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ryan-williams authored Oct 12, 2023
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Expand Up @@ -48,13 +48,13 @@ It's faily "alpha" (see [/issues][apvd issues]), but afaik it's the first tool t

[Here's the best layout][Variant callers - best] I've found using ∧p∨d:

![](public/img/variant%20callers%20-%20best.png)
<img src="public/img/variant%20callers%20-%20best.png" width="500" />

The error is just under 0.2%: about 1/500th of the overall area is in the wrong region.

Here's a closer look at the center, with region-size labels:

![](public/img/variant%20callers%20-%20best%20-%20detail.png)
<img src="public/img/variant%20callers%20-%20best%20-%20detail.png" width="500" />

The "1.86" (Red ∩ Blue ∩ Yellow) should be 0, and there a missing { Red ∩ Green ∩ Yellow } of size 1. I use a rudimentary penalty that moves shapes closer together when a region is missing (the converse happens naturally via gradient descent), but it could definitely be made smarter[^1].

Expand All @@ -67,7 +67,7 @@ From [the supplement][mpower supplement]:

∧p∨d [struggles a bit][mpower best] with this one:

![](public/img/mpower%20best.png)
<img src="public/img/mpower%20best.png" width="500" />

Error is 22.9 (4.64%); half of that is { Red ∩ Yellow ∩ Blue }, which is 1.56 instead of 12. Incorporating each region's relative error would likely produce more intuitive results[^2].

Expand All @@ -83,7 +83,7 @@ Also [discussed by Lior Pachter][lior pachter zhang 2014]:

This one basically [converges][zhang 2014 best], though it took 100k's of steps:

![](public/img/zhang%20et%20al%202014%20best.png)
<img src=public/img/zhang%20et%20al%202014%20best.png width=500 />

Lots of room to position the labels better…

Expand Down Expand Up @@ -118,7 +118,7 @@ Allowing just one set to be an ellipse (even "aligned" to the axes, with no rota

Here is its solution to the example above:

![](public/img/eulerAPE%20benfred.png)
<img src=public/img/eulerAPE%20benfred.png width=600 />

[Their paper][eulerAPE paper] is a great reference, and includes many examples from published papers.

Expand Down Expand Up @@ -195,18 +195,21 @@ https://www.combinatorics.org/files/Surveys/ds5/ds5v3-2005/VennTriangleEJC.html
https://www.combinatorics.org/files/Surveys/ds5/ds5v3-2005/VennPoly67EJC.html

> Shown below is a 6-Venn diagram formed entirely from curves drawn from axis-aligned edges. It is a minimum-area diagram; that is, each region is composed of a single square of unit area. Note that many edges overlap, so the diagram is [infinitely intersecting](https://www.combinatorics.org/files/Surveys/ds5/ds5v3-2005/VennOtherEJC.html#infinite). As with many other diagrams in these pages, regions are coloured by weight. The diagrams on this page are from \[[CR05](https://www.combinatorics.org/files/Surveys/ds5/ds5v3-2005/VennRefs.html#CR05)\].
>
> <img src="./public/img/polyvenn6-diag.png" width="300" />
>
> The six component curves of the diagram, overlaid on a grayed-out version of the entire diagram:
>
> <img src="public/img/polyvenn6-curves.png" width="500" />
>
> This is a 7-Venn diagram formed entirely from curves drawn from axis-aligned edges. Like the above it is minimum-area and infinitely intersecting.
>
> <img src="./public/img/polyvenn7-diag.png" width="300" />
> <img src=public/img/polyvenn7-diag.png width=300 />
>
> The seven component curves:
>
> <img src="./public/img/polyvenn7-curves.png" width="300" />
>
### Related libraries <a id="libs"></a>

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