The Widths of Strict Outerconfluent Graphs

Strict outerconfluent drawing is a style of graph drawing in which vertices are drawn on the boundary of a disk, adjacencies are indicated by the existence of smooth curves through a system of tracks within the disk, and no two adjacent vertices are connected by more than one of these smooth tracks. We investigate graph width parameters on the graphs that have drawings in this style. We prove that the clique-width of these graphs is unbounded, but their twin-width is bounded.Comment: 15 pages, 2 figure

Scalability considerations for multivariate graph visualization

Real-world, multivariate datasets are frequently too large to show in their entirety on a visual display. Still, there are many techniques we can employ to show useful partial views-sufficient to support incremental exploration of large graph datasets. In this chapter, we first explore the cognitive and architectural limitations which restrict the amount of visual bandwidth available to multivariate graph visualization approaches. These limitations afford several design approaches, which we systematically explore. Finally, we survey systems and studies that exhibit these design strategies to mitigate these perceptual and architectural limitations

Edge routing with ordered bundles

Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling that draws each edge of a bundle separately as in metro-maps and call our method ordered bundles. To produce aesthetically looking edge routes, it minimizes a cost function on the edges. The cost function depends on the ink, required to draw the edges, the edge lengths, widths and separations. The cost also penalizes for too many edges passing through narrow channels by using the constrained Delaunay triangulation. The method avoids unnecessary edge-node and edge-edge crossings. To draw edges with the minimal number of crossings and separately within the same bundle, we develop an efficient algorithm solving a variant of the metro-line crossing minimization problem. In general, the method creates clear and smooth edge routes giving an overview of the global graph structure, while still drawing each edge separately and thus enabling local analysis. © 2015 Elsevier B.V

A multi-chamber microfluidic intestinal barrier model using Caco-2 cells for drug transport studies

This paper presents the design and fabrication of a multi-layer and multi-chamber microchip system using thiol-ene 'click chemistry' aimed for drug transport studies across tissue barrier models. The fabrication process enables rapid prototyping of multi-layer microfluidic chips using different thiol-ene polymer mixtures, where porous Teflon membranes for cell monolayer growth were incorporated by masked sandwiching thiol-ene-based fluid layers. Electrodes for trans-epithelial electrical resistance (TEER) measurements were incorporated using low-melting soldering wires in combination with platinum wires, enabling parallel real-time monitoring of barrier integrity for the eight chambers. Additionally, the translucent porous Teflon membrane enabled optical monitoring of cell monolayers. The device was developed and tested with the Caco-2 intestinal model, and compared to the conventional Transwell system. Cell monolayer differentiation was assessed via in situ immunocytochemistry of tight junction and mucus proteins, P-glycoprotein 1 (P-gp) mediated efflux of Rhodamine 123, and brush border aminopeptidase activity. Monolayer tightness and relevance for drug delivery research was evaluated through permeability studies of mannitol, dextran and insulin, alone or in combination with the absorption enhancer tetradecylmaltoside (TDM). The thiol-ene-based microchip material and electrodes were highly compatible with cell growth. In fact, Caco-2 cells cultured in the device displayed differentiation, mucus production, directional transport and aminopeptidase activity within 9-10 days of cell culture, indicating robust barrier formation at a faster rate than in conventional Transwell models. The cell monolayer displayed high TEER and tightness towards hydrophilic compounds, whereas co-administration of an absorption enhancer elicited TEER-decrease and increased permeability similar to the Transwell cultures. The presented cell barrier microdevice constitutes a relevant tissue barrier model, enabling transport studies of drugs and chemicals under real-time optical and functional monitoring in eight parallel chambers, thereby increasing the throughput compared to previously reported microdevices