization and recognition. A
popular way to characterize a graph class is to list a minimal set of forbidden
induced subgraphs. Unfortunately this strategy usually does not lead to an
efficient recognition algorithm. On the other hand, many graph classes can be
efficiently recognized by techniques based on some interesting orderings of the
nodes, such as the ones given by traversals.
We study specifically graph classes that have an ordering avoiding some
ordered structures. More precisely, we consider what we call patterns on three
nodes, and the recognition complexity of the associated classes. In this
domain, there are two key previous works. Damashke started the study of the
classes defined by forbidden patterns, a set that contains interval, chordal
and bipartite graphs among others. On the algorithmic side, Hell, Mohar and
Rafiey proved that any class defined by a set of forbidden patterns can be
recognized in polynomial time. We improve on these two works, by characterizing
systematically all the classes defined sets of forbidden patterns (on three
nodes), and proving that among the 23 different classes (up to complementation)
that we find, 21 can actually be recognized in linear time.
Beyond this result, we consider that this type of characterization is very
useful, leads to a rich structure of classes, and generates a lot of open
questions worth investigating.Comment: Third version version. 38 page
On grounded L-graphs and their relatives
We consider the graph class Grounded-L corresponding to graphs that admit an
intersection representation by L-shaped curves, where additionally the topmost
points of each curve are assumed to belong to a common horizontal line. We
prove that Grounded-L graphs admit an equivalent characterisation in terms of
vertex ordering with forbidden patterns.
We also compare this class to related intersection classes, such as the
grounded segment graphs, the monotone L-graphs (a.k.a. max point-tolerance
graphs), or the outer-1-string graphs. We give constructions showing that these
classes are all distinct and satisfy only trivial or previously known
inclusions.Comment: 16 pages, 6 figure
Transmission Electron Microscope Studies of LiNi1/3Mn1/3Co1/3O2 before and after Long-Term Aging at 70°C
LiNi1/3Mn1/3Co1/3O2 is a potential cathode material for high-power applications in lithium-ion batteries. While cation ordering on a sqrt(3)Ăsqrt(3) R30° in-plane superlattice was proposed for the layered structure, the experimental data do not fully support this model. Here, we present a systematic electron diffraction study of LiNi1/3Mn1/3Co1/3O2 in the pristine state and after aging. Our results show that a mixture of different phases in the starting material transforms to the O3-type phase and the cubic spinel phase after aging, accompanied by an increase in the percentage of polycrystals
Anick-type resolutions and consecutive pattern avoidance
For permutations avoiding consecutive patterns from a given set, we present a
combinatorial formula for the multiplicative inverse of the corresponding
exponential generating function. The formula comes from homological algebra
considerations in the same sense as the corresponding inversion formula for
avoiding word patterns comes from the well known Anick's resolution.Comment: 16 pages. Preliminary version, comments are welcom
Structural changes at the semiconductor-insulator phase transition in the single layered La0.5Sr1.5MnO4 perovskite
The semiconductor-insulator phase transition of the single-layer manganite
La0.5Sr1.5MnO4 has been studied by means of high resolution synchrotron x-ray
powder diffraction and resonant x-ray scattering at the Mn K edge. We conclude
that a concomitant structural transition from tetragonal I4/mmm to orthorhombic
Cmcm phases drives this electronic transition. A detailed symmetry-mode
analysis reveals that condensation of three soft modes -Delta_2(B2u), X1+(B2u)
and X1+(A)- acting on the oxygen atoms accounts for the structural
transformation. The Delta_2 mode leads to a pseudo Jahn-Teller distortion (in
the orthorhombic bc-plane only) on one Mn site (Mn1) whereas the two X1+ modes
produce an overall contraction of the other Mn site (Mn2) and expansion of the
Mn1 one. The X1+ modes are responsible for the tetragonal superlattice
(1/2,1/2,0)-type reflections in agreement with a checkerboard ordering of two
different Mn sites. A strong enhancement of the scattered intensity has been
observed for these superlattice reflections close to the Mn K edge, which could
be ascribed to some degree of charge disproportion between the two Mn sites of
about 0.15 electrons. We also found that the local geometrical anisotropy of
the Mn1 atoms and its ordering originated by the condensed Delta_2 mode alone
perfectly explains the resonant scattering of forbidden (1/4,1/4,0)-type
reflections without invoking any orbital ordering.Comment: 3 tables and 10 figures; accepted in Phys. Rev.
Symmetry of re-entrant tetragonal phase in Ba1-xNaxFe2As2: Magnetic versus orbital ordering mechanism
Magneto-structural phase transitions in Ba1-xAxFe2As2 (A = K, Na) materials
are discussed for both magnetically and orbitally driven mechanisms, using a
symmetry analysis formulated within the Landau theory of phase transitions.
Both mechanisms predict identical orthorhombic space-group symmetries for the
nematic and magnetic phases observed over much of the phase diagram, but they
predict different tetragonal space-group symmetries for the newly discovered
re-entrant tetragonal phase in Ba1-xNaxFe2As2 (x ~ 0.24-0.28). In a magnetic
scenario, magnetic order with moments along the c-axis, as found
experimentally, does not allow any type of orbital order, but in an orbital
scenario, we have determined two possible orbital patterns, specified by
P4/mnc1' and I4221' space groups, which do not require atomic displacements
relative to the parent I4/mmm1' symmetry and, in consequence, are
indistinguishable in conventional diffraction experiments. We demonstrate that
the three possible space groups are however, distinct in resonant X-ray Bragg
diffraction patterns created by Templeton & Templeton scattering. This provides
an experimental method of distinguishing between magnetic and orbital models
Small Superpatterns for Dominance Drawing
We exploit the connection between dominance drawings of directed acyclic
graphs and permutations, in both directions, to provide improved bounds on the
size of universal point sets for certain types of dominance drawing and on
superpatterns for certain natural classes of permutations. In particular we
show that there exist universal point sets for dominance drawings of the Hasse
diagrams of width-two partial orders of size O(n^{3/2}), universal point sets
for dominance drawings of st-outerplanar graphs of size O(n\log n), and
universal point sets for dominance drawings of directed trees of size O(n^2).
We show that 321-avoiding permutations have superpatterns of size O(n^{3/2}),
riffle permutations (321-, 2143-, and 2413-avoiding permutations) have
superpatterns of size O(n), and the concatenations of sequences of riffles and
their inverses have superpatterns of size O(n\log n). Our analysis includes a
calculation of the leading constants in these bounds.Comment: ANALCO 2014, This version fixes an error in the leading constant of
the 321-superpattern siz
Signed graph embedding: when everybody can sit closer to friends than enemies
Signed graphs are graphs with signed edges. They are commonly used to
represent positive and negative relationships in social networks. While balance
theory and clusterizable graphs deal with signed graphs to represent social
interactions, recent empirical studies have proved that they fail to reflect
some current practices in real social networks. In this paper we address the
issue of drawing signed graphs and capturing such social interactions. We relax
the previous assumptions to define a drawing as a model in which every vertex
has to be placed closer to its neighbors connected via a positive edge than its
neighbors connected via a negative edge in the resulting space. Based on this
definition, we address the problem of deciding whether a given signed graph has
a drawing in a given -dimensional Euclidean space. We present forbidden
patterns for signed graphs that admit the introduced definition of drawing in
the Euclidean plane and line. We then focus on the -dimensional case, where
we provide a polynomial time algorithm that decides if a given complete signed
graph has a drawing, and constructs it when applicable
Bandt-Pompe symbolization dynamics for time series with tied values: A data-driven approach
In 2002, Bandt and Pompe [Phys. Rev. Lett. 88, 174102 (2002)] introduced a successfully symbolic encoding scheme based on the ordinal relation between the amplitude of neighboring values of a given data sequence, from which the permutation entropy can be evaluated. Equalities in the analyzed sequence, for example, repeated equal values, deserve special attention and treatment as was shown recently by Zunino and co-workers [Phys. Lett. A 381, 1883 (2017)]. A significant number of equal values can give rise to false conclusions regarding the underlying temporal structures in practical contexts. In the present contribution, we review the different existing methodologies for treating time series with tied values by classifying them according to their different strategies. In addition, a novel data-driven imputation is presented that proves to outperform the existing methodologies and avoid the false conclusions pointed by Zunino and co-workers.Fil: Traversaro Varela, Francisco. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional de LanĂșs; ArgentinaFil: Redelico, Francisco Oscar. Hospital Italiano; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Risk, Marcelo. Hospital Italiano; Argentina. Instituto TecnolĂłgico de Buenos Aires; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Frery, Alejandro CĂ©sar. Universidade Federal de Alagoas; BrasilFil: Rosso, Osvaldo AnĂbal. Hospital Italiano; Argentina. Universidade Federal de Alagoas; Brasil. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad de Los Andes; Chil
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