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

Sphingosine Kinase 1 Mediation of Expression of the Anaphylatoxin Receptor C5L2 Dampens the Inflammatory Response to Endotoxin

The complement anaphylatoxin C5a has a pathogenetic role in endotoxin-induced lung inflammatory injury by regulating phagocytic cell migration and activation. Endotoxin and C5a activate the enzyme sphingosine kinase (Sphk) 1 to generate the signaling lipid sphingosine-1-phosphate (S1P), a critical regulator of phagocyte function. We assessed the function of Sphk1 and S1P in experimental lung inflammatory injury and determined their roles in anaphylatoxin receptor signaling and on the expression of the two C5a receptors, C5aR (CD88) and C5L2, on phagocytes. We report that Sphk1 gene deficient (Sphk1−/−) mice had augmented lung inflammatory response to endotoxin compared to wild type mice. Sphk1 was required for C5a-mediated reduction in cytokine and chemokine production by macrophages. Moreover, neutrophils from Sphk1−/− mice failed to upregulate the anaphylatoxin receptor C5L2 in response to LPS. Exogenous S1P restored C5L2 cell surface expression of Sphk1−/− mouse neutrophils to wild type levels but had no effect on cell surface expression of the other anaphylatoxin receptor, CD88. These results provide the first genetic evidence of the crucial role of Sphk1 in regulating the balance between expression of CD88 and C5L2 in phagocytes. S1P-mediated up-regulation of C5L2 is a novel therapeutic target for mitigating endotoxin-induced lung inflammatory injury

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

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

T-Cell Promiscuity in Autoimmune Diabetes

OBJECTIVE—It is well established that the primary mediators of β-cell destruction in type 1 diabetes are T-cells. Nevertheless, the molecular basis for recognition of β-cell–specific epitopes by pathogenic T-cells remains ill defined; we seek to further explore this issue