Efficient computation of Linking number with certification

Enrico Bertolazzi; Riccardo Ghiloni; Ruben Specogna

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Efficient computation of Linking number with certification

Enrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna

Algebraic Topology · Submitted 31 Dec 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim An efficient numerical algorithm for the computation of linking number is presented.

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arXiv ID1912.13121 (version 1)

Pith IDGL3ST76J, Pith's permanent record of this paper and its review

CitationEnrico Bertolazzi, Riccardo Ghiloni, Ruben Specogna. "Efficient computation of Linking number with certification." arXiv:1912.13121 (2019). https://pith.science/paper/GL3ST76J

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.05 · mentions code or data availability 0.03.

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An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	An efficient numerical algorithm for the computation of linking number is presented.	contribution 0.98	0.90	0.58	asserted 1.00
s1	The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.	method 0.88	0.85	0.20	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.79.

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arXiv listing abstract v1

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

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Original abstract

An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.

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3 arXiv papers cite this in 5 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Uses its method or tool 2 papers

When this is a single-threaded computation, the approach from [ref] removes all arctangents by using angle summations (counting negative $x$-axis crossings) instead.

Fast Linking Numbers for Topology Verification of Loopy Structures · Method 2: Direct Summation (DS) · 0.89
For the linking number calculation, we use the implementation in [ref] since it returns a linking number with certified accuracy by tracking rounding errors in the calculation.

Direct stellarator coil design using global optimization: application to a comprehensive exploration of quasi-axisymmetric devices · Bounding boxes · 1.00

Cites it as background 2 papers

In the computational DNA topology community, many papers [ref] use topological invariants such as the linking number, twist, and writhe to understand DNA ribbons; in particular, [ref] summarizes how to compute these quantities, and [ref] present more robust exact expressions for line segment curves using the signed solid angle formula [ref] .

Fast Linking Numbers for Topology Verification of Loopy Structures · Related Work · 0.97
An efficient implementation of the solid angle approach to the linking number is discussed in [ref] .

A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour · Past results about the Gauss integral for the linking number · 0.81

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