Bar 1-Visibility Graphs and their relation to other Nearly Planar Graphs

A graph is called a strong (resp. weak) bar 1-visibility graph if its vertices can be represented as horizontal segments (bars) in the plane so that its edges are all (resp. a subset of) the pairs of vertices whose bars have a $\epsilon$-thick vertical line connecting them that intersects at most one other bar. We explore the relation among weak (resp. strong) bar 1-visibility graphs and other nearly planar graph classes. In particular, we study their relation to 1-planar graphs, which have a drawing with at most one crossing per edge; quasi-planar graphs, which have a drawing with no three mutually crossing edges; the squares of planar 1-flow networks, which are upward digraphs with in- or out-degree at most one. Our main results are that 1-planar graphs and the (undirected) squares of planar 1-flow networks are weak bar 1-visibility graphs and that these are quasi-planar graphs

Flud: a hybrid crowd-algorithm approach for visualizing biological networks

Modern experiments in many disciplines generate large quantities of network (graph) data. Researchers require aesthetic layouts of these networks that clearly convey the domain knowledge and meaning. However, the problem remains challenging due to multiple conflicting aesthetic criteria and complex domain-specific constraints. In this paper, we present a strategy for generating visualizations that can help network biologists understand the protein interactions that underlie processes that take place in the cell. Specifically, we have developed Flud, an online game with a purpose (GWAP) that allows humans with no expertise to design biologically meaningful graph layouts with the help of algorithmically generated suggestions. Further, we propose a novel hybrid approach for graph layout wherein crowdworkers and a simulated annealing algorithm build on each other's progress. To showcase the effectiveness of Flud, we recruited crowd workers on Amazon Mechanical Turk to lay out complex networks that represent signaling pathways. Our results show that the proposed hybrid approach outperforms state-of-the-art techniques for graphs with a large number of feedback loops. We also found that the algorithmically generated suggestions guided the players when they are stuck and helped them improve their score. Finally, we discuss broader implications for mixed-initiative interactions in human computation games.Comment: This manuscript is currently under revie

Visual Exploration of Dynamic Multichannel EEG Coherence Networks

Electroencephalography (EEG) coherence networks represent functional brain connectivity, and are constructed by calculating the coherence between pairs of electrode signals as a function of frequency. Visualization of such networks can provide insight into unexpected patterns of cognitive processing and help neuroscientists to understand brain mechanisms. However, visualizing dynamic EEG coherence networks is a challenge for the analysis of brain connectivity, especially when the spatial structure of the network needs to be taken into account. In this paper, we present a design and implementation of a visualization framework for such dynamic networks. First, requirements for supporting typical tasks in the context of dynamic functional connectivity network analysis were collected from neuroscience researchers. In our design, we consider groups of network nodes and their corresponding spatial location for visualizing the evolution of the dynamic coherence network. We introduce an augmented timeline-based representation to provide an overview of the evolution of functional units (FUs) and their spatial location over time. This representation can help the viewer to identify relations between functional connectivity and brain regions, as well as to identify persistent or transient functional connectivity patterns across the whole time window. In addition, we introduce the time-annotated FU map representation to facilitate comparison of the behaviour of nodes between consecutive FU maps. A colour coding is designed that helps to distinguish distinct dynamic FUs. Our implementation also supports interactive exploration. The usefulness of our visualization design was evaluated by an informal user study. The feedback we received shows that our design supports exploratory analysis tasks well. The method can serve as a first step before a complete analysis of dynamic EEG coherence networks