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- Publications
- Influence

Morse Theory for Filtrations and Efficient Computation of Persistent Homology

- K. Mischaikow, Vidit Nanda
- Mathematics, Computer Science
- Discret. Comput. Geom.
- 27 July 2013

We introduce an efficient preprocessing algorithm to reduce the number of cells in a filtered cell complex while preserving its persistent homology groups. The technique is based on an extension of… Expand

Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps

- S. Harker, K. Mischaikow, M. Mrozek, Vidit Nanda
- Computer Science, Mathematics
- Found. Comput. Math.
- 1 February 2014

We provide explicit and efficient reduction algorithms based on discrete Morse theory to simplify homology computation for a very general class of complexes. A set-valued map of top-dimensional cells… Expand

The Efficiency of a Homology Algorithm based on Discrete Morse Theory and Coreductions

- S. Harker, K. Mischaikow, +4 authors Pawel Dlotko
- Mathematics
- 2010

Two implementations of a homology algorithm based on the Forman’s discrete Morse theory combined with the coreduction method are presented. Their efficiency is compared with other implementations of… Expand

- 34
- 3

Local Cohomology and Stratification

- Vidit Nanda
- Computer Science, Mathematics
- Found. Comput. Math.
- 2 July 2017

We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The… Expand

Simplicial Models and Topological Inference in Biological Systems

- Vidit Nanda, R. Sazdanovic
- Computer Science
- 2014

This article is a user’s guide to algebraic topological methods for data analysis with a particular focus on applications to datasets arising in experimental biology. We begin with the combinatorics… Expand

Persistence Paths and Signature Features in Topological Data Analysis

- I. Chevyrev, Vidit Nanda, H. Oberhauser
- Mathematics, Computer Science
- IEEE Transactions on Pattern Analysis and Machine…
- 1 June 2018

We introduce a new feature map for barcodes as they arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then… Expand

A topological measurement of protein compressibility

- M. Gameiro, Y. Hiraoka, S. Izumi, M. Kramár, K. Mischaikow, Vidit Nanda
- Mathematics
- 1 March 2015

In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a… Expand

Discrete Morse Theory for Computing Cellular Sheaf Cohomology

- J. Curry, R. Ghrist, Vidit Nanda
- Mathematics, Computer Science
- Found. Comput. Math.
- 23 December 2013

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf… Expand

Simultaneous delay and power optimization in global placement

- M. Ekpanyapong, K. Balakrishnan, Vidit Nanda, S. Lim
- Computer Science
- IEEE International Symposium on Circuits and…
- 23 May 2004

Delay and power minimization are two important objectives in the current circuit designs. Retiming is a very effective way for delay optimization for sequential circuits. In this paper we propose a… Expand

Topological Measurement of Protein Compressibility via Persistence Diagrams

- M. Gameiro, マルシオ ガメイロ, +11 authors ヴィディット ナンダ
- Mathematics
- 4 June 2012

We exploit recent advances in computational topology to study the compressibility of various proteins found in the Protein Data Bank (PDB). Our fundamental tool is the persistence diagram, a… Expand