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 $S$ of directions symmetric with respect to the origin. Our results on Ordered Level Planarity imply $NP$-hardness for any $S$ with $|S|\ge 4$ even if the given graph is a matching. Katz, Krug, Rutter and Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where $S$ contains precisely the horizontal and vertical directions, can be solved in polynomial time [GD'09]. Our results imply that this is incorrect unless $P=NP$. 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

Thermal stabilization of metal matrix nanocomposites by nanocarbon reinforcements

Metal matrix composites reinforced by nanocarbon materials, such as carbon nanotubes or nanodiamonds, are very promising materials for a large number of functional and structural applications. Carbon nanotubes and nanodiamonds-reinforced metal matrix nanocomposites with different concentrations of the carbon phase were processed by high-pressure torsion deformation and the evolving nanostructures were thoroughly analyzed by electron microscopy. Particular emphasis is placed on the thermal stability of the nanocarbon reinforced metal matrix composites, which is less influenced by the amount of added nanocarbon reinforcements than by the nanocarbon reinforcement type and its distribution in the metal matrix

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

GraphCombEx: A Software Tool for Exploration of Combinatorial Optimisation Properties of Large Graphs

We present a prototype of a software tool for exploration of multiple combinatorial optimisation problems in large real-world and synthetic complex networks. Our tool, called GraphCombEx (an acronym of Graph Combinatorial Explorer), provides a unified framework for scalable computation and presentation of high-quality suboptimal solutions and bounds for a number of widely studied combinatorial optimisation problems. Efficient representation and applicability to large-scale graphs and complex networks are particularly considered in its design. The problems currently supported include maximum clique, graph colouring, maximum independent set, minimum vertex clique covering, minimum dominating set, as well as the longest simple cycle problem. Suboptimal solutions and intervals for optimal objective values are estimated using scalable heuristics. The tool is designed with extensibility in mind, with the view of further problems and both new fast and high-performance heuristics to be added in the future. GraphCombEx has already been successfully used as a support tool in a number of recent research studies using combinatorial optimisation to analyse complex networks, indicating its promise as a research software tool

T cell sensitivity to TGF-β is required for the effector function but not the generation of splenic CD8+ regulatory T cells induced via the injection of antigen into the anterior chamber

The introduction of antigen into the anterior chamber (AC) of the eye induces the production of antigen-specific splenic CD8+ regulatory T cells (AC-SPL cells) that suppress a delayed-type hypersensitivity (DTH) reaction in immunized mice. Because the generation of these regulatory T cells is also induced by exposure to transforming growth factor (TGF)-β and antigen or F4/80+ cells exposed to TGF-β and antigen in vitro, we investigated (i) whether these cells are produced in dominant negative receptor for transforming growth factor β receptor type II (dnTGFβRII) or Cbl-b−/− mice whose T cells are resistant to TGF-β, (ii) whether DTH is suppressed by wild type (WT) CD8+ AC-SPL cells in Cbl-b−/− and dnTGFβRII mice and (iii) the effect of antibodies to TGF-β on the suppression of DTH by CD8+ AC-SPL cells. DnTGFβRII immunized and Cbl-b−/− mice produced splenic CD8+ regulatory cells after the intracameral injection of antigen and immunization. The suppression of a DTH reaction by CD8+ AC-SPL cells in WT mice was blocked by the local inclusion of antibodies to TGF-β when WT splenic CD8+ AC-SPL cells were injected into the DTH reaction site. Moreover, the DTH reaction in immunized dnTGFβRII and Cbl-b−/− mice was not suppressed by the transfer of WT CD8+ AC-SPL cells to the site challenged with antigen. In aggregate, these observations suggest that T cell sensitivity to TGF-β is not an obligate requirement for the in vivo induction of CD8+ AC-SPL T cells but the suppression of an in vivo DTH reaction by CD8+ AC-SPL cells is dependent on TGF-β

Hanani-Tutte for radial planarity

A drawing of a graph G is radial if the vertices of G are placed on concentric circles C 1 , . . . , C k with common center c , and edges are drawn radially : every edge intersects every circle centered at c at most once. G is radial planar if it has a radial embedding, that is, a crossing-free radial drawing. If the vertices of G are ordered or partitioned into ordered levels (as they are for leveled graphs), we require that the assignment of vertices to circles corresponds to the given ordering or leveling. We show that a graph G is radial planar if G has a radial drawing in which every two edges cross an even number of times; the radial embedding has the same leveling as the radial drawing. In other words, we establish the weak variant of the Hanani-Tutte theorem for radial planarity. This generalizes a result by Pach and Toth

Quorum sensing in African Trypanosomes

Many microbial eukaryotes exhibit cell-cell communication to co-ordinate group behaviours as a strategy to exploit a changed environment, adapt to adverse conditions or regulate developmental responses. Although best characterised in bacteria, eukaryotic microbes have also been revealed to cooperate to optimise their survival or dissemination. An excellent model for these processes are African trypanosomes, protozoa responsible for important human and animal disease in sub Saharan Africa. These unicellular parasites use density sensing in their mammalian host to prepare for transmission. Recently, the signal and signal transduction pathway underlying this activity have been elucidated, revealing that the parasite exploits oligopeptide signals generated by released peptidases to monitor cell density and so generate transmission stages. Here we review the evidence for this elegant quorum sensing mechanism and its parallels with similar mechanisms in other microbial systems. We also discuss its implications for disease spread in the context of coinfections involving different trypanosome species