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Morse Theory for Filtrations and Efficient Computation of Persistent Homology
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 ofExpand
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Discrete Morse Theoretic Algorithms for Computing Homology of Complexes and Maps
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 cellsExpand
  • 61
  • 3
The Efficiency of a Homology Algorithm based on Discrete Morse Theory and Coreductions
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 ofExpand
  • 34
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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. TheExpand
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Simplicial Models and Topological Inference in Biological Systems
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 combinatoricsExpand
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Persistence Paths and Signature Features in Topological Data Analysis
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 thenExpand
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A topological measurement of protein compressibility
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 aExpand
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Discrete Morse Theory for Computing Cellular Sheaf Cohomology
Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheafExpand
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Simultaneous delay and power optimization in global placement
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 aExpand
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  • 1
Topological Measurement of Protein Compressibility via Persistence Diagrams
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, aExpand
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