From 6ee527b8d89b0614a5015207e6fd392d70248f90 Mon Sep 17 00:00:00 2001 From: "Daniel S. Katz" Date: Thu, 16 Nov 2023 09:00:34 -0700 Subject: [PATCH] minor paper change --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 98e8bab..c9b706a 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -77,7 +77,7 @@ DREiMac implements this using integer linear programming. ![Parametrizing the circularity of a trefoil knot in 3D. Here we display a 2-dimensional representation, but the 3-dimensional point cloud does not have self intersections (in the sense that it is locally 1-dimensional everywhere). On the right, the output of the circular coordinates algorithm without applying the algebraic procedure to fix the lift of the cohomology class. On the left, the ouput of DREiMac, which implements this fix. Details about this example can be found in the documentation. \label{figure:fix-cocycle}](fix-cocycle.png){width=70%} Another practical issue of the circular coordinates algorithm is its performance in the presence of more than one large scale circular feature (Figures \ref{figure:genus-two-toroidal} and \ref{figure:genus-two-circular}). -To address this, DREiMac implements the toroidal coordinates algorithm, introduced in [@toroidal-coords], which allows the user to select several 1-dimensional cohomology classes and returns coordinates that parametrize these circular features in a simpler fashion. +To address this, DREiMac implements the toroidal coordinates algorithm, introduced in @toroidal-coords, which allows the user to select several 1-dimensional cohomology classes and returns coordinates that parametrize these circular features in a simpler fashion. ![Parametrizing the circularity of a surface of genus two in 3D. Here we display a 2-dimensional representation, but the 3-dimensional point cloud does not have self intersections (in the sense that it is locally 2-dimensional everywhere). This is DREiMac's output obtained by running the toroidal coordinates algorithm. The output of running the circular coordinates algorithm is in Figure \ref{figure:genus-two-circular}. Details about this example can be found in the documentation. \label{figure:genus-two-toroidal}](genus-2-toroidal-c.png){width=80%}