Jekyll2018-06-15T15:36:37+00:00https://11011110.github.io/blog/11011110Geometry, graphs, algorithms, and moreDavid EppsteinLinkage2018-06-15T15:23:00+00:002018-06-15T15:23:00+00:00https://11011110.github.io/blog/2018/06/15/linkage<ul>
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<p><a href="http://matsysdesign.com/2014/07/13/scripted-movement-drawings-series-1/">Scripted Movement Drawings Series 1</a> (<a href="https://plus.google.com/100003628603413742554/posts/dDtFrB9g7HT">G+</a>, <a href="http://www.bldgblog.com/2014/11/art-arm/">via</a>). Andrew Kudless makes generative art by programming a robot arm to use a calligraphy brush.</p>
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<p><a href="https://twitter.com/johncarlosbaez/status/1001140149332336641">John Baez observes that packing the plane by squares and regular heptagons is much more efficient than packing heptagons alone, and asks where the packing came from</a> (<a href="https://plus.google.com/100003628603413742554/posts/N7sAWnCHueC">G+</a>). Maybe from the <a href="https://commons.wikimedia.org/wiki/File:Whirl_square_tiling.svg">truncated Cairo pentagonal tiling</a>? But there’s another packing (below) by regular pentagons and regular heptagons, that I think is even more efficient. If you tightened it up a little bit to make an actual tiling, it would be difficult to tell that the tiles are not regular polygons. (See G+ comment thread for tightened version and basketweave version.)</p>
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<p style="text-align:center"><img src="/blog/assets/2018/heptagons-and-pentagons.svg" alt="Near-tiling by regular pentagons and regular heptagons" /></p>
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<p><a href="https://en.wikipedia.org/wiki/Carl_St%C3%B8rmer">Carl Størmer</a> (<a href="https://plus.google.com/100003628603413742554/posts/jm8iJyuHP79">G+</a>). Another newly promoted Wikipedia Good Article. Størmer was a number theorist, astrophysicist, and amateur street photographer. My favorite result of his is <a href="https://en.wikipedia.org/wiki/St%C3%B8rmer%27s_theorem">Størmer’s theorem</a>, which provides a method based on Pell equations for finding pairs of consecutive smooth numbers like 80 and 81; <a href="/blog/2007/03/23/smooth-pairs.html">I wrote about implementing it in an earlier post</a>.</p>
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<p><a href="http://drops.dagstuhl.de/portals/lipics/index.php?semnr=16070">Proceedings of the 16th Scandinavian Symposium and Workshops on Algorithm Theory</a> (SWAT 2018; <a href="https://plus.google.com/100003628603413742554/posts/6jPV6E7wW3F">G+</a>).</p>
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<p><a href="https://gilkalai.wordpress.com/2018/06/06/a-mysterious-duality-relation-for-4-dimensional-polytopes/">A mysterious duality relation for 4-dimensional polytopes</a>, by Gil Kalai (<a href="https://plus.google.com/100003628603413742554/posts/ZEiWCEwWTzn">G+</a>, <a href="https://plus.google.com/117271457236114081433/posts/6U2jGHD6Huf">via</a>).</p>
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<p><a href="https://westy31.home.xs4all.nl/PoincareMeetsMandelbrot/PoincareMeetsMandelbrot.html">Using circle packings to generate hyperbolic tilings of fractals</a> (<a href="https://plus.google.com/100003628603413742554/posts/NfRTh5qdHyp">G+</a>, <a href="https://plus.google.com/100749485701818304238/posts/1X7Zr8ASq1c">via</a>).</p>
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<p><a href="https://www.eff.org/deeplinks/2018/06/eus-copyright-proposal-extremely-bad-news-everyone-even-especially-wikipedia">The EU’s copyright proposal is extremely bad news for everyone, even (especially!) Wikipedia</a> (<a href="https://plus.google.com/100003628603413742554/posts/PLMQm9oy7Jp">G+</a>, <a href="https://news.ycombinator.com/item?id=17260148">via</a>, <a href="https://boingboing.net/2018/06/07/thanks-axel-voss.html">also via</a>). This proposed law would require Wikipedia and other publishers of user-submitted content to pay for, install, and run expensive commercial filter software that automatically checks all submissions against a database of commercial content and automatically blocks any matches. There would be no safeguards against the already-rampant abuse of such filters to claim copyright on things that are not copyrighted. The article notes that “The drafters of Article 13 have tried to carve Wikipedia out of the rule, but thanks to sloppy drafting, they have failed: the exemption is limited to “noncommercial activity”. Every file on Wikipedia is licensed for commercial use.”</p>
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<p><a href="https://plus.google.com/u/0/+JeffErickson/posts/3Uu4L1pzrsC">Congratulations octor Chang!</a> (<a href="https://plus.google.com/u/0/100003628603413742554/posts/hRnPu5QCtgA">G+</a>). Hsien-Chih Chang (a student of Jeff Erickson) successfully defends his thesis on <em>Tightening Curves and Graphs on Surfaces</em>.</p>
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<p><a href="https://naegle.wustl.edu/2018/06/05/signing-my-peer-review-unintended-consequences-and-gender/">Why de-anonymizing peer review might not be a good idea</a> (<a href="https://plus.google.com/100003628603413742554/posts/TCASa5NQaSn">G+</a>, <a href="https://retractionwatch.com/2018/06/09/weekend-reads-scientists-citing-themselves-gender-and-clinical-trials-jail-after-plagiarism/">via</a>). If the reviewer is a woman, it might cause her review to be taken a lot less respectfully than if it were anonymous.</p>
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<p><a href="http://www.clevelandart.org/art/2009.343">Gabriel Orozco’s <em>Mapa estelar en árbol</em>, 2009</a> (<a href="https://plus.google.com/100003628603413742554/posts/SoZBvSHU6jX">G+</a>). If you like this, or Orozco’s other pieces involving circle and sphere tangencies, there’s plenty more in his book <em>Orbita Nocturna</em>. I picked up a copy the last time I visited MOCA.</p>
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<p><a href="https://mappingignorance.org/2018/05/07/down-in-the-depths-on-caratheodorys-theorem/">Down in the depths on Carathéodory’s theorem</a> (<a href="https://plus.google.com/100003628603413742554/posts/YVnjTznCHsa">G+</a>, <a href="http://aperiodical.com/2018/06/carnival-of-mathematics-158/">via</a>). David Orden describes some new connections between two notions of how central a point is to a sample, from robust statistics: Tukey depth (points that can’t be separated by a line from most of a sample set) and Tverberg depth (points that can be surrounded by many disjoint subsets of a sample set). Based on <a href="https://doi.org/10.1007/s00454-017-9893-8">a recent paper by Fabila-Monroy and Huemer</a>.</p>
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<p><a href="https://en.wikipedia.org/wiki/Hercules%27_Dog_Discovers_Purple_Dye">Hercules’ Dog Discovers Purple Dye</a> (<a href="https://plus.google.com/100003628603413742554/posts/GWo5JU9z1VH">G+</a>). This painting by Rubens shows the wrong kind of snail shell. It should be a dye murex, but it looks more like a nautilus, which is not even actually a snail.</p>
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<p><a href="http://www.thisiscolossal.com/2018/06/unique-weathering-chain-link-fence/">Unique Weathering Pattern Creates Fascinating Geometric Ripples on a Chain Link Fence</a> (<a href="https://plus.google.com/100003628603413742554/posts/BZM85iq4Xpa">G+</a>, <a href="https://plus.google.com/+Colossal/posts/b4pkQgQUZY2">via</a>). It looks like a reaction-diffusion system, but it’s not clear what’s reacting and diffusing.</p>
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<p><a href="https://plus.google.com/113086553300459368002/posts/excZpEqQRsD">Gödel, Escher … what?</a> (<a href="https://plus.google.com/100003628603413742554/posts/jhCPn6zoSjZ">G+</a>). Greg Egan makes five-dimensional shapes with ten different two-dimensional shadows.</p>
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<p><a href="https://www.insidehighered.com/news/2018/06/14/conference-scholars-asia-turns-dispute-over-academic-freedom">The conference of the (American) Association for Asian Studies, located in India, is banning participation by Pakistanis and by other scholars of Pakistani descent</a> (<a href="https://plus.google.com/100003628603413742554/posts/6ELQWhJBJbf">G+</a>). I’m sure it’s possible to point to many similar situations for other combinations of countries; for instance, for several years it has been difficult or impossible for scholars based in Iran to attend US-based conferences. But there should be no place for discrimination or exclusion based on ethnicity, gender, religion (or its absence), or national origin, in the activities of any legitimate scholarly discipline.</p>
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</ul>David EppsteinScripted Movement Drawings Series 1 (G+, via). Andrew Kudless makes generative art by programming a robot arm to use a calligraphy brush.Linkage2018-05-31T21:30:00+00:002018-05-31T21:30:00+00:00https://11011110.github.io/blog/2018/05/31/linkage<ul>
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<p>If you’re coming to Southern California for STOC (June 25–29 in Los Angeles), you should stay through the end of the last day for the <a href="http://www.cs.uci.edu/workshop-to-celebrate-vijay-vaziranis-contributions-to-theoretical-computer-science/">Workshop to Celebrate Vijay Vazirani’s Contributions to Theoretical Computer Science</a> (<a href="https://plus.google.com/100003628603413742554/posts/hvZ4ofJ9bAW">G+</a>). See also the <a href="https://www.cs.umd.edu/users/samir/stoc2018/">detailed schedule at the workshop web site</a>.</p>
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<p><a href="https://tierneylab.blogs.nytimes.com/2009/05/04/the-hamiltonian-puzzle">The Hamiltonian puzzle</a> (<a href="https://plus.google.com/100003628603413742554/posts/317XDDSK741">G+</a>). Fill 26 squares with the letters A–Z so that each two consecutive letters land in adjacent squares. Based on the <a href="https://en.wikipedia.org/wiki/26-fullerene_graph">26-Fullerene graph</a>; see <a href="http://www.mathematica-journal.com/issue/v11i3/contents/superhamilton/superhamilton.pdf">Ed Pegg’s explanation of the underlying mathematics</a>.</p>
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<p><a href="https://richardelwes.co.uk/2018/05/18/magforming-the-johnson-solids/">Magforming the Johnson Solids</a> (<a href="https://plus.google.com/100003628603413742554/posts/MothV5T9J4e">G+</a>, <a href="https://plus.google.com/+RichardElwes/posts/WP2qs9w2p57">via</a>). Richard Elwes steals his kids’ toys and has some geometric adventures with them.</p>
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<p><a href="https://gilkalai.wordpress.com/2018/05/20/dubcan-dauvergne-and-balint-virag-settled-the-random-sorting-networks-conjectures/">Solution to the random sorting network conjectures</a> (<a href="https://plus.google.com/100003628603413742554/posts/gymSPmwyqdT">G+</a>, <a href="https://plus.google.com/117271457236114081433/posts/Jkzod16nQCm">via</a>). “Sorting network” here really means a wiring diagram or allowable sequence of permutations — almost the same thing as a pseudoline arrangement or a rhombic tiling of a regular polygon. Randomly chosen sorting networks are now proven to behave nicely. But as Gil says towards the end of his post, one of the major questions about their non-random behavior — how many crossings can occur at the middle level of the diagram — a pseudoline version of the <a href="https://en.wikipedia.org/wiki/K-set_(geometry)"><script type="math/tex">k</script>-set problem from discrete geometry</a> — remains open.</p>
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<p><a href="https://www.smbc-comics.com/comic/hansel-and-gretel">Hansel and Gretel and algorithms</a> (<a href="https://plus.google.com/100003628603413742554/posts/LmaFeaSs59s">G+</a>, <a href="https://plus.google.com/+JeffErickson/posts/BkyE7tKkcEW">via</a>). Short webcomic.</p>
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<p><a href="https://www.cis.cornell.edu/cs-professor-tardos-deliver-sonia-kovalevsky-lecture">Éva Tardos will be this year’s Sonia Kovelevsky lecturer, at the July SIAM meeting</a> (<a href="https://plus.google.com/100003628603413742554/posts/M8WJ7w8MHBb">G+</a>).</p>
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<p><a href="https://en.wikipedia.org/wiki/Witch_of_Agnesi">The Witch of <s>Angmar</s> <s>Endor</s> Agnesi</a> (<a href="https://plus.google.com/100003628603413742554/posts/fDBw81Qhbii">G+</a>). In <a href="http://doi.org/10.5840/jphil20121091233">a paper from 2012</a>, J. McKenzie Alexander asks the following (trick) question. We choose uniformly at random a line through the point <script type="math/tex">(1,1)</script> in the Euclidean plane; suppose this line hits the horizontal axis at the point <script type="math/tex">(x,0)</script>. Based on this random value you get <script type="math/tex">x</script> dollars: if <script type="math/tex">x</script> is positive you win but if it is negative you have to pay <script type="math/tex">-x</script>. How much should you pay up front for this to be a fair bet?
The shape of the probability distribution for this experiment is given by the Witch. I posted the link as a way to beg readers to help me find a reference to a different fact about the witch, involving its osculating circle, but then I found it myself.</p>
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<p><a href="https://arxiv.org/abs/1712.05142"><script type="math/tex">\forall \exists \mathbb{R}</script>-completeness and area-universality</a> (<a href="https://plus.google.com/100003628603413742554/posts/UxeoJuWz7CA">G+</a>). For some time now <a href="https://en.wikipedia.org/wiki/Existential_theory_of_the_reals">the first (existential) level of the theory of the real numbers</a> has been very fruitful in classifying the complexity of problems in computational geometry and geometric graph theory. This paper from WG 2018 starts looking at the second level: an alternation between two levels of quantifiers. They conjecture that whether a planar graph has straight-line drawings of all possible face areas (that is, whether it is area-universal) is complete for this second level.</p>
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<p><a href="http://www.latimes.com/business/la-fi-blockchain-ecoli-20180527-story.html">Could blockchain have solved the mystery of the romaine lettuce E. coli outbreak?</a> (<a href="https://plus.google.com/100003628603413742554/posts/2YhK71H5vfE">G+</a>). Walmart has started using blockchain, not for cryptocurrency, but to secure and trace the provenance of the food it sells. The technology reduces the time to figure out where something originally came from (useful information in disease outbreaks, as the headline suggests) from roughly a week to seconds. But in the comments, Brian Slesinsky asks the age-old question: how is this any better than a standard distributed database?</p>
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<p><a href="http://jdh.hamkins.org/fun-with-orthoprojections/">Fun with orthoprojections!</a> (<a href="https://plus.google.com/100003628603413742554/posts/fbRyh4RjDK2">G+</a>, <a href="https://plus.google.com/+JoelDavidHamkins1/posts/F3P6ktRGicv">via</a>). Joel David Hamkins asks kids to figure out how blocks are stacked together, from <a href="https://en.wikipedia.org/wiki/Multiview_projection">multiview projections</a>. It’s also an amusing puzzle for adults.</p>
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<p>A wartime aberration in copyright law caused German publications to become copyright-free in the US. <a href="https://boingboing.net/2018/05/28/67-pct-more-citations.html">The result was a significant increase in how highly cited they became</a> (<a href="https://plus.google.com/100003628603413742554/posts/CSmRkG1NJ5b">G+</a>). So if (like I think most academics) you care more about your research being read and cited than about someone else making a profit from it, you should prefer open access publication. See also <a href="http://www.nber.org/papers/w24255">the original research report by Barbara Biasi and Petra Moser</a> and <a href="https://voxeu.org/article/effects-copyrights-science">its summary</a>.</p>
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<p><a href="https://en.wikipedia.org/wiki/Tennis_ball_theorem">The tennis ball theorem</a> (<a href="https://plus.google.com/100003628603413742554/posts/31V1Tcpjuxf">G+</a>). The seam of a tennis ball (like that of a baseball) divides the surface into two pieces of equal areas. Whenever a smooth curve on a sphere does this, it has at least four inflection points (intuitively, points where it changes from turning left to turning right…but if it goes straight for a while, all those points also count as inflections). New article on Wikipedia.</p>
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<p><a href="http://blogs.lse.ac.uk/impactofsocialsciences/2018/05/29/alphabetical-name-ordering-is-discriminatory-and-harmful-to-collaborations/">Alphabetical name ordering is discriminatory and harmful to collaborations</a> (<a href="https://plus.google.com/100003628603413742554/posts/hjoifZ8jE62">G+</a>, <a href="https://plus.google.com/+JoelDavidHamkins1/posts/ACA9NbqGUxY">via</a>). Maybe, but that doesn’t mean we have to emulate other disciplines’ habit of encrypting other information in a noisy and low-bandwidth channel. See the “via” link for an interesting discussion of this issue and how it might affect mathematical subjects. Along with comments on the quality of the study, they include whether and how randomization can be made to work, and if so how to convince outsiders not to impute anything from author ordering.</p>
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</ul>David EppsteinIf you’re coming to Southern California for STOC (June 25–29 in Los Angeles), you should stay through the end of the last day for the Workshop to Celebrate Vijay Vazirani’s Contributions to Theoretical Computer Science (G+). See also the detailed schedule at the workshop web site.LIPIcs autoref lemma2018-05-25T22:28:00+00:002018-05-25T22:28:00+00:00https://11011110.github.io/blog/2018/05/25/lipics-autoref-lemma<p>Many computer science conferences these days are being published open-source in the <a href="https://www.dagstuhl.de/en/publications/lipics">LIPIcs</a> online book series, and that’s a good thing.</p>
<p>If you’ve formatted your papers for LIPIcs, you might know that it automatically includes the <a href="https://ctan.org/pkg/hyperref">hyperref package</a>, which has at least three benefits:</p>
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<p>It automatically produces hyperlinks from one part of your paper to another whenever you refer to a numbered entity like the name of a theorem.</p>
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<p>It also produces hyperlinks from within your paper to web resources (like the papers you reference) as long as you include those links as urls or dois in your bibliography files.</p>
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<p>Instead of writing <code>Theorem~\ref{thm:its-label}</code> you can use a shorthand macro, <code>\autoref{thm:its-label}</code>. If you do this, it will fill in the “Theorem” part itself. But it will also hyperlink the word “Theorem”, as well as the theorem number, making it easier for people who want to follow the link to click on it.</p>
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<p>Alternatively, you might know that LIPIcs automatically includes the <a href="https://ctan.org/pkg/amsthm">amsthm package</a>. Again, this has some benefits:</p>
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<p>You can use <code>\qedhere</code> to control where the end-of-proof marker goes.</p>
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<p>It allows theorems, lemmas, definitions, etc., all to be numbered within a single sequence (and LIPIcs does this), making it easier for readers to search for them in the text and harder for them to get confused about multiple things with the same number.</p>
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<p>If you prefer, you can set LIPIcs’ “numberwithinsects” option to <s>insert lots of bugs into your theorems</s> make the numbering include the section number, again to make it easier for readers to find things.</p>
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<p>However, if you’ve tried to use all of these nice features, you might have noticed that they don’t all play nicely together. In particular, you can’t use <code>\autoref</code> on lemmas, because it will call them theorems instead and then (despite the nice numbering) your readers will be confused. “Where’s Theorem 5.3?” “Oh, that’s actually a lemma.”</p>
<p>It’s too late to save a couple of my papers that this bug bit, but in case anyone else runs into this, here’s the fix. It involves undefining the lemma, corollary, etc. environments, and then using some magic involving the <a href="https://ctan.org/pkg/aliascnt">aliascnt package</a> to redefine them in a way that works with both amsthm and hyperref autoref. I forget where I learned this technique but it might have been from <a href="https://tex.stackexchange.com/questions/187388/amsthm-with-shared-counters-messes-up-autoref-references/187395">this stackexchange thread</a> or something similar. Anyway, just copy this into your paper’s header:</p>
<figure class="highlight"><pre><code class="language-latex" data-lang="latex"><span class="c">%%% Fix bug in lipics-v2018 with \autoref{lemma} and corollary</span>
<span class="k">\usepackage</span><span class="p">{</span>aliascnt<span class="p">}</span>
<span class="k">\makeatletter</span>
<span class="k">\let\corollary\@</span>undefined
<span class="k">\let\endcorollary\@</span>undefined
<span class="k">\let\lemma\@</span>undefined
<span class="k">\let\endlemma\@</span>undefined
<span class="k">\makeatother</span>
<span class="k">\theoremstyle</span><span class="p">{</span>theorem<span class="p">}</span>
<span class="k">\newaliascnt</span><span class="p">{</span>lemma<span class="p">}{</span>theorem<span class="p">}</span>
<span class="k">\newtheorem</span><span class="p">{</span>lemma<span class="p">}</span>[lemma]<span class="p">{</span>Lemma<span class="p">}</span>
<span class="k">\aliascntresetthe</span><span class="p">{</span>lemma<span class="p">}</span>
<span class="k">\newcommand</span><span class="p">{</span><span class="k">\lemmaautorefname</span><span class="p">}{</span>Lemma<span class="p">}</span>
<span class="k">\newaliascnt</span><span class="p">{</span>corollary<span class="p">}{</span>theorem<span class="p">}</span>
<span class="k">\newtheorem</span><span class="p">{</span>corollary<span class="p">}</span>[corollary]<span class="p">{</span>Corollary<span class="p">}</span>
<span class="k">\aliascntresetthe</span><span class="p">{</span>corollary<span class="p">}</span>
<span class="k">\newcommand\corollaryautorefname</span><span class="p">{</span>Corollary<span class="p">}</span>
<span class="c">%%% End fix bug</span></code></pre></figure>
<p>I also <a href="/blog/2014/11/25/lipics-formatting-tricks.html">wrote about this in 2014</a>, for an older version of the LIPIcs formatting macros. My recommendation then was to remember not to use autoref in LIPIcs, but then I failed to follow this advice myself in some of my later papers. I think this method is more robust and produces better results.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/BuitS1FyXuJ">G+</a>)</p>David EppsteinMany computer science conferences these days are being published open-source in the LIPIcs online book series, and that’s a good thing.Lies to children2018-05-20T16:44:00+00:002018-05-20T16:44:00+00:00https://11011110.github.io/blog/2018/05/20/lies-to-children<p>Here’s an instructive if somewhat horrifying episode in the history of the history of women in mathematics (and why we need to be careful what we consider as reliable sources, on Wikipedia and elsewhere). It’s mostly drawn from <a href="https://en.wikipedia.org/w/index.php?title=Talk:Hypatia&oldid=842230434#"Training_program"_and_upbringing">this discussion</a> on Wikipedia, where credit is due to Wikipedia editors Phso2 and Katolophyromai for uncovering it.</p>
<p>It seems that in the early 20th century, <a href="https://en.wikipedia.org/wiki/Elbert_Hubbard">Elbert Hubbard</a> wrote a series of historical fiction pieces aimed at children, collected in his 14-volume <em>Little Journeys to the Homes of Great Teachers</em>. <a href="https://archive.org/details/littlejourneyst191610hubb">One of the volumes</a> (first published in 1908) includes a story about <a href="https://en.wikipedia.org/wiki/Hypatia">Hypatia</a>. We don’t know much about Hypatia’s actual life, so Hubbard’s story is almost entirely made up from Hubbard’s own imagination: the training regimen her father set her, her journey to Athens to visit Plutarch, the 20th-century rationalist doctrines her father instilled in her (later to be attributed as quotes to her), all fiction.</p>
<p>But in the late 20th century, some authors began collecting information about the lives of women mathematicians, and were not very careful about where this information came from. One of these was Lynn M. Osen, who published <em>Women in Mathematics</em> as a work of scholarship through the MIT Press in 1974; Osen relied heavily on Hubbard for her coverage of Hypatia. From Osen the fiction spread to Margaret Alic, whose <em>Hypatia’s Heritage: A History of Women in Science from Antiquity to the Late Nineteenth Century</em> (Women’s Press 1986) in turn relied on Osen. And as recently as 2007, Lisa Yount’s <em>A to Z of Women in Science and Math</em> (Infobase Publishing) continued to include the same myths. Apparently (the Wikipedia article now says) at least one college course was based on this material, as well. <a href="https://commons.wikimedia.org/wiki/File:Hypatia_portrait.png">Jules Maurice Gaspard’s equally-fictional cover image for Hubbard’s story</a> (below) has now become “by far, the most iconic and widely reproduced image” of Hypatia.</p>
<p style="text-align:center"><img src="/blog/assets/2018/Gaspard-Hypatia.png" alt="Jules Maurice Gaspard's 1908 children's-book illustration of Hypatia, now her "most iconic and widely reproduced image"" /></p>
<p>Fortunately, all this has now been rooted out of the historical part of the Wikipedia Hypatia article, and relegated to a section on modern fictional treatments of Hypatia, where it is clearly marked as non-factual. But Osen, Alic, and Yount continue to be used as the sources for several other Wikipedia articles. If they were this sloppy about Hypatia, who knows what other made-up claims from them are still being treated as factual? Or which other sources, cribbing from these ones, will continue to be thought reliable?</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/eo6RyqLn1oB">G+</a>)</p>David EppsteinHere’s an instructive if somewhat horrifying episode in the history of the history of women in mathematics (and why we need to be careful what we consider as reliable sources, on Wikipedia and elsewhere). It’s mostly drawn from this discussion on Wikipedia, where credit is due to Wikipedia editors Phso2 and Katolophyromai for uncovering it.Book arrival2018-05-17T21:25:00+00:002018-05-17T21:25:00+00:00https://11011110.github.io/blog/2018/05/17/book-arrival<p>Look what arrived in the mail yesterday! It’s both the hardback and paperback editions of my new book, <a href="https://www.cambridge.org/eppstein"><em>Forbidden Configurations in Discrete Geometry</em></a>!</p>
<p style="text-align:center"><img src="http://www.ics.uci.edu/~eppstein/pix/forbidden-configurations/forbidden-configurations-m.jpg" alt="Forbidden Configurations in Discrete Geometry" style="border-style:solid;border-color:black;" /></p>
<p>(The props don’t have much to do with the content of the book. They’re mostly there because I needed something to hold the books in place while I photographed them.)</p>
<p>I really like how it came out as a physical object. They’re using a high-quality, thin but opaque enough, and very glossy paper that works well with the printing, there’s color on every page, and the color reproduction looks good. (I’m still pleased with how the content came out, too, but that’s more for other people to judge.)</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/bcAdJJgogkx">G+</a>)</p>David EppsteinLook what arrived in the mail yesterday! It’s both the hardback and paperback editions of my new book, Forbidden Configurations in Discrete Geometry!Linkage2018-05-15T20:56:00+00:002018-05-15T20:56:00+00:00https://11011110.github.io/blog/2018/05/15/linkage<ul>
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<p><a href="https://boingboing.net/2018/05/01/public-sphere-v-elsevier.html">AI researchers shun <em>Nature Machine Intelligence</em></a> (<a href="https://plus.google.com/100003628603413742554/posts/R4cUhmJYYCt">G+</a>). Apparently it’s not a good time to launch a closed journal in a field where “virtually all of the major outlets make no charge for access to or publication of papers”.</p>
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<p><a href="https://www.ghacks.net/2017/06/02/why-i-wont-be-using-adobe-scan/">Why I won’t be using Adobe Scan</a> (<a href="https://plus.google.com/100003628603413742554/posts/U2NGr42aQ4z">G+</a>). As Martin Brinkmann writes, “I won’t use an application that forces registration and cloud saving on me.” Well, I kind of do with my email, but the fewer other corporations that I give copies of my scanned documents the better.</p>
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<p><a href="https://blog.wikimedia.org/2018/05/03/why-i-women-wikipedia/">Why I write about women on Wikipedia</a> (<a href="https://plus.google.com/100003628603413742554/posts/3qRwuHCiLes">G+</a>). Editor SusunW discusses her motivation for contributing to women’s biographies on Wikipedia.</p>
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<p><a href="https://en.wikipedia.org/wiki/Golomb_graph">The Golomb graph</a> (<a href="https://plus.google.com/100003628603413742554/posts/3nDNhCFW3nv">G+</a>). It’s mostly famous as a (nonplanarly-drawn) unit distance graph, but it’s also polyhedral. In the G+ comments, I challenge my readers to find drawings of it as a convex polyhedron. My favorite is Greg Egan’s rotating version using only equilateral and isosceles triangles and regular pentagons (below), but Refurio Anachro’s almost-convex unit distance representation of the dual (a tetrahedron glued onto a <a href="https://en.wikipedia.org/wiki/Triangular_cupola">triangular cupola</a>) is also nice.</p>
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<p style="text-align:center"><img src="/blog/assets/2018/Egan-Golomb-polyhedron.gif" alt="Greg Egan's visualization of the Golomb graph as a polyhedron with equilateral and isosceles triangles and regular pentagons as its faces" /></p>
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<p><a href="https://www.cambridge.org/core/books/forbidden-configurations-in-discrete-geometry/0A90D6B522B1DFF59641F086F149EA45"><em>Forbidden Configurations in Discrete Geometry</em></a> (<a href="https://plus.google.com/100003628603413742554/posts/RM1UhNUBL66">G+</a>). My new book exists! Or at least, you can get the e-reader version. Be careful if you have a black-and-white Kindle, as I do: it has lots of color illustrations. The print version will come later this year. <a href="http://www.cs.uci.edu/eppstein-publishes-new-book-forbidden-patterns-in-discrete-geometry-for-mathematicians-and-computer-scientists/">Here’s my department’s news item about it</a>.</p>
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<p><a href="http://aperiodical.com/2018/05/how-to-join-in-with-our-distributed-wiki-edit-day/">Wiki Editing Day</a> (<a href="https://plus.google.com/100003628603413742554/posts/3Gm1WBtL7Jv">G+</a>, <a href="https://plus.google.com/+Aperiodical/posts/c4c3JNAwRxy">via</a>). An online project to improve Wikipedia’s coverage related to female mathematicians, now past.</p>
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<p><a href="http://www.math3ma.com/mathema/2017/8/21/dear-autocorrect">Dear Autocorrect… (Sincerely, Mathematician)</a> (<a href="https://plus.google.com/100003628603413742554/posts/CSUN1QTLkHJ">G+</a>). From <a href="http://www.math3ma.com/">math3ma</a>, the blog of mathematics graduate student Tai-Danae Bradley (most other posts of which are in large part about category theory).</p>
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<p><a href="https://blog.plover.com/math/finite-projective-planes.html">Katara constructs finite projective planes</a> (<a href="https://plus.google.com/100003628603413742554/posts/SZSRG8UZHau">G+</a>). An amusing application of finite geometry to children’s games.</p>
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<p><a href="https://cameroncounts.wordpress.com/2018/05/11/london-combinatorics-colloquia-3/">London Combinatorics Colloquia</a> (<a href="https://plus.google.com/100003628603413742554/posts/6KDK15AUwGb">G+</a>). Peter Cameron summarizes a collection of interesting sounding combinatorics talks: János Pach on triangling the triangle, Carsten Thomassen on nowhere-zero flows, Paul Russell on additive combinatorics, Katherine Staden on induced Turán theorems, Agelos Georgakopoulos on percolation, and Nikhil Bansal on discrepancy.</p>
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<p><a href="http://www.tate.org.uk/whats-on/tate-modern/exhibition/shape-light">Shape of Light: 100 Years of Photography and Abstract Art</a> (<a href="https://plus.google.com/100003628603413742554/posts/6zYQH891AzQ">G+</a>, <a href="http://www.artlyst.com/previews/shape-of-light-photographys-relationship-with-abstract-art-tate-modern/">via</a>). Unfortunately I don’t think I’ll be in London any time between now and the October close of this exhibit at the Tate Modern on the relation between photography and abstract art. But if I were it would be high on my priorities to see.</p>
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<p><a href="https://twitter.com/tilingbot">Tiling Bot</a> (<a href="https://plus.google.com/100003628603413742554/posts/85UgbaQvg1Q">G+</a>, <a href="https://plus.google.com/+RoiceNelson/posts/1NuGBzMwzW7">via</a>, <a href="http://linescurvesspirals.blogspot.co.uk/2018/05/carnival-of-mathematics-157.html">also via</a>). A pretty tiling on twitter, daily.</p>
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<p><a href="https://theconversation.com/maria-agnesi-the-greatest-female-mathematician-youve-never-heard-of-94378">Maria Agnesi, the greatest female mathematician you’ve never heard of</a> (<a href="https://plus.google.com/100003628603413742554/posts/JbGmXUuNf9w">G+</a>). Possibly the author underestimates how much we’ve heard of her and her <a href="https://en.wikipedia.org/wiki/Witch_of_Agnesi">witch</a>, but it’s a nice piece anyway.</p>
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</ul>David EppsteinAI researchers shun Nature Machine Intelligence (G+). Apparently it’s not a good time to launch a closed journal in a field where “virtually all of the major outlets make no charge for access to or publication of papers”.Planet reconfiguration2018-05-13T14:42:00+00:002018-05-13T14:42:00+00:00https://11011110.github.io/blog/2018/05/13/planet-reconfiguration<p>Suppose you’re designing a planet for a computer game. You’ve already divided its surface into sectors, with at most three sectors meeting at any point, and you decide to place cities at some of the points where triples of sectors meet. Is there a way of assigning some of the sectors to be continents and others to be oceans in such a way that all your cities are on the coast?</p>
<p style="text-align:center"><img src="/blog/assets/2018/four-sector-planet.svg" alt="A planet with four cities and four sectors" /></p>
<p>The abstract combinatorial problem underlying this planet design problem comes with a somewhat intimidating name, “planar monotone <a href="https://en.wikipedia.org/wiki/Not-all-equal_3-satisfiability">not-all-equal 3-sat</a>”. In reverse order: it’s a form of 3-sat because you are trying to satisfy constraints on triples of sectors, and each sector has a binary value (land or water). It’s not-all-equal 3-sat because, in order for a city to be on the coast, the three sectors meeting there must not all be the same type. It’s planar because the surfaces of most planets are topological spheres, which is more or less the same as a plane for the purposes of this problem. And it’s monotone because…well, that one’s harder to explain. It comes from viewing the type of each sector as a Boolean variable and the cities as a certain kind of Boolean gate (with three inputs, producing a true output if they’re not all the same and false otherwise). The circuit you get from this interpretation has no not-gates. One way to get a non-monotone version of the same problem would be to add more cities, on borders between two sectors rather than three. Those would force the two sectors to be of opposite types, acting like a not gate.</p>
<p>Anyway, if you’re used to 3-sat being one of the canonical NP-complete problems, it may come as a surprise that <a href="https://www.cs.unm.edu/~moret/nae3sat.ps">planar not-all-equal 3-sat has a polynomial solution</a>. The proof of the general case is short but a little messy, but in the planet design problem it’s much easier, at least in the case where all triples of sectors are cities. At each city, you have to decide which of its three sector boundaries is to be land-land or water-water. The chosen boundaries connect pairs of cities, forming a <a href="https://en.wikipedia.org/wiki/Matching_(graph_theory)">perfect matching</a>. And if you can choose some of the boundaries in any way that perfectly matches the cities, the remaining boundaries can be used to separate land from water and solve the problem. (This is where we’re using the assumption that the planet’s suface is spherical rather than a torus or higher-genus surface: on a torus, the remaining boundaries might not separate land from water.) So all we have to do is apply a perfect matching algorithm to the graph whose vertices are cities and whose edges are sector boundaries.</p>
<p>In the case where some triples of sectors do not have cities on them, it’s a little more complicated, because two or three land-land or water-water boundaries can meet at those points. The usual proof goes through two levels of translation, but I think it’s easier to skip one of the levels (max cut) and go directly to the second one (the maximum weight even-degree subgraph). To do so, give each sector boundary a weight, 0, 1, or 2, equal to the number of cities at its endpoints. Then whenever any subgraph of the graph of sector boundaries and their endpoints has even degree everywhere, it can be used as a boundary between land and water having that subgraph as its coastline. (Again, this is where we use the shape of the planet.) And the total weight of a subgraph equals twice the number of cities that it places on the coast. So there is a solution if and only if there is an even-degree subgraph with total weight equal to twice the number of cities.</p>
<p>But now we’re almost done. The maximum weight even-degree subgraph of any non-negatively-weighted graph is complementary to the minimum weight subgraph that has odd degree at all odd vertices. And this minimum odd subgraph is (with some care about zero-weight edges) the edge-disjoint union of a collection of paths that can be found by a different matching problem: the minimum weight perfect matching, in a complete graph whose vertices are the odd vertices of the input and whose edges are weighted by shortest path distance.</p>
<p>My new preprint “Reconfiguration of Satisfying Assignments and Subset Sums: Easy to Find, Hard to Connect” (<a href="https://arxiv.org/abs/1805.04055">arXiv:1805.04055</a>, to appear in <a href="http://cocoon2018.sdu.edu.cn/">COCOON 2018</a>, with Jean Cardinal, Erik Demaine, Bob Hearn, and Andrew Winslow) takes this question a step further, and looks at the connectivity of the solution space of the problem. If you can find a single solution with all cities on the coast, can you get from there to every other solution, by a sequence of steps in which you change the land-water state of a single sector at a time? Can you get from one particular solution to another by the same sorts of steps? The answer is not always yes: the map shown above has six solutions, the six ways of choosing two sectors to be wet and two to be dry. But you can’t get from one to another by changing a single sector, because that would leave you with three wet and one dry or three dry and one wet, flooding or landlocking one of the cities.</p>
<p>It turns out to be PSPACE-hard to tell whether the solution space is connected, or whether a pair of solutions are connected to each other. The map of the figure forms one of the important gadgets in the proof, a truth-setting device, because of its property of having only isolated solutions in its solution space. (In the paper it is drawn more like the graph of a cube, because we draw both the sectors and the cities as vertices in a graph). The preprint also contains additional examples of this phenomenon of a problem in which it is easy to find a single solution but hard to find a connection between solutions. As well as planar monotone nae-3sat (or the planet building problem), they include the subset sum problem (with integers of polynomial magnitude) and the problem of getting from vertex to vertex in a polytope formed by making a constant number of slices to a hypercube.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/9hfuvQqQrCN">G+</a>)</p>David EppsteinSuppose you’re designing a planet for a computer game. You’ve already divided its surface into sectors, with at most three sectors meeting at any point, and you decide to place cities at some of the points where triples of sectors meet. Is there a way of assigning some of the sectors to be continents and others to be oceans in such a way that all your cities are on the coast?Sorting when the sorted order keeps changing2018-05-09T10:58:00+00:002018-05-09T10:58:00+00:00https://11011110.github.io/blog/2018/05/09/sorting-when-sorted<p>Even though we know it doesn’t mean much, there are plenty of systems that maintain opinion-based rankings of things: the best movies, songs, or albums of all time, the best names to give babies, safest or most interesting places to live, best local restaurants, or even the top computer science departments.
The problem is, because they’re opinion-based, the rankings keep changing. Different styles of movie, food, or computer science research fall into or out of fashion, and this causes the ordering of who is the best to change. And it’s obviously really important to have an accurate ordering. So what can you do?</p>
<p>One approach would be to stop the world and re-rank everybody periodically, as <i>Newsweek</i> does every year for academics. But then your ranking will regularly become a whole year out of date. Wouldn’t it be better to change your reported ranking continuously, as the actual rankings change? That way everyone will have to visit your ranking site more often to keep up with how their favorites are doing. But it wouldn’t do to make each fine-grained update be as expensive as recomputing the whole ranking from scratch. It would be better if you could only ask the people who produce the ranking for a little bit of information at a time, just enough to keep your ranking accurate as opinions change under it.</p>
<p>That is the problem modeled mathematically by Anagnostopoulos, Kumar, Mahdian, and Upfal in a paper from ICALP 2009 and later published in the journal <i>Theoretical Computer Science</i>, “<a href="https://doi.org/10.1016/j.tcs.2010.10.003">Sorting and selection on dynamic data</a>”. The specific ranking website they chose to describe (bix.com) has since gone defunct, but the principle remains: maintain a ranking of a set of objects by asking users binary questions about which of two objects is better. The objects are assumed to have an underlying linear ordering, which is changing randomly by a process that selects a random consecutive pair of objects in the underlying ordering and swaps them. At the same time, the ranking algorithm is maintaining its own ordering (not the same as the underlying ordering), and changing it by a process in which it selects any pair of two objects, asks what the underlying order of those two objects is, and uses the result to update its ordering somehow. Since human opinions are noisy, I suspect that the process of asking about the underlying order of two objects isn’t just presenting a comparison to a single user, but rather showing the same binary comparison to many users and letting them vote.
Anyway, assuming the two processes operate at roughly the same rate (one swap in the underlying order per comparison by the ranking algorithm), can a smart enough ranking algorithm keep up?</p>
<p>Here “keep up” means maintaining a ranking that is a small number of inversions away from the correct underlying ranking; the number of inversions is called the <a href="https://en.wikipedia.org/wiki/Kendall_tau_distance">Kendall tau distance</a>. Anagnostopoulos et al. showed that it is possible to keep this distance small: if there are <script type="math/tex">n</script> items to rank, an algorithm that repeatedly runs quicksort can maintain a ranking that is within Kendall tau distance <script type="math/tex">O(n\log\log n)</script> of the underlying ranking. And that’s close to optimal, because the distance could be as big as quadratic, and because they also proved a lower bound that, no matter how you choose pairs to compare and how to update your ranking, the expected distance between your ranking and the underlying ranking will be at least <script type="math/tex">\Omega(n)</script>. This is because the random positioning of changes in the underlying ranking means that, no matter how you look for them, you have too small a chance of seeing most of the very recent changes.</p>
<p>So now I have a new paper on this problem: “Optimally Sorting Evolving Data” (<a href="https://arxiv.org/abs/1805.03350">arXiv:1805.03350</a>, with Besa, Devanny, Goodrich, and Johnson, to appear in ICALP). It gets rid of that last log-log factor and shows how to stay within distance <script type="math/tex">O(n)</script> of the underlying ranking, by being less clever. Instead of using a clever and fast sorting algorithm like quicksort, we use a simpler and slower one, a variation of bubble sort: just scan through the pairs of elements comparing each pair until you find two that are out of order, swap the out-of-order pair, and then scan backwards comparing the smaller element with earlier elements to find where to put it. Continue the outer scan until everything has been put into place. And then repeat again, because once we think we’ve sorted everything we start over again from the beginning.</p>
<p>How can this slow sorting algorithm be better than quicksort? The trick is that it’s only slow when it has a lot of work to do. Each comparison that it makes, beyond the initial scan, reduces the number of inversions by one. So unless the number of inversions is already very small, the algorithm will on average decrease the distance to the underlying ranking by close to one inversion per step. On the other hand, the random swapping process on the underlying ranking is generally acting to increase the distance, but it will do so by less than one unit per step (in expectation), because it has some probability of reversing its own swaps before the ranking algorithm finds them. So (unless the distance is already small) the ranking algorithm makes the distance smaller more quickly than the random swapping makes it larger, and it eventually becomes small. Making this reasoning formal and rigorous (and accounting for the fact that the two processes are not independent: random swaps can make the ranking algorithm do something other than correctly sorting its input) takes up the main part of the paper.</p>
<p>This is actually the second paper we’ve written on the subject, but <s>the first one isn't on arXiv yet so</s> I haven’t mentioned it here before.<sup id="fnref:1"><a href="#fn:1" class="footnote">1</a></sup> It is “<a href="http://doi.org/10.1137/1.9781611975055.8">Quadratic time algorithms appear to be optimal for sorting evolving data</a>” from ALENEX 2018. Our new paper relies heavily in its proof technique on the number of steps in the random swap process and the number of comparison steps in the ranking algorithm being equal, and on the specifics of the sorting algorithm we chose, but the ALENEX paper shows experimentally that these assumptions shouldn’t be necessary. The same algorithm, or any of several other bubble-sort-like algorithms, work well even if the rate of random change is higher (plausibly, any constant factor times the rate of comparisons). Quicksort is not as good at low rates of change, but becomes better in comparison to the bubble sorts as the rate of change becomes higher. And (unsurprisingly) quicksort takes many fewer steps than bubble sort to converge to a stable distance from the underlying ranking. So for low rates of change, what seems likely to be best would be to start with a pass of quicksort to get close to the right ranking, and then switch to repeated bubble sort after that. But we don’t know how to prove most of this, so there’s plenty more still to do.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/GrKB4UmMmCr">G+</a>)</p>
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<p>Update 2018-05-15: The ALENEX paper is now up at <a href="https://arxiv.org/abs/1805.05443">arXiv:1805.05443</a>. <a href="#fnref:1" class="reversefootnote">↩</a></p>
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</div>David EppsteinEven though we know it doesn’t mean much, there are plenty of systems that maintain opinion-based rankings of things: the best movies, songs, or albums of all time, the best names to give babies, safest or most interesting places to live, best local restaurants, or even the top computer science departments. The problem is, because they’re opinion-based, the rankings keep changing. Different styles of movie, food, or computer science research fall into or out of fashion, and this causes the ordering of who is the best to change. And it’s obviously really important to have an accurate ordering. So what can you do?Fair open access2018-05-02T20:15:00+00:002018-05-02T20:15:00+00:00https://11011110.github.io/blog/2018/05/02/fair-open-access<p>Mark C. Wilson has asked me for a statement of public support of the <a href="https://www.fairopenaccess.org/">Fair Open Access principles</a>. I’m posting my answer here, which is “yes, but…”</p>
<p>I wholeheartedly support principles 2-5: authors retain copyright, all articles are published open access with an explicit open access license, submission and publication are not conditional on payment of fees nor on memberships, and any fees paid to publishers are low, transparent, and proportional.</p>
<p>My main concern is with principle 1, requiring ownership of the journal by an editorial board or a democratically controlled scholarly society. In principle this sounds like a good idea. It prevents uncertainty over “what if the editor leaves academia” or “what if the editor decides to take the journal to a closed-access model”? In such cases the previously published papers would still be open-access licensed but there could still be legal or availability-of-backups issues with setting up a mirror of the formerly-open journal. We would want to forestall such moves in any case. And principle 1 also rules out journals run as a private fiefdom by their founder, and the associated abuses (lack of proper peer review, pressure to cite the founder’s own papers, etc) that we’ve seen from such journals.</p>
<p>In practice, though, principle 1 seems likely to prevent the creation of qualifying new open journals. It would disallow journals from being run on an informal basis by a team of volunteer academics (what generally happens now), because such a team is not a legal entity and cannot legally own the journal; instead, if it became disputed, the courts would most likely rule that one particular member of the team owned the journal. So while the principles say “This could be ownership by an editorial board”, my understanding is that claiming ownership of that form would be a lie. You can certainly operate a journal by a democratically elected editorial board without any other form of legal recognition of the board, but that only works until a serious dispute arises and the courts step in. It is not stable and robust. And without that, why is it any better than the individual-ownership model?</p>
<p>Principle 1 would also disallow journals from being owned by a university with which one of its editors is associated, because universities do not in general have “a transparent ownership structure, controlled by and responsive to the scholarly community”. The only remaining possibilities would appear to be to find a scholarly society (meeting the other conditions) willing to sponsor the journal, or to set up a legal entity (a corporation) to run it. Scholarly societies tend to be big and hidebound, with a high barrier to entry, and it would not always be possible to find such a society that has a suitable ownership structure. I don’t think ACM would qualify, for instance, because the community that controls it has much broader participation from industry than from academia. And setting up a corporation likely would incur both setup costs (legal fees and registration) on the order of a few thousand dollars and annual costs (legally-required accounting) on the order of a few hundred dollars; not impossible, but a bit of a gamble if the only source is the personal money of the founders. See for instance the <a href="http://www.marktwainjournal.com/volume_56.1_Spring2018.html">Mark Twain Journal</a>, a print-based non-open journal (for some reason <a href="https://www.insidehighered.com/quicktakes/2018/05/01/historians-resist-publishing-online">historians are averse to online publication</a>) in which for different reasons the editor put approximately $7000 of his own money into the journal to keep it running — we should not require that of journal founders.</p>
<p>I do think journals that become successful should be encouraged to move towards meeting principle 1. For instance, I think the time is ripe for the freed-from-ACM Symposium on Computational Geometry to incorporate (as has been discussed by its steering committee for a few years now), with an item in the registration-fee-supported annual conference budget to support the incorporation costs, with the ability to carry over money from one year’s conference budget to the next, and for the Journal of Computational Geometry (currently run on an informal basis by a team of volunteers) to transfer its ownership officially to the resulting society. But I think it should be possible to start a journal that does not yet meet principle 1, under the assumption that should it become successful it will move towards meeting that principle. I would not like to see the open access journals I use and support (primarily JoCG, JGAA, and EJC) be blackballed, or un-whitelisted, as insufficiently pure, merely for not yet meeting principle 1.</p>
<p>If what we want from principle 1 is a proper, fair, and non-corrupt editorial system, we should say that more directly. The ownership or steering committee affects that, but indirectly.</p>
<p>Also, I think there should be a principle 6: the journal should follow best practices in making its content readable by viewers, accessible to the disabled, reliable in the event of failures, and available for indexing. (That is, use standard file formats, follow the standards for those formats, set up proper backups or mirrors, provide properly formatted metadata, and inform the search engines that need informing that you and your papers exist.) If we’re going to set standards for what a reputable open access journal should do, these things are important.</p>
<p>With all that as caveat, I support the Fair Open Access principles.</p>
<p>(<a href="https://plus.google.com/100003628603413742554/posts/JcXeebfPBtG">G+</a>)</p>David EppsteinMark C. Wilson has asked me for a statement of public support of the Fair Open Access principles. I’m posting my answer here, which is “yes, but…”Linkage2018-04-30T22:22:00+00:002018-04-30T22:22:00+00:00https://11011110.github.io/blog/2018/04/30/linkage<ul>
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<p><a href="http://jdh.hamkins.org/infinite-sudoku-and-the-sudoku-game/">Infinite Sudoku and the Sudoku game</a> (<a href="https://plus.google.com/100003628603413742554/posts/UDkQXBtP4hh">G+</a>, <a href="https://plus.google.com/+JoelDavidHamkins1/posts/2spmHW31y25">via</a>). The game is to alternate choosing values (with no repetitions allowed per row, column, or smaller square) until stuck. Joel Hamkins provides a complete analysis of who wins, not only on any finite <script type="math/tex">n^2\times n^2</script> board, but also in an analogous infinite game where one player is trying to fill the entire board and the other is trying to block a solution.</p>
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<p><a href="https://gilkalai.wordpress.com/2018/04/13/coloring-problems-for-arrangements-of-circles-and-pseudocircles/">Coloring problems for arrangements of circles (and pseudocircles)</a> (<a href="https://plus.google.com/100003628603413742554/posts/RqS6t1xoC5w">G+</a>). In connection with Aubrey de Gray’s breakthrough on the Hadwiger–Nelson problem, Gil Kalai posts some related problems on coloring circles.</p>
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<p><a href="http://www.unicodeit.net/">Convert LaTeX markup to unicode text</a> (<a href="https://plus.google.com/100003628603413742554/posts/MycSn8VjKVe">G+</a>). Likely useful for underfeatured social media like Google+ that don’t allow MathJax.</p>
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<p><a href="https://en.wikipedia.org/wiki/Three-gap_theorem">Three-gap theorem</a> (<a href="https://plus.google.com/100003628603413742554/posts/Y84eCvocSJH">G+</a>). New Wikipedia article on the mathematics behind the spacing of plant leaves and the intervals of musical scales.</p>
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<p><a href="https://plus.google.com/+TimHutton/posts/4QWhKWtp2r6">Girl-guide dreamcatchers tile the plane with similar kites</a> (<a href="https://plus.google.com/100003628603413742554/posts/HyHYUi2g5uC">G+</a>). One of them looks like the kite-only version of my <a href="/blog/2012/07/23/diamonds-kites-and.html">diamond-kite meshes</a>, or would if the girls were more accurate.</p>
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<p><a href="http://bit.ly/2JC8EAP">Anna Haensch collects links on the origins of mathematical notation</a> (<a href="https://plus.google.com/100003628603413742554/posts/eTc75c3veHe">G+</a>, <a href="https://plus.google.com/+AmsOrg/posts/bLBaUtgiPBS">via</a>). See also <a href="https://twitter.com/worrydream/status/773757030364352512">Bret Victor on THE BIG INTEGRAL</a>.</p>
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<p>Sašo Krajnc, aka Cvern, <a href="https://boingboing.net/2018/04/24/artist-creates-portraits-from.html">creates portraits from intricate string art</a> (<a href="https://plus.google.com/100003628603413742554/posts/WTq16WW3Cpq">G+</a>). It’s just a circular frame and a loop of string that visits every peg around the frame once. How could it produce any kind of complicated picture? But it does.</p>
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<p><a href="https://www.smithsonianmag.com/science-nature/how-poetry-and-math-intersect-180968869/">How poetry and math intersect</a> (<a href="https://plus.google.com/100003628603413742554/posts/33uiNumHxwD">G+</a>). As Evelyn Lamb writes, “Both require economy and precision—and each perspective can enhance the other.”</p>
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<p><a href="https://www.benfrederickson.com/better-venn-diagrams/">Area-proportional Venn diagrams</a> (<a href="https://plus.google.com/100003628603413742554/posts/2WN1uDUn1SM">G+</a>, <a href="https://news.ycombinator.com/item?id=16838890">via</a>). The goal is not only to have a desired pattern of intersections, but to have the areas of each intersection approximate some desired target. It’s straightforward for two circles via binary search, but for larger numbers (where there might not be an exact solution), which heuristics are most accurate?</p>
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<p><a href="https://www.buzzfeed.com/zoetillman/the-justice-department-deleted-language-about-press-freedom">The Justice Department deleted language about press freedom And racial gerrymandering from its internal manual</a> (<a href="https://plus.google.com/100003628603413742554/posts/W43pw5pgmce">G+</a>, <a href="https://www.metafilter.com/173805/the-great-wolf-Fenris-rose-from-the-deep#7388217">via</a>). It may not come as much of a surprise that the current US administration is not among those of us interested in fixing the problems of gerrymandered and politically and racially biased electoral districts…</p>
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<p><a href="http://oujifei.com/gauss-braid/">Gauss’s braid: braided paper strips as a method for form generation</a> (<a href="https://plus.google.com/100003628603413742554/posts/5AR67vmmRyU">G+</a>). “Gauss’s braid” more commonly refers to a specific element of the four-strand <a href="https://en.wikipedia.org/wiki/Braid_group">braid group</a>, used by Gauss as an example in his work on an <a href="https://en.wikipedia.org/wiki/Linking_number#Gauss's_integral_definition">integral formula for the linking number</a>. Gauss was interested in this because of the possibility that planetary orbits might be linked; see <a href="https://doi.org/10.1007/BF03024400">“Orbits of asteroids, a braid, and the first link invariant” (Epple 1998)</a> for details. Gauss’s braid is shown in Epple’s Figure 2, which credits it as “Page 283 of Gauss’s Handbuch 7”. While searching for all this, I found this link on paperforms. I don’t see how it has much to do with Gauss (<a href="https://www.google.com/doodles/johann-carl-friedrich-gaus-241st-birthday">whose birthday is today</a>), but it still looks interesting.</p>
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</ul>David EppsteinInfinite Sudoku and the Sudoku game (G+, via). The game is to alternate choosing values (with no repetitions allowed per row, column, or smaller square) until stuck. Joel Hamkins provides a complete analysis of who wins, not only on any finite board, but also in an analogous infinite game where one player is trying to fill the entire board and the other is trying to block a solution.