3D Visibility Representations of 1-planar Graphs

We prove that every 1-planar graph G has a z-parallel visibility representation, i.e., a 3D visibility representation in which the vertices are isothetic disjoint rectangles parallel to the xy-plane, and the edges are unobstructed z-parallel visibilities between pairs of rectangles. In addition, the constructed representation is such that there is a plane that intersects all the rectangles, and this intersection defines a bar 1-visibility representation of G.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Testing replica predictions in experiments

We review the predictions of the replica approach both for the statics and for the off-equilibrium dynamics. We stress the importance of the Cugliandolo-Kurchan off-equilibrium fluctuation-dissipation relation in providing a bridge between the statics and the dynamics. We present numerical evidence for the correctness of these relations. This approach allows an experimental determination of the basic parameters of the replica theory.Comment: To appear in Chiarotti's Festschrift Volume (8 Pages, 3 figures

Prediction of Fretting Crack Location and Orientation in a Single Crystal Nickel Alloy

Fretting is a structural damage mechanism arising between two nominally clamped surfaces subjected to an oscillatory loading. A critical location for fretting induced damage has been identified at the blade/disk and blade/damper interfaces of gas turbine engine turbomachinery and space propulsion components. The high- temperature, high-frequency loading environment seen by these components lead to severe stress gradients at the edge-of-contact that could potentially foster crack growth leading to component failure. These contact stresses drive crack nucleation in fretting and are very sensitive to the geometry of the contacting bodies, the contact loads, materials, temperature, and contact surface tribology (friction). Recently, a high-frequency, high-temperature load frame has been designed for experimentally investigating fretting damage of single crystal nickel materials employed in aircraft and spacecraft turbomachinery. A modeling method for characterizing the fretting stresses of the spherical fretting contact stress behavior in this experiment is developed and described. The calculated fretting stresses for a series of experiments are then correlated to the observed fretting damage. Results show that knowledge of the normal stresses and resolved shear stresses on each crystal plane can aid in predicting crack locations and orientations

Bar 1-Visibility Drawings of 1-Planar Graphs

A bar 1-visibility drawing of a graph $G$ is a drawing of $G$ where each vertex is drawn as a horizontal line segment called a bar, each edge is drawn as a vertical line segment where the vertical line segment representing an edge must connect the horizontal line segments representing the end vertices and a vertical line segment corresponding to an edge intersects at most one bar which is not an end point of the edge. A graph $G$ is bar 1-visible if $G$ has a bar 1-visibility drawing. A graph $G$ is 1-planar if $G$ has a drawing in a 2-dimensional plane such that an edge crosses at most one other edge. In this paper we give linear-time algorithms to find bar 1-visibility drawings of diagonal grid graphs and maximal outer 1-planar graphs. We also show that recursive quadrangle 1-planar graphs and pseudo double wheel 1-planar graphs are bar 1-visible graphs.Comment: 15 pages, 9 figure

The Effect of Planarization on Width

We study the effects of planarization (the construction of a planar diagram $D$ from a non-planar graph $G$ by replacing each crossing by a new vertex) on graph width parameters. We show that for treewidth, pathwidth, branchwidth, clique-width, and tree-depth there exists a family of $n$-vertex graphs with bounded parameter value, all of whose planarizations have parameter value $\Omega(n)$. However, for bandwidth, cutwidth, and carving width, every graph with bounded parameter value has a planarization of linear size whose parameter value remains bounded. The same is true for the treewidth, pathwidth, and branchwidth of graphs of bounded degree.Comment: 15 pages, 6 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Hierarchical Partial Planarity

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to construct layouts of these graphs in which the readability of an edge is proportional to its importance, that is, more important edges have fewer crossings. We formalize this problem and study the case in which there exist three different degrees of importance. We give a polynomial-time testing algorithm when the graph induced by the two most important sets of edges is biconnected. We also discuss interesting relationships with other constrained-planarity problems.Comment: Conference version appeared in WG201

Earth-Moon Lagrangian points as a testbed for general relativity and effective field theories of gravity

We first analyse the restricted four-body problem consisting of the Earth, the Moon and the Sun as the primaries and a spacecraft as the planetoid. This scheme allows us to take into account the solar perturbation in the description of the motion of a spacecraft in the vicinity of the stable Earth-Moon libration points L4 and L5 both in the classical regime and in the context of effective field theories of gravity. A vehicle initially placed at L4 or L5 will not remain near the respective points. In particular, in the classical case the vehicle moves on a trajectory about the libration points for at least 700 days before escaping away. We show that this is true also if the modified long-distance Newtonian potential of effective gravity is employed. We also evaluate the impulse required to cancel out the perturbing force due to the Sun in order to force the spacecraft to stay precisely at L4 or L5. It turns out that this value is slightly modified with respect to the corresponding Newtonian one. In the second part of the paper, we first evaluate the location of all Lagrangian points in the Earth-Moon system within the framework of general relativity. For the points L4 and L5, the corrections of coordinates are of order a few millimeters and describe a tiny departure from the equilateral triangle. After that, we set up a scheme where the theory which is quantum corrected has as its classical counterpart the Einstein theory, instead of the Newtonian one. In other words, we deal with a theory involving quantum corrections to Einstein gravity, rather than to Newtonian gravity. By virtue of the effective-gravity correction to the long-distance form of the potential among two point masses, all terms involving the ratio between the gravitational radius of the primary and its separation from the planetoid get modified. Within this framework, for the Lagrangian points of stable equilibrium, we find quantum corrections of order two millimeters, whereas for Lagrangian points of unstable equilibrium we find quantum corrections below a millimeter. In the latter case, for the point L1, general relativity corrects Newtonian theory by 7.61 meters, comparable, as an order of magnitude, with the lunar geodesic precession of about 3 meters per orbit. The latter is a cumulative effect accurately measured at the centimeter level through the lunar laser ranging positioning technique. Thus, it is possible to study a new laser ranging test of general relativity to measure the 7.61-meter correction to the L1 Lagrangian point, an observable never used before in the Sun-Earth-Moon system. Performing such an experiment requires controlling the propulsion to precisely reach L1, an instrumental accuracy comparable to the measurement of the lunar geodesic precession, understanding systematic effects resulting from thermal radiation and multi-body gravitational perturbations. This will then be the basis to consider a second-generation experiment to study deviations of effective field theories of gravity from general relativity in the Sun-Earth-Moon system

On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively). For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Yellow tails in the Red Sea: phylogeography of the Indo-Pacific goatfish Mulloidichthys flavolineatus reveals isolation in peripheral provinces and cryptic evolutionary lineages

Aim: Broadly distributed reef fishes tend to have high gene flow mediated by a pelagic larval phase. Here, we survey a reef-associated fish distributed across half the tropical oceans, from the Red Sea to the central Pacific. Our goal is to determine whether genetic structure of the broadly distributed Yellowstripe Goatfish (Mulloidichthys flavolineatus) is defined by biogeographical barriers, or facilitated via larval dispersal. Location: Red Sea, Indian Ocean, Pacific Ocean. Methods: Specimens were obtained at 19 locations from the Red Sea to Hawai'i. Genetic data include mtDNA cytochrome b (n = 217) and 12 microsatellite loci (n = 185). Analysis of molecular variance (AMOVA), structure, a parsimony network and coalescence analyses were used to resolve recent population history and connectivity. Results: Population structure was significant (mtDNA ϕST = 0.68, P < 0.001; microsatellite FST = 0.08, P < 0.001), but mostly driven by samples from the North-western (NW) Indian Ocean (including the Red Sea) and Hawai'i. There was little population structure across the Indian Ocean to the central Pacific. Hawai'i was distinguished as an isolated population (mtDNA ϕST = 0.03–0.08, P = n.s.; microsatellites FST = 0.05–0.10, P < 0.001). Specimens from the NW Indian Ocean clustered as a distinct phylogenetic lineage that diverged approximately 493 ka (d = 1.7%), which indicates that these fish persisted in isolation through several Pleistocene glacial cycles. Main conclusions: These data reinforce the emerging themes that: (1) phylogeographical breaks within species often coincide with biogeographical breaks based on species distributions, and (2) populations on the periphery of the range (NW Indian Ocean and Hawai'i) are isolated and may be evolutionary incubators producing new species

The development of the Meaning in Life Index (MILI) and its relationship with personality and religious behaviours and beliefs among UK undergraduate students

The scales available for assessing meaning in life appear to be confounded with several related constructs, including purpose in life, satisfaction with life, and goal-directed behaviour. The Meaning in Life Index (MILI), a new instrument devised as a specific measure of meaning in life, was developed from responses to a pool of 22 items rated by a sample of 501 undergraduate students in Wales. The nine-item scale demonstrated sufficient face validity, internal consistency, and scale reliability to commend the instrument for future use. With respect to personality, the MILI scores were most strongly predicted by neuroticism (negatively), and less strongly by extraversion (positively) and psychoticism (negatively). With respect to several religious behavioural variables, those who attended church at least weekly returned significantly higher MILI scores than those who attended church less frequently. Intrinsic religiosity was the only orientation to be significantly associated with the MILI scale scores, although the magnitude of the association was smaller than anticipated. These results suggest that meaning in life is associated more strongly with individual differences in personality than with specific religious behaviours and attitudes. The implications of these results are discussed in terms of individual's personal values and attitudes that might underlie their experience of a meaning in life