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Spatial networks are networks whose graph topology is constrained by their embedded spatial space. Understanding the coupled spatial-graph properties is crucial for extracting powerful representations from spatial networks. Therefore,…
Spatial Social Networks (SSN) build on the node and edge structure used in Social Network Analysis (SNA) by incorporating spatial information. Thus, SSNs include both topological and spatial data. The geographic embedding of the nodes makes…
Natural and man-made transport webs are frequently dominated by dense sets of nested cycles. The architecture of these networks, as defined by the topology and edge weights, determines how efficiently the networks perform their function.…
Generalized Pythagoras trees were developed for visualizing hierarchical data, producing organic, fractal-like representations. However, the drawback of the original layout algorithm is visual overlap of tree branches. To avoid such…
Many real-world networks, including social and information networks, are dynamic structures that evolve over time. Such dynamic networks are typically visualized using a sequence of static graph layouts. In addition to providing a visual…
The information technology explosion has dramatically increased the application of new mathematical ideas and has led to an increasing use of mathematics across a wide range of fields that have been traditionally labeled "pure" or…
Topological analysis of the magnetic field in simulated plasmas allows the study of various physical phenomena in a wide range of settings. One such application is magnetic reconnection, a phenomenon related to the dynamics of the magnetic…
Dynamic networks can be challenging to analyze visually, especially if they span a large time range during which new nodes and edges can appear and disappear. Although it is straightforward to provide interfaces for visualization that…
Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…
Timelines are common visualizations to represent and manipulate temporal data, from historical events storytelling to animation authoring. However, timeline visualizations rarely consider spatio-temporal 3D data (e.g. mesh or volumetric…
Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…
Understanding the response of an output variable to multi-dimensional inputs lies at the heart of many data exploration endeavours. Topology-based methods, in particular Morse theory and persistent homology, provide a useful framework for…
Composite visualization is a popular design strategy that represents complex datasets by integrating multiple visualizations in a meaningful and aesthetic layout, such as juxtaposition, overlay, and nesting. With this strategy, numerous…
We have developed (1) a graph visualization system that allows users to explore graphs by viewing them as a succession of spanning trees selected interactively, (2) a radial graph layout algorithm, and (3) an animation algorithm that…
Ubiquitous geometric objects can be precisely and efficiently represented as polyhedra. The transformation of a polyhedron into a vector, known as polyhedra representation learning, is crucial for manipulating these shapes with mathematical…
Round fold maps are smooth maps on closed manifolds which are locally represented as the product maps of Morse functions and identity maps on open disks and whose singularity is realized as concentrically embedded spheres. The author…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Data immersion has advantages in astrophysical visualization. Complex multi-dimensional data and phase spaces can be explored in a seamless and interactive viewing environment. Putting the user in the data is a first step toward immersive…
The real world and its geographic objects are modeled and represented in different spatial databases. Each of these databases provides only a partial description (in space and time) of the geographic objects represented. Sometimes,…