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Given a set of alternatives to be ranked, and some pairwise comparison data, ranking is a least squares computation on a graph. The vertices are the alternatives, and the edge values comprise the comparison data. The basic idea is very simple and old – come up with values on vertices such that their differences match the given edge data. Since an exact… (More)

- Anil N. Hirani, Kaushik Kalyanaraman, Seth Watts
- 2015 IEEE International Parallel and Distributed…
- 2015

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)

- Anil N. Hirani, Kaushik Kalyanaraman, Evan VanderZee
- Computer-Aided Design
- 2013

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)

In this paper, we present an augmentation to an existing machine learning algorithm used to predict the outcome of a DotA2 match and as a hero recommender in a recommendation engine. We briefly discuss existing work on DotA2 recommendation engines as well another effort in applying traditional machine learning algorithms to predict its outcome. We then… (More)

- Anil N. Hirani, Kaushik Kalyanaraman, Seth Watts
- ArXiv
- 2010

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)

We describe algorithms for finding harmonic cochains, an essential ingredient for solving elliptic partial differential equations using finite element or discrete exterior calculus. Harmonic cochains are also useful in computational topology and computer graphics. We focus on finding harmonic cochains cohomologous to a given cocycle. Amongst other things,… (More)

- Anil N. Hirani, Kaushik Kalyanaraman
- ArXiv
- 2011

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)

- Anil N. Hirani, Kaushik Kalyanaraman, Han Wang, Seth Watts
- ArXiv
- 2010

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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