Jekyll2017-04-25T18:08:38+00:00https://11011110.github.io/blog/11011110Geometry, graphs, algorithms, and moreDavid EppsteinRussian Gulch photos2017-04-16T16:34:00+00:002017-04-16T16:34:00+00:00https://11011110.github.io/blog/2017/04/16/russian-gulch-photos<p>A couple of weekends ago I returned to Mendocino for a surprise 80th birthday party for my father. There’s now nonstop service from Orange County to Santa Rosa that makes this sort of short trip much more convenient: it’s only two more hours driving from there rather than four from any other airport we could reach.</p>
<p>Anyway, while there, we took a hike along the Fern Creek trail of Russian Gulch State Park, to the waterfall at the end of the trail. <a href="http://www.ics.uci.edu/~eppstein/pix/ferncreek/">My photos from the hike</a> are mostly studies of the green spring textures of the area. There is one of the actual waterfall, but because I packed light for the trip I didn’t have a wide enough lens to take it all in at once. Here’s a photo of a patch of forget-me-nots and horsetails by the side of the trail:</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/ferncreek/5-m.jpg" alt="Forget-me-nots and horsetails on the Fern Creek Trail, Russian Gulch State Park, California" style="border-style:solid;border-color:black;" /></p>
<p><a href="https://plus.google.com/100003628603413742554/posts/6GaCjpULpBE">(Google+ discussion thread for this post)</a></p>David EppsteinA couple of weekends ago I returned to Mendocino for a surprise 80th birthday party for my father. There’s now nonstop service from Orange County to Santa Rosa that makes this sort of short trip much more convenient: it’s only two more hours driving from there rather than four from any other airport we could reach.First linkage for my new site2017-04-15T16:17:00+00:002017-04-15T16:17:00+00:00https://11011110.github.io/blog/2017/04/15/first-linkage-for<p>…and the first one I’m doing in markdown instead of html. Moving gives me a chance to rethink any blogging habits I might have gotten into, and change the ones that aren’t working, but I think I’ll keep doing these — regardless of whether others like them, I find them useful for myself for finding my old G+ posts. On the other hand, I’m changing up the format a little, to put longer description after the links instead of trying to limit each to a single line.</p>
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<p><a href="https://www.insidehighered.com/blogs/world-view/attack-independent-universities">Attacks on independent Universities in Europe</a> (<a href="https://plus.google.com/100003628603413742554/posts/QD9htP9fbgA">G+</a>). The Central European University in Hungary is under attack from the Hungarian government, but it’s not the only one.</p>
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<p><a href="https://plus.google.com/+LuisGuzmanJr/posts/cNdYGCm8Ric">The Collatz conjecture in color</a> (<a href="https://plus.google.com/100003628603413742554/posts/ad5A1bKV6Sp">G+</a>). This visualization of the branching process inverse to the Collatz-conjecture process draws an infinite binary tree by turning a small amount left or right at each branch. It makes pretty organic-looking curved tangles of lines but I don’t think it is very helpful in distinguishing it from any other branching process with similar parameters.</p>
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<p><a href="https://www.quantamagazine.org/20170404-gerrymandering-math-standard/">Quanta on gerrymandering</a> (<a href="https://plus.google.com/100003628603413742554/posts/EoY63gMG3cn">G+</a>). 30 years after “a ruling that rejected nearly every available test for partisan gerrymandering”, will the Supreme Court accept the “efficiency gap” standard used in a Wisconsin ruling from a lower court?</p>
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<p><a href="http://news.livejournal.com/151767.html">Livejournal announces new terms of service</a> (<a href="https://plus.google.com/100003628603413742554/posts/6o4yfaepsTe">G+</a>). I moved my journal here and have now deleted my account from LJ (forgoing five months of already-paid service) because I cannot accept their newly-ubiquitous ads, restrictions on speech, rejection of pseudonymity, and promises to spam my email. See also <a href="http://www.metafilter.com/166250/LiveJournal-now-bans-political-talk-LGBT-talk">a related Metafilter discussion</a> which clarifies the mysterious “Federal act 149-ФЗ” parts of the ToS.</p>
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<p><a href="http://www.latimes.com/local/abcarian/la-me-abcarian-pence-marriage-20170405-story.html">If professional women and men cannot be alone together, women are the ones who will pay a price</a> (<a href="https://plus.google.com/100003628603413742554/posts/U5k4HhFkx1o">G+</a>). Although ostensibly about Vice President Mike Pence and the US political right, this is also relevant for academia and the ongoing push from the left to shut down inappropriate relations between faculty and students.</p>
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<p><a href="https://www.mathjax.org/cdn-shutting-down/">You need to update the MathJax library address in your web pages</a> (<a href="https://plus.google.com/100003628603413742554/posts/NFbUtWmp4ba">G+</a>). <a href="http://unix.stackexchange.com/questions/112023/how-can-i-replace-a-string-in-a-files">Here’s how</a>.</p>
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<p><a href="https://www.smashingmagazine.com/2014/08/build-blog-jekyll-github-pages/">Building a blog with Jekyll and GitHub Pages</a> (<a href="https://plus.google.com/100003628603413742554/posts/dEUHR5WwLsz">G+</a>). What I did to move my blog. The comments discuss some related alternatives.</p>
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<p><a href="http://retractionwatch.com/2017/04/05/supreme-court-nominee-gorsuch-lifted-earlier-works-scholarly-papers-report/">New Supreme Court Justice Gorsuch is a plagiarist</a> (<a href="https://plus.google.com/100003628603413742554/posts/Kp5zLiCjRWb">G+</a>). Not that that’s anywhere close to the worst thing about him or about the Trump administration that stole his seat for him.</p>
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<p><a href="https://plus.google.com/+DavidRoberts/posts/R5XDjVpb6qc">Elsevier changed the terms of their “Open Access” user license</a> (<a href="https://plus.google.com/100003628603413742554/posts/FnK4qpAG5M3">G+</a>).
In particular it no longer seems to be permissible to display, adapt, or redistribute their papers. (If we can’t display them, how are we supposed to read them?) <a href="https://sbseminar.wordpress.com/2017/04/09/and-elsevier-taketh-away/">The secret blogging seminar has more analysis</a>.</p>
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<p><a href="https://backchannel.com/how-google-book-search-got-lost-c2d2cf77121d">How Google Book Search got lost</a> (<a href="https://plus.google.com/100003628603413742554/posts/g4AUUHw7Xzc">G+</a>). The project doesn’t seem to be dead, exactly, but it’s stagnating. Via bit_player.</p>
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<p><a href="After hyping itself as antidote to fake news, New York Times hires extreme climate denier">https://thinkprogress.org/new-york-times-hires-extreme-climate-denier-after-hyping-itself-as-antidote-to-fake-news-441826c4071d</a> (<a href="https://plus.google.com/100003628603413742554/posts/QioGH2Hrtgs">G+</a>). Bret Stephens may be an anti-Trump Republican but that doesn’t prevent him from being a shill on other matters.</p>
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<p><a href="http://dangerousminds.net/comments/soap_bubbles_become_psychedelic_works_of_art">Soap bubble photography</a> by <a href="http://williamhortonphotography.com/">William Horton</a> (<a href="https://plus.google.com/100003628603413742554/posts/jCgmt3147jC">G+</a>). Via <a href="http://www.metafilter.com/166297/Thin-line-between-heaven-and-here">Metafilter</a>.</p>
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<p><a href="https://mathoverflow.net/q/263667/440">Drawing trees on small number of lines in 2D and 3D</a> (<a href="https://plus.google.com/100003628603413742554/posts/SXYxF2rwi2k">G+</a>). By re-using the same line for many edges, it is possible to draw some trees on many fewer lines than the number of edges in the tree. Does it help use fewer lines to use lines in 3d instead of in the plane?</p>
</li>
</ul>David Eppstein…and the first one I’m doing in markdown instead of html. Moving gives me a chance to rethink any blogging habits I might have gotten into, and change the ones that aren’t working, but I think I’ll keep doing these — regardless of whether others like them, I find them useful for myself for finding my old G+ posts. On the other hand, I’m changing up the format a little, to put longer description after the links instead of trying to limit each to a single line.Stable grid matching2017-04-11T17:17:00+00:002017-04-11T17:17:00+00:00https://11011110.github.io/blog/2017/04/11/stable-grid-matching<p>A group of us at UCI have been trying to understand algorithmic problems in political redistricting (with the goal of finding methods that are fair, difficult to gerrymander, and efficient to calculate). Although the real goal is political fairness (a difficult concept to define let alone optimize for), there are other important criteria in redistricting: districts should be close to equal in population, and should be geographically compact.</p>
<p><a href="/blog/2016/06/15/linkage.html">In a post last year</a> I linked to some interesting work from Yuval Peres and others at Microsoft Research on <a href="http://yuvalperes.com/stable/stable.html">Voronoi diagrams defined from stable marriages</a> rather than closest distances. This method takes a region of the plane (the unit square, say) and a collection of center points within the region, and divides the region into equal-area subregions that are (mostly) close to their centers; an example is shown below, with colors distinguishing the different subregions from each other. We thought this might make a good abstraction to the redistricting problem: if the centers represent voting places, and units of area represent numbers of voters (so the voters are uniformly spread around the square) then it will give us subregions for each voting place that are of equal population and near their voting place. More specifically, by definition, there should be no pair <script type="math/tex">(v,p)</script> where <script type="math/tex">v</script> is a voter whose assigned polling place is <script type="math/tex">p</script> and <script type="math/tex">p</script> is a polling place whose assigned voters include people farther than <script type="math/tex">v</script>.</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/0xDE/stable-grid-matching.png" alt="900 x 900 stable grid matching" /></p>
<p>Our new preprint, “<a href="https://arxiv.org/abs/1704.02303">Algorithms for Stable Matching and Clustering in a Grid</a>” (arXiv:1704.02303, to appear at IWCIA) starts by looking at efficient algorithms for this problem. It turns out that the fact that the preferences are symmetric (both voters and voting places prioritize each other by the same distances) really helps. One could use a dynamic nearest-neighbor data structure to repeatedly find and match voters to places until each voter has a place and each place has enough voters, but one can do even better than that by applying the <a href="https://en.wikipedia.org/wiki/Nearest-neighbor_chain_algorithm">nearest-neighbor chain algorithm</a> to repeatedly find mutual nearest neighbors of unplaced voters and not-yet-full voting places, avoiding the overhead of nearest neighbors. Based on this idea, we show that constructing images such as the one above by matching an <script type="math/tex">n\times n</script> grid of pixels to some smaller number of centers can be performed in time <script type="math/tex">O(n^2\log^5 n)</script>. This is the first application I’m aware of outside of hierarchical clustering for nearest-neighbor chains. But the underlying nearest neighbor data structures used in these algorithms are still too complicated to be practical, so instead we implemented and experimented with simpler heuristics that nevertheless obtain significant speedups over naive stable marriage algorithms.</p>
<p>Choosing the voting places (the centers of each region) uniformly at random tends not to work too well. Random fluctuation causes some parts of the grid to have too many centers and others too few, and when that happens the centers in the dense regions have to reach out a long distance to find voters in the sparse regions who can be assigned to them. We end up getting disconnected regions with very high radius. (In the above image, the boundaries are straight lines and circular arcs centered on the voting places, so you can find these bad regions by looking for high-radius curved boundaries.) We thought we would be able to fix these problems by using a variant of <a href="https://en.wikipedia.org/wiki/Lloyd%27s_algorithm">Lloyd’s algorithm</a> adapted for this kind of Voronoi diagram: alternate between steps that compute the stable matching and that move the centers to a more central point within their region. But although it did lead to better-behaved subdivisions, it didn’t entirely eliminate the problems.</p>
<p>Of course, actual voters must deal with road distance not straight-line distance. For instance, Lucia, California and King City, California had very different road distances and straight line distances, even before the recent <a href="http://www.mercurynews.com/2017/03/20/caltrans-highway-1-replacement-bridge-in-big-sur-ready-in-six-months/">bridge outage on Highway 1</a> making it essentially impossible to get from one to the other. And populations are not evenly distributed by area. So, beyond the question of finding an equal-area stable subdivision, turning this into a usable redistricting algorithm will require additional research.</p>
<p><a href="https://plus.google.com/100003628603413742554/posts/BketmBvibi4">(Google+ discussion thread for this post)</a></p>David EppsteinA group of us at UCI have been trying to understand algorithmic problems in political redistricting (with the goal of finding methods that are fair, difficult to gerrymander, and efficient to calculate). Although the real goal is political fairness (a difficult concept to define let alone optimize for), there are other important criteria in redistricting: districts should be close to equal in population, and should be geographically compact.Back up and running2017-04-10T17:59:00+00:002017-04-10T17:59:00+00:00https://11011110.github.io/blog/2017/04/10/back-up<p>My transition from LiveJournal (taken over by Russians with new and unacceptably restrictive terms of service) to another journaling system is more or less complete. I think all of my old posts and most or all of the comments are now here at this new address (11011110.github.io/blog/ at least for now — in principle I could replace that with a custom domain name but I haven’t seen the need to do so yet). Because I’m hosting this through github, the actual <a href="https://github.com/11011110/blog">source code for the blog</a> is also public. The old LiveJournal site still exists but I’m likely to take it down sometime before the next automatic renewal of my paid account in September, so now would be a good time to update links. If I ever do get a custom domain or otherwise change hosts, I’m very likely to keep the same naming scheme, so future updates should be a lot easier.</p>
<p>Some miscellaneous observations on the transition:</p>
<ul>
<li>
<p>Keep backups of content you host on third-party sites! They’re what allowed me to make this transition as easily as I did. And the inability to continue making backups was what first alerted me to the fact that something had gone seriously wrong at LiveJournal.</p>
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<p>I’m using Jekyll, a static site generator, to turn blog entry text or markup (but without all the boilerplate html connecting the entries to the rest of the blog) into web pages. GitHub automatically runs Jekyll so I don’t have to, but for the past few days while I convert the old entries to the new format I’ve been running a local copy of the Jekyll server code, so I can preview what the entries look like without having to put them up for the world to see. Rebuilding the whole site (around 1300 posts) takes between 30 and 90 seconds depending on which machine I run it on, not really real-time but a lot better than some old complaints about Jekyll that I found on the net. This workflow should even allow me to work with the blog on airplanes or other locations without network connectivity, and the fact that it’s all in git (a version management system I’m already familiar with from using for my papers) gives me a local backup automatically and makes synchronization between machines easy.</p>
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<p>Because I’m using a static site generator, I don’t have a place for people to leave comments on the posts (the old comments are baked in and I don’t plan to allow new ones). Probably Jekyll can integrate with third-party commenting services like Disqus but I’m not looking into doing anything like that. Instead my current plan is simply to link to new posts on Google+ (as I have been doing anyway) and then adding a link to each new post pointing to the Google+ link as a place where comments can be added. Disallowing third parties from adding any content to this site saves me from a lot of headaches involving security and spam.</p>
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<p>As well as comments, the other feature I don’t have any more is tags. It is possible to generate tags in Jekyll but my impression is that it creates significant slowdowns in build time. I’m not sure how easy it is to get them to work on GitHub. And I don’t think I was making very effective use of them on LiveJournal, so if I did start using tags again I’d want to rethink how I categorize things.</p>
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<p>All the old posts are formatted in html but for newer ones I am likely to use markdown (or actually kramdown, the default for new Jekyll sites) to save on having to get the details right (like making sure I close all of my tags). As part of the process of converting the old blog entries to the new format, I found and fixed quite a few errors of this type. And it looks like if I want to do something trickier in html, it should usually be possible to do it within a larger markdown post. Both formats allow MathJax-formatted mathematical expressions: Jekyll and kramdown support MathJax almost out of the box, with the only change needed being to add the appropriate JavaScript to my headers. They also provide syntax highlighting for code snippets. I have used these features to clean up the formatting on some old posts but many of them remain in their old pre-MathJax state.</p>
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<p>I’m using the vanilla theme that comes with Jekyll, “minima”, with only a few customizations e.g. to what appears in the page headers and footers. Github only supports a small number of themes (if you host elsewhere there are many more to choose from) and I liked the simplicity of this one better than the others. It doesn’t get in the way of reading the actual posts with too much decoration. One of the mistakes I made, though, was thinking that I needed to use github’s “set theme” pulldown menu. Minima is not one of the themes listed in this pulldown and when I tried it I broke the site.</p>
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<p>There are still a couple hundred links from my posts to other posts, pointing to the old location of the blog. It will take a concerted effort to clean all of these up, if I ever bother to do so. Unfortunately there’s no good way to automatically translate the addresses of those old posts into the new addressing scheme; it’s a matter of looking them up one-by-one by hand. Probably there are other ongoing issues with bad formatting. If you discover any (especially on posts that have some ongoing significance, which is far from all of them) please let me know so I can fix them.</p>
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</ul>
<p><a href="https://plus.google.com/100003628603413742554/posts/KSuMcfE7AxQ">(Leave comments on Google+)</a></p>David EppsteinMy transition from LiveJournal (taken over by Russians with new and unacceptably restrictive terms of service) to another journaling system is more or less complete. I think all of my old posts and most or all of the comments are now here at this new address (11011110.github.io/blog/ at least for now — in principle I could replace that with a custom domain name but I haven’t seen the need to do so yet). Because I’m hosting this through github, the actual source code for the blog is also public. The old LiveJournal site still exists but I’m likely to take it down sometime before the next automatic renewal of my paid account in September, so now would be a good time to update links. If I ever do get a custom domain or otherwise change hosts, I’m very likely to keep the same naming scheme, so future updates should be a lot easier.Snapshots from Bellairs2017-04-04T20:36:00+00:002017-04-04T20:36:00+00:00https://11011110.github.io/blog/2017/04/04/snapshots-from-bellairs<p><a href="http://www.ics.uci.edu/~eppstein/pix/bbd17/index.html">Here are a few snapshots</a> from last January when I made my annual pilgrimage to the Bellairs Research Institute on Barbados. The one below is my favorite, Tomohiro Tachi looking cool as usual.</p>
<p style="text-align:center"><img alt="Tomohiro Tachi" src="http://www.ics.uci.edu/~eppstein/pix/bbd17/7-m.jpg" style="border-style:solid;border-color:black;"></p>David EppsteinHere are a few snapshots from last January when I made my annual pilgrimage to the Bellairs Research Institute on Barbados. The one below is my favorite, Tomohiro Tachi looking cool as usual.Linkage for April Fools2017-04-01T23:49:00+00:002017-04-01T23:49:00+00:00https://11011110.github.io/blog/2017/04/01/linkage-for-april<p>(No actual April Fools jokes among these, sorry.)</p>
<ul>
<li><p><a href="http://arthurcarabott.com/superhydrophobic-fountain/">Superhydrophobic fountain uses surface coatings to control the flow of water</a> (<a href="https://plus.google.com/100003628603413742554/posts/fomSWKSrGWE">G+</a>)</p></li>
<li><p><a href="http://www.thisiscolossal.com/2017/03/a-fold-apart-a-nasa-physicist-turned-origami-artist/">Interview with Robert Lang about what it feels like to fold origami</a> (<a href="https://plus.google.com/100003628603413742554/posts/8ZWfqzvE9pY">G+</a>)</p></li>
<li><p><a href="http://bit-player.org/2017/the-uniqueness-constraint">How the constraint of having a unique solution can be used to help solve puzzles</a> (<a href="https://plus.google.com/100003628603413742554/posts/T7rz2SV7NV7">G+</a>)</p></li>
<li><p><a href="https://plus.google.com/113086553300459368002/posts/42NQGEvZabD">Desargues' concertina</a> — Greg Egan animates unit-distance drawings of one of my favorite partial cubes (<a href="https://plus.google.com/100003628603413742554/posts/XVUE8h1pPZv">G+</a>)</p></li>
<li><p><a href="http://bit.ly/2nW1sEa">Missing faces of women scientists on Wikipedia</a> (<a href="https://plus.google.com/100003628603413742554/posts/has6CWqutvZ">G+</a>)</p></li>
<li><p><a href="https://arxiv.org/abs/1703.03687">Escaping from two lions in a bounded polygonal stadium</a> (<a href="https://plus.google.com/100003628603413742554/posts/jhBCJF5wrFB">G+</a>)</p></li>
<li><p><a href="http://hyperallergic.com/362638/the-sculptural-desserts-of-an-architect-turned-pastry-chef/">3d-printed desserts</a> (or really dessert molds; <a href="https://plus.google.com/100003628603413742554/posts/Fuxy3pGEVc8">G+</a>)</p></li>
<li><p><a href="http://scienceguide.nl/201703/leaked-elsevier-contract-reveals-pushback.aspx">The Dutch get a bad deal on open access from Elsevier</a> (<a href="https://plus.google.com/100003628603413742554/posts/SLJQChNKsMp">G+</a>; <a href="https://plus.google.com/+TimothyGowers0/posts/D1oWqRfNTYm">more</a>)</p></li>
<li><p><a href="https://www.newscientist.com/article/2125741-maths-explains-how-pedestrians-avoid-bumping-into-one-another/">New developments in mathematical crowd modeling</a> (<a href="https://plus.google.com/100003628603413742554/posts/LWAvdHYhrGo">G+</a>)</p></li>
<li><p><a href="http://mathoverflow.net/q/263692/440">Periodic tiling by regular polygons with no two perpendicular periodicity vectors</a> (<a href="https://plus.google.com/100003628603413742554/posts/CjuYUiBz6qS">G+</a>)</p></li>
<li><p><a href="https://wordplay.blogs.nytimes.com/2013/03/25/erdos/">The improbable life of Paul Erdős</a> (<a href="https://plus.google.com/100003628603413742554/posts/9ZxEA72kY5j">G+</a>)</p></li>
<li><p><a href="http://retractionwatch.com/2017/03/27/multiple-omics-journals-delisted-major-index-concerns/">Allegedly-predatory publisher OMICS gets in trouble with SCOPUS</a> (<a href="https://plus.google.com/100003628603413742554/posts/gc68SikJ2oE">G+</a>)</p></li>
<li><p><a href="http://boingboing.net/2017/03/25/ze-zir.html">AP stylebook takes baby steps towards accepting singular they</a> (<a href="https://plus.google.com/100003628603413742554/posts/FzFNL3XHecj">G+</a>)</p></li>
<li><p><a href="http://www.rigb.org/blog/2017/march/science-on-paper">Some gems from the Royal Institution’s book and paper archive, including an origami nun by Michael Faraday</a> (<a href="https://plus.google.com/100003628603413742554/posts/822AyXCuuo9">G+</a>)</p></li>
<li><p><a href="https://divisbyzero.com/2017/03/30/a-geometric-proof-of-brookss-trisection/">Geometric proof of a neusis trisection by a carpenter's right angle</a> (<a href="https://plus.google.com/100003628603413742554/posts/3eAETQJeomC">G+</a>)</p></li>
</ul>David Eppstein(No actual April Fools jokes among these, sorry.)Errera deltahedron2017-03-27T16:06:00+00:002017-03-27T16:06:00+00:00https://11011110.github.io/blog/2017/03/27/errera-deltahedron<p>The regular icosahedron hides many regular pentagons, surrounding each of its vertices. Cut it through the planes of two parallel pentagons, and you decompose it into two pyramids and a pentagonal antiprism. But what if you add a second antiprism, and glue the result back together?</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/0xDE/Errera-dissection.svg" alt="icosahedron, sliced icosahedron, sliced Errera, and Errera"></p>
<p>The result is a 17-vertex triangulated planar graph called the <a href="https://en.wikipedia.org/wiki/Errera_graph">Errera graph</a>. Its main claim to fame is as one of the counterexamples to Kempe's false proof of the four color theorem, but it also describes the shape of clusters of gold atoms. Its dual graph (a planar graph with 12 pentagonal faces and 6 hexagonal faces) is one of the fullerenes, although too small to be a stable one.</p>
<p>This construction from an icosahedron shows that the Errera graph can be realized as a non-convex deltahedron, a polyhedron in which all faces are equilateral triangles. It can also be made convex, but at the expense of making its faces non-regular. You can also think of the same construction as forming the Errera graph from two icosahedra by slicing a vertex off each one and gluing them together on the resulting pentagonal faces.</p>
<p>I had somehow acquired the impression that the Errera graph got its name as an unusual spelling of "error", from the fact that it was used to point out Kempe's error. But that impression itself turns out to be erroneous. It's actually someone's name: Belgian mathematician <a href="https://en.wikipedia.org/wiki/Alfred_Errera">Alfred Errera</a>, who published it in his 1921 doctoral dissertation.</p>
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<h3>Comments:</h3>
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<b>asher63</b><br />
<b>March 28 2017, 00:43:33 UTC</b><br />
Hmm, I just learned a new word. So an "antiprism" is a solid in which sides and vertices lie opposite one another along the axis?
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<b>11011110</b><br />
<b>March 28 2017, 01:41:20 UTC</b><br />
Yep. See <a href="https://en.wikipedia.org/wiki/Antiprism">https://en.wikipedia.org/wiki/Antiprism</a>
</div>David EppsteinThe regular icosahedron hides many regular pentagons, surrounding each of its vertices. Cut it through the planes of two parallel pentagons, and you decompose it into two pyramids and a pentagonal antiprism. But what if you add a second antiprism, and glue the result back together?Linkage for the Ides of March2017-03-15T21:45:00+00:002017-03-15T21:45:00+00:00https://11011110.github.io/blog/2017/03/15/linkage-for-ides<ul>
<li><p><a href="http://www.designboom.com/technology/harvard-crossfunctional-metamaterial-02-24-2017/">Using foldable nanostructure to make materials that can transform from soft to stiff, dense to sparse, etc</a> (<a href="https://plus.google.com/100003628603413742554/posts/SjWujTpGUNS">G+</a>)</p></li>
<li><p><a href="https://www.youtube.com/watch?v=ZAz9mDlsWgQ">Voronoi analysis of soccer plays</a> (<a href="https://plus.google.com/100003628603413742554/posts/WvC3aC2wmyT">G+</a>)</p></li>
<li><p><a href="https://en.wikipedia.org/wiki/Bricard_octahedron">Bricard's flexible octahedra</a> (<a href="https://plus.google.com/100003628603413742554/posts/AR31bVYvQrK">G+</a>)</p></li>
<li><p><a href="http://fuckyeahfluiddynamics.tumblr.com/post/157906567307/surface-tension-holds-small-droplets-in-a-partial">What happens to soap bubbles when gravity becomes too big to ignore</a> (<a href="https://plus.google.com/100003628603413742554/posts/L2sbzn5dUEb">G+</a>)</p></li>
<li><p><a href="https://www.newscientist.com/article/2123354-why-the-dark-net-is-more-resilient-to-attack-than-the-internet/">Randomized routing and a lack of super-connected nodes help the darknet stay robust</a> (<a href="https://plus.google.com/100003628603413742554/posts/BU4MVnHA9Tk">G+</a>)</p></li>
<li><p><a href="https://www.washingtonpost.com/news/energy-environment/wp/2017/03/03/white-house-proposes-steep-budget-cut-to-leading-climate-science-agency/">No more federally-funded oceanography</a> (<a href="https://plus.google.com/100003628603413742554/posts/UbQeACrfs4D">G+</a>)</p></li>
<li><p><a href="https://www.youtube.com/watch?v=FkHjG759ABY">Using lasers to simulate old vector-graphics game hardware</a>, with bonus kinetic data structures (<a href="https://plus.google.com/100003628603413742554/posts/TBXK7mda1Mw">G+</a>)</p></li>
<li><p><a href="https://www.sciencenews.org/blog/scicurious/views-bias-can-be-biased">Male scientists biased against research about gender bias in science</a> (<a href="https://plus.google.com/100003628603413742554/posts/E2wY2XML9gy">G+</a>)</p></li>
<li><p><a href="https://en.wikipedia.org/wiki/Nearest-neighbor_chain_algorithm">The nearest-neighbor chain algorithm for hierarchical clustering</a> (<a href="https://plus.google.com/100003628603413742554/posts/eij5AyiJNmq">G+</a>)</p></li>
<li><p><a href="https://www.eff.org/wp/digital-privacy-us-border-2017">How to keep your data and privacy safe when crossing the US border</a> (<a href="https://plus.google.com/100003628603413742554/posts/VPs428iQHDS">G+</a>)</p></li>
<li><p><a href="http://bit.ly/2mu1xBh">AMS Feature Column on permutation patterns</a> (<a href="https://plus.google.com/100003628603413742554/posts/STW6McZAdye">G+</a>)</p></li>
<li><p><a href="http://boingboing.net/2017/03/08/mens-et-manus-et-mathematica.html">Free 1000-page MIT textbook on freshman discrete math</a> (<a href="https://plus.google.com/100003628603413742554/posts/DwtUuNa5vna">G+</a>)</p></li>
<li><p><a href="http://aperiodical.com/2017/03/cutting-an-oval-pizza-video/">Affine transformations help cut oval pizza evenly</a> (<a href="https://plus.google.com/100003628603413742554/posts/ELiYcuXQYsW">G+</a>)</p></li>
<li><p><a href="https://www.washingtonpost.com/news/wonk/wp/2014/05/15/americas-most-gerrymandered-congressional-districts/">Isoperimetric ratio highlights the country's most gerrymandered districts</a> (<a href="https://plus.google.com/100003628603413742554/posts/UnLKSp9byVG">G+</a>)</p></li>
</ul>David EppsteinUsing foldable nanostructure to make materials that can transform from soft to stiff, dense to sparse, etc (G+) Voronoi analysis of soccer plays (G+) Bricard's flexible octahedra (G+) What happens to soap bubbles when gravity becomes too big to ignore (G+) Randomized routing and a lack of super-connected nodes help the darknet stay robust (G+) No more federally-funded oceanography (G+) Using lasers to simulate old vector-graphics game hardware, with bonus kinetic data structures (G+) Male scientists biased against research about gender bias in science (G+) The nearest-neighbor chain algorithm for hierarchical clustering (G+) How to keep your data and privacy safe when crossing the US border (G+) AMS Feature Column on permutation patterns (G+) Free 1000-page MIT textbook on freshman discrete math (G+) Affine transformations help cut oval pizza evenly (G+) Isoperimetric ratio highlights the country's most gerrymandered districts (G+)Fast K-best optimization for graphs of bounded treewidth2017-03-11T15:00:00+00:002017-03-11T15:00:00+00:00https://11011110.github.io/blog/2017/03/11/fast-k-best<p>Denis Kurz, a student of Petra Mutzel at Dortmund, visited Irvine last year. Since Kurz had already done some work on \( k \) shortest simple paths with Mutzel, that's what we worked on during his visit. Our paper is now online as a preprint: "\( K \)-Best Solutions of MSO Problems on Tree-Decomposable Graphs", <a href="https://arxiv.org/abs/1703.02784">arXiv:1703.02784</a>.</p>
<p>If you just want the \( k \) shortest paths between two vertices in a graph, and you don't care whether a path might have repeated vertices in it, you can do it in constant time per path after a near-linear amount of preprocessing — this is the result from my FOCS'94 / SICOMP'98 paper "Finding the \( k \) shortest paths", still my most heavily cited paper. This works well, for instance, when the input is a DAG, because in that case repeated vertices are impossible. But it's less interesting in road networks: you wouldn't want to ask your GPS for an alternative route and be told to follow the same route as before except for turning into a short cul-de-sac and then coming back out of it, somewhere in the middle of the route.</p>
<p>What is often used instead is an algorithm for \( k \) shortest simple paths: each path has to avoid repeated vertices and edges. They can still be found, but not as efficiently. Although heuristic improvements have been developed, the best algorithm (in terms of its worst-case complexity) is still the one from a 1971 paper by Jin-Yu Yen, whose time is \( O(mn) \) per path, much slower. And there's some evidence in a FOCS'10 paper of Williams and Williams that this time bound, which is cubic for dense graphs, is the best possible: it can't be improved to have a better exponent of \( n \) than three without making similar improvements to several other famous algorithmic problems. Their result doesn't rule out moving the cubic part of the cost from being per-path to being part of the preprocessing, but I don't know how to do that either.</p>
<p>So instead, Denis and I considered whether the time for finding simple paths could be improved if we assumed that the graphs had some additional structure. The answer is yes: for graphs of bounded treewidth we can find the \( k \) shortest simple paths in only logarithmic time per path. It's not quite constant, but it is exponentially faster per path than Yen.</p>
<p>It's not entirely surprising that an improvement is possible for bounded-treewidth graphs (a lot of things are easier for them) but proving it involved a novel combination of algorithmic components including shallow tree decompositions, logical formulations of graph properties, dynamic graph data structures, path-copying partial persistence, and selection in heap-ordered infinite trees.</p>
<p>In part because of the generality of these tools, our main result also ended up being very general: instead of just applying to simple paths, we can find the \( k \) best solutions to a broad family of combinatorial optimization problems on graphs, basically the problems that can be solved efficiently using <a href="https://en.wikipedia.org/wiki/Courcelle%27s_theorem">Courcelle's theorem</a>. For instance, we can find the \( k \) best traveling salesperson tours, no less efficiently than the \( k \) shortest simple paths.</p>David EppsteinDenis Kurz, a student of Petra Mutzel at Dortmund, visited Irvine last year. Since Kurz had already done some work on \( k \) shortest simple paths with Mutzel, that's what we worked on during his visit. Our paper is now online as a preprint: "\( K \)-Best Solutions of MSO Problems on Tree-Decomposable Graphs", arXiv:1703.02784.Linkage2017-02-28T21:35:00+00:002017-02-28T21:35:00+00:00https://11011110.github.io/blog/2017/02/28/linkage<ul>
<li><p><a href="http://www.thisiscolossal.com/2017/02/forest-of-60000-rainbow-numbers/">Emmanuelle Moureaux's walk-through forest of colored digits</a> reminds me of some <a href="https://en.wikipedia.org/wiki/I_Saw_the_Figure_5_in_Gold">earlier digital art</a> (<a href="https://plus.google.com/100003628603413742554/posts/LepqHiHNhvV">G+</a>)</p></li>
<li><p><a href="https://plus.google.com/101113174615409489753/posts/NpmFMDyCKai">Sariel peels huge grids</a>, with the result appearing to approximate the affine curve-shortening flow (<a href="https://plus.google.com/100003628603413742554/posts/BU3stE1JWU9">G+</a>)</p></li>
<li><p><a href="https://www.brainpickings.org/2012/12/03/berenice-abbott-documenting-science/">Berenice Abbott's vintage scientific photography</a> (<a href="https://plus.google.com/100003628603413742554/posts/5xBE1oMghJM">G+</a>)</p></li>
<li><p><a href="https://twitter.com/MikeTaylor/status/832973591847202816/photo/1">The growth of perverse incentives in academia</a> or <a href="https://en.wikipedia.org/wiki/Campbell%27s_law">Campbell's law</a> in action (<a href="https://plus.google.com/100003628603413742554/posts/cH5mmTTNoMm">G+</a>)</p></li>
<li><p><a href="http://www.chronicle.com/article/Meet-the-Math-Professor/239260">Moon Duchin fights gerrymandering with geometry</a> (<a href="https://plus.google.com/100003628603413742554/posts/6x5KnZKYqYd">G+</a>)</p></li>
<li><p><a href="https://doi.org/10.1137/1.9781611974782.122">Orlin and Sedeño-Noda find shortest cycles</a> using an elegant new algorithm resembling Johnson's (<a href="https://plus.google.com/100003628603413742554/posts/QrQPH9cFspV">G+</a>)</p></li>
<li><p><a href="https://plus.google.com/113086553300459368002/posts/eecry6w2hbq">Quasiperiodic girih zoom</a> by Greg Egan (<a href="https://plus.google.com/100003628603413742554/posts/PaaL4xDEJTU">G+</a>)</p></li>
<li><p><a href="http://blog.plover.com/lang/anagram-scoring-2.html">Scoring anagram quality</a> by using maximum independent sets in a graph of grid points (<a href="https://plus.google.com/100003628603413742554/posts/3xefYk8uoLG">G+</a>)</p></li>
<li><p><a href="http://laughingsquid.com/an-origami-inspired-ballistic-shield-designed-to-stop-bullets-and-protect-law-enforcement/">Origami police siege sheild</a> (<a href="https://plus.google.com/100003628603413742554/posts/AF9FrXF3gQS">G+</a>)</p></li>
<li><p><a href="https://ecotonemagazine.org/map/mystic-island/">Interdigitating trees of land and water in an NJ subdivision</a> (<a href="https://plus.google.com/100003628603413742554/posts/dRfrQcqfRr3">G+</a>)</p></li>
<li><p><a href="http://mathoverflow.net/q/263370/440">Are all Dehn invariants achievable?</a> (<a href="https://plus.google.com/100003628603413742554/posts/aVX15bs7NQk">G+</a>)</p></li>
</ul>David EppsteinEmmanuelle Moureaux's walk-through forest of colored digits reminds me of some earlier digital art (G+) Sariel peels huge grids, with the result appearing to approximate the affine curve-shortening flow (G+) Berenice Abbott's vintage scientific photography (G+) The growth of perverse incentives in academia or Campbell's law in action (G+) Moon Duchin fights gerrymandering with geometry (G+) Orlin and Sedeño-Noda find shortest cycles using an elegant new algorithm resembling Johnson's (G+) Quasiperiodic girih zoom by Greg Egan (G+) Scoring anagram quality by using maximum independent sets in a graph of grid points (G+) Origami police siege sheild (G+) Interdigitating trees of land and water in an NJ subdivision (G+) Are all Dehn invariants achievable? (G+)