Differential topology, and specifically Morse theory, provide a suitable setting for formalizing
and solving several problems related to shape analysis. The fundamental idea behind …

Flow visualization research has made rapid advances in recent years, especially in the area
of topology-based flow visualization. The ever increasing size of scientific data sets favors …

Massive simulations and arrays of sensing devices, in combination with increasing
computing resources, have generated large, complex, high-dimensional datasets used to …

Persistent homology captures the topology of a filtration-a one-parameter family of
increasing spaces-in terms of a complete discrete invariant. This invariant is a multiset of …

The Morse-Smale (MS) complex has proven to be a useful tool in extracting and visualizing
features from scalar-valued data. However, efficient computation of the MS complex for large …

Large-scale simulations are increasingly being used to study complex scientific and
engineering phenomena. As a result, advanced visualization and data analysis are also …

When a heavy fluid is placed above a light fluid, tiny vertical perturbations in the interface
create a characteristic structure of rising bubbles and falling spikes known as Rayleigh …

Data reduction is increasingly being applied to scientific data for numerical simulations,
scientific visualizations and data analyses. It is most often used to lower I/O and storage …

The theory of multidimensional persistence captures the topology of a multifiltration–a
multiparameter family of increasing spaces. Multifiltrations arise naturally in the topological …

Topology provides a foundation for the development of mathematically sound tools for
processing and exploration of scalar fields. Existing topology-based methods can be used to …