45,952 research outputs found

    Graph classes and forbidden patterns on three vertices

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    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

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    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

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    LiNi1/3Mn1/3Co1/3O2 is a potential cathode material for high-power applications in lithium-ion batteries. While cation ordering on a sqrt(3)×sqrt(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

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    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

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    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

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    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

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    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

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    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 ℓ\ell-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 11-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

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    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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