Parameterized Complexity of Vertex Splitting to Pathwidth at most 1

Motivated by the planarization of 2-layered straight-line drawings, we consider the problem of modifying a graph such that the resulting graph has pathwidth at most 1. The problem Pathwidth-One Vertex Explosion (POVE) asks whether such a graph can be obtained using at most $k$ vertex explosions, where a vertex explosion replaces a vertex $v$ by deg$(v)$ degree-1 vertices, each incident to exactly one edge that was originally incident to $v$. For POVE, we give an FPT algorithm with running time $O(4^k \cdot m)$ and an $O(k^2)$ kernel, thereby improving over the $O(k^6)$-kernel by Ahmed et al. [GD 22] in a more general setting. Similarly, a vertex split replaces a vertex $v$ by two distinct vertices $v_1$ and $v_2$ and distributes the edges originally incident to $v$ arbitrarily to $v_1$ and $v_2$. Analogously to POVE, we define the problem variant Pathwidth-One Vertex Splitting (POVS) that uses the split operation instead of vertex explosions. Here we obtain a linear kernel and an algorithm with running time $O((6k+12)^k \cdot m)$. This answers an open question by Ahmed et al. [GD22]. Finally, we consider the problem $\Pi$ Vertex Splitting ($\Pi$-VS), which generalizes the problem POVS and asks whether a given graph can be turned into a graph of a specific graph class $\Pi$ using at most $k$ vertex splits. For graph classes $\Pi$ that can be tested in monadic second-order graph logic (MSO$_2$), we show that the problem $\Pi$-VS can be expressed as an MSO$_2$ formula, resulting in an FPT algorithm for $\Pi$-VS parameterized by $k$ if $\Pi$ additionally has bounded treewidth. We obtain the same result for the problem variant using vertex explosions

Enamel Structure in Astrapotheres and Its Functional Implications

Astrapotheres, large extinct ungulates of South America, share with rhinoceroses vertical prism decussation in the cheek tooth enamel. The similarity extends beyond merely the direction of the planes of decussation. The vertical decussation in astrapotheres is confined to the inner part of the enamel and has uniformly well-defined zones in which the prism direction differs by nearly 90° and the zones are separated by narrow transitional borders of intermediate prism direction. The outer enamel consists of predominantly occlusally and outwardly directed prisms. Within the outer enamel is a region of horizontally decussating prisms; here the angle of decussation is usually smaller than that of the inner vertically decussating prisms. Except for the horizontal decussation in the outer enamel, these conditions match structures that have been described for rhinocerotoids. These features, together with the similarity in premortem crack direction and gross shape of the cheek teeth, imply that astrapotheres and rhinocerotoids shared essentially the same system of cheek tooth mechanics. However, the microstructure of the canine enamel in the astrapotheres is distinct. The lower canine enamel of the Oligocene Parastrapotherium exhibits a form of vertical decussation modified by a wavelike bending of prism zones, whereas the decussation in the rhinocerotoid canine is horizontal. The lower canine in Parastrapotherium was subjected to different loading conditions, judging from multiple sets of premortem crack directions. The modified vertical decussation would in theory resist cracking under different directions of tensile stresses. This is confirmed by the sinuous paths of cracks that run in directions differing by up to 90°. That diverse stresses were generated in the enamel during life is confirmed by the pattern of premortem cracks in Parastrapotherium. The enamel in the upper canine of a late Miocene astrapothere lacks decussation but may have resisted cracking under varied loading conditions by virtue of a 3-dimensional wavelike bending of the prisms

Técnicas estadísticas y separación del ruido ambiental

6 pp.-- PACS nr.: 43.50.Rq.-- Comunicación presentada en los siguientes congresos: XXXIV Congreso Nacional de Acústica – TecniAcústica 2003. Encuentro Ibérico de Acústica. EAA Symposium on Architectural Acoustics. Expoacústica 2003 (Bilbao, 15-17 Octubre 2003).Publicado en número especial de la Revista de Acústica: Vol. 34, núm. 3-4 (2003).[EN] In this work the noise pollution produced by an airport in its surroundings is studied, when other noise sources, with analogous temporal and spectral characteristics, is present. A statistical analysis of level distributions allows breaking down the environmental noise into its constituent noise sources. This procedure works well for simple cases as the studied carried out here. Nevertheless, it is so restrictive that its use, for the moment, cannot be extended to more general problems.[ES] Se estudia el impacto acústico producido por un aeropuerto en presencia de otras fuentes de ruido con características análogas, tanto temporales como espectrales. Para ello se realiza un análisis basado en la distribución de niveles de ruido ambiente, desglosándolo en las distribuciones de los ruidos componentes. El procedimiento es aplicable para casos sencillos como el estudiado, sin embargo sus limitaciones son suficientemente restrictivas para que, de momento, no sea generalizable.Peer reviewe

Cálculo inverso de la resistividad al flujo de aire de lanas minerales

6 pages, 2 figures.-- PACS nr.: 43.20.Hg.-- Comunicación presentada en: XXXVI Jornadas Nacionales de Acústica – TecniAcústica 2005, Encuentro Ibérico de Acústica y EAA Symposium "Southern Europe Workshop on Environmental Acoustics and IMAGINE project" (Terrassa, 19-21 Oct 2005).Publicado en número especial de la Revista de Acústica: Vol 36, 3-4 (2005).Una magnitud importante para el uso de modelos analíticos que describen el comportamiento acústico de materiales absorbentes fibrosos y la propagación de la onda sonora a su través es la resistividad al flujo de aire. Aunque existen procedimientos bien establecidos para la medición de esta magnitud, la presencia del tipo de equipos necesarios para su obtención no es habitual en los laboratorios de ensayos acústicos. En este trabajo se presenta un procedimiento alternativo mediante el cual se puede estimar la resistividad al flujo de materiales fibrosos a través de medidas del coeficiente de absorción en tubo de ondas estacionarias. Con este fin se ha implementado un procedimiento inverso de cálculo numérico que liga ambas magnitudes a través de modelos analíticos conocidos y ampliamente utilizados. Por último, se ha aplicado el procedimiento desarrollado a una serie de casos que permiten ilustrar y valorar sus prestaciones.El presente trabajo se ha realizado con el soporte económico del Proyecto del Plan Nacional con referencia DPI2004-05504-C0201.Peer reviewe

Parameterized Complexity of Simultaneous Planarity

Given $k$ input graphs $G_1, \dots ,G_k$, where each pair $G_i$, $G_j$ with $i \neq j$ shares the same graph $G$, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks whether there exists a planar drawing for each input graph such that all drawings coincide on $G$. While SEFE is still open for the case of two input graphs, the problem is NP-complete for $k \geq 3$ [Schaefer, JGAA 13]. In this work, we explore the parameterized complexity of SEFE. We show that SEFE is FPT with respect to $k$ plus the vertex cover number or the feedback edge set number of the the union graph $G^\cup = G_1 \cup \dots \cup G_k$. Regarding the shared graph $G$, we show that SEFE is NP-complete, even if $G$ is a tree with maximum degree 4. Together with a known NP-hardness reduction [Angelini et al., TCS 15], this allows us to conclude that several parameters of $G$, including the maximum degree, the maximum number of degree-1 neighbors, the vertex cover number, and the number of cutvertices are intractable. We also settle the tractability of all pairs of these parameters. We give FPT algorithms for the vertex cover number plus either of the first two parameters and for the number of cutvertices plus the maximum degree, whereas we prove all remaining combinations to be intractable.Comment: Appears in the Proceedings of the 31st International Symposium on Graph Drawing and Network Visualization (GD 2023

Experimental Comparison of PC-Trees and PQ-Trees

PQ-trees and PC-trees are data structures that represent sets of linear and circular orders, respectively, subject to constraints that specific subsets of elements have to be consecutive. While equivalent to each other, PC-trees are conceptually much simpler than PQ-trees; updating a PC-tree so that a set of elements becomes consecutive requires only a single operation, whereas PQ-trees use an update procedure that is described in terms of nine transformation templates that have to be recursively matched and applied. Despite these theoretical advantages, to date no practical PC-tree implementation is available. This might be due to the original description by Hsu and McConnell [Hsu et al., 2003] in some places only sketching the details of the implementation. In this paper, we describe two alternative implementations of PC-trees. For the first one, we follow the approach by Hsu and McConnell, filling in the necessary details and also proposing improvements on the original algorithm. For the second one, we use a different technique for efficiently representing the tree using a Union-Find data structure. In an extensive experimental evaluation we compare our implementations to a variety of other implementations of PQ-trees that are available on the web as part of academic and other software libraries. Our results show that both PC-tree implementations beat their closest fully correct competitor, the PQ-tree implementation from the OGDF library [Markus Chimani et al., 2014; Leipert, 1997], by a factor of 2 to 4, showing that PC-trees are not only conceptually simpler but also fast in practice. Moreover, we find the Union-Find-based implementation, while having a slightly worse asymptotic runtime, to be twice as fast as the one based on the description by Hsu and McConnell

Influence of the Heating Rate on the Foaming Behavior of Various Aluminium Alloys

Powders of metallurgically prepared precursors expand to a foam differently depending on how fast they are heated to their foaming temperature. The foaming behavior of four alloys was studied with heating rates varying from 0.1 K/s to 18 K/s. It was found that each alloy shows its own non-linear behavior of expansion values. Alloys not containing magnesium exhibit a maximum at intermediate heating rates, whereas Mg-containing alloys tend to expand more for higher heating rates

Practical modeling for load paths in a realistic, light-frame wood house

The objective of this study was to develop and validate practical modeling methods for investigating load paths and system behavior in a realistic, light-frame wood structure. The modeling methods were validated against full-scale tests on subassemblies and an L-shaped house. The model of the L-shaped house was then modified and used to investigate the effects of re-entrant corners, wall openings and gable-end retrofits on system behavior and load paths. Results from this study showed that the effects of adding re-entrant corners and wall openings on uplift load distributions were dependent on the orientation of the trusses with respect to the walls. Openings added to walls parallel to the trusses had the least effect on loads carried by the remaining walls in the building. Varying re-entrant corner dimensions of the L-shaped house under ASCE 7-05 (ASCE 2005) design wind loads caused increasing degrees of torsion throughout the house, depending on the relative location and stiffness of the in-plane walls (parallel to the applied wind loads) as well as the assumed direction of the wind loads. Balancing the stiffness of the walls on either side of the house with the largest re-entrant corner helped to decrease torsion in the structure somewhat. Finally, although previous full-scale tests on gable-end sections verified the effectiveness of the gable-end retrofit that was recently adopted into the 2010 Florida building code, questions remained about the effects of the retrofit on torsion in a full building. The current study found that adding the gable-end retrofits to the L-shaped house did not cause additional torsion