Kaushik Kalyanaraman

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There are several classes of operators on graphs to consider in deciding on a collection of building blocks for graph algorithms. One class involves traditional graph operations such as breadth first or depth first search, finding connected components, spanning trees, cliques and other sub graphs, operations for editing graphs and so on. Another class(More)
We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such(More)
Given a set of alternatives and some pairwise comparison values, ranking is a least squares computation on a graph. The graph vertices are the alternatives, with a weighted oriented edge between each pair for which there is a pairwise score. The orientations are arbitrary. The set of edges may be sparse or dense. The basic idea of the computation is very(More)
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus. However, we are not aware of any numerical experiments where mixed finite elements derived from discretizations of(More)
My research agenda is built on formulating problems in analysis, geometry and topology for a computational realization and conversely, use of computation for formalizing notions in analysis, geometry and topology. The former stems from a motivation to provide solutions for problems in science and engineering using tools of scientific and high performance(More)
We give new algorithms for computing basis cochains for real-valued homology, cohomology, and harmonic cochains on manifold simplicial complexes. We discuss only planar, surface, and solid meshes. Our algorithms are based on a least squares formulation. Previous methods for computing homology and cohomology have relied on persistence algorithm or Smith(More)
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