Compact Drawings of 1-Planar Graphs with Right-Angle Crossings and Few Bends

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex. A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices. We study the relations of these beyond-planar graph classes (beyond-planar graphs is a collective term for the primary attempts to generalize the planar graphs) to right-angle crossing (RAC) graphs that admit compact drawings on the grid with few bends. We present four drawing algorithms that preserve the given embeddings. First, we show that every $n$-vertex NIC-planar graph admits a NIC-planar RAC drawing with at most one bend per edge on a grid of size $O(n) \times O(n)$. Then, we show that every $n$-vertex 1-planar graph admits a 1-planar RAC drawing with at most two bends per edge on a grid of size $O(n^3) \times O(n^3)$. Finally, we make two known algorithms embedding-preserving; for drawing 1-planar RAC graphs with at most one bend per edge and for drawing IC-planar RAC graphs straight-line

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

q-Deformed Superalgebras

The article deals with q-analogs of the three- and four-dimensional Euclidean superalgebra and the Poincare superalgebra.Comment: 38 pages, LateX, no figures, corrected typo

DOK3 Negatively Regulates LPS Responses and Endotoxin Tolerance

Innate immune activation via Toll-like receptors (TLRs), although critical for host defense against infection, must be regulated to prevent sustained cell activation that can lead to cell death. Cells repeatedly stimulated with lipopolysaccharide (LPS) develop endotoxin tolerance making the cells hypo-responsive to additional TLR stimulation. We show here that DOK3 is a negative regulator of TLR signaling by limiting LPS-induced ERK activation and cytokine responses in macrophages. LPS induces ubiquitin-mediated degradation of DOK3 leading to SOS1 degradation and inhibition of ERK activation. DOK3 mice are hypersensitive to sublethal doses of LPS and have altered cytokine responses in vivo. During endotoxin tolerance, DOK3 expression remains stable, and it negatively regulates the expression of SHIP1, IRAK-M, SOCS1, and SOS1. As such, DOK3-deficient macrophages are more sensitive to LPS-induced tolerance becoming tolerant at lower levels of LPS than wild type cells. Taken together, the absence of DOK3 increases LPS signaling, contributing to LPS-induced tolerance. Thus, DOK3 plays a role in TLR signaling during both naïve and endotoxin-induced tolerant conditions

Basement membrane proteins as a substrate for efficient Trypanosoma brucei differentiation in vitro

The ability to reproduce the developmental events of trypanosomes that occur in their mammalian host in vitro offers significant potential to assist in understanding of the underlying biology of the process. For example, the transition from bloodstream slender to bloodstream stumpy forms is a quorum-sensing response to the parasite-derived peptidase digestion products of environmental proteins. As an abundant physiological substrate in vivo, we studied the ability of a basement membrane matrix enriched gel (BME) in the culture medium to support differentiation of pleomorphic Trypanosoma brucei to stumpy forms. BME comprises extracellular matrix proteins, which are among the most abundant proteins found in connective tissues in mammals and known substrates of parasite-released peptidases. We previously showed that two of these released peptidases are involved in generating a signal that promotes slender-to-stumpy differentiation. Here, we tested the ability of basement membrane extract to enhance parasite differentiation through its provision of suitable substrates to generate the quorum sensing signal, namely oligopeptides. Our results show that when grown in the presence of BME, T. brucei pleomorphic cells arrest at the G0/1 phase of the cell cycle and express the differentiation marker PAD1, the response being restricted to differentiation-competent parasites. Further, the stumpy forms generated in BME medium are able to efficiently proceed onto the next life cycle stage in vitro, procyclic forms, when incubated with cis-aconitate, further validating the in vitro BME differentiation system. Hence, BME provides a suitable in vitro substrate able to accurately recapitulate physiological parasite differentiation without the use of experimental animals

The NuGO proof of principle study package: a collaborative research effort of the European Nutrigenomics Organisation

Acknowledgments This project is funded by the Nutrigenomics Organisation, EC funded Network of Excellence, grant nr.FOOD- 2004-506360.Peer reviewedPublisher PD