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All You Need To Know About Dog Ear Infections

Otitis externa, better known as a dog's ear infections, are one of the most common health issues that plague our canine compadres today. They are also particularly troublesome because, after one infection, your dog typically contracts more and more. Much of what will decide on the severity of the condition would be the dog ear infection treatment provided...

Linkage for April Fools

(No actual April Fools jokes among these, sorry.)Superhydrophobic fountain uses surface coatings to control the flow of water (G+)Interview with Robert Lang about what it feels like to fold origami (G+)How the constraint of having a unique solution can be used to help solve puzzles (G+)Desargues' concertina — Greg Egan animates unit-distance drawings...

Errera deltahedron

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?The result is a 17-vertex triangulated planar graph called the Errera...

Linkage for the Ides of March

Using 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...

Fast K-best optimization for graphs of bounded treewidth

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", arXiv:1703.02784.If you just want the k shortest...

Linkage

Emmanuelle 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...

Triangle-free penny graphs are 2-degenerate

A penny graph (the topic of today's new Wikipedia article) is what you get from pennies by shoving them together on a tabletop, keeping them only one layer thick, and looking at which pairs of pennies are touching each other. In a 2009 paper, Konrad Swanepoel suggested that, when there are no three mutually-touching pennies, the number of adjacencies...

An unsuccessful attempt to use CairoSVG to generate small vector-graphics PDF files

The following image shows the onion layers of a 6 × 6 grid (see Sariel's post for context). It consists of 42 circles, 36 with a fill and a stroke and 6 with only a stroke.My usual workflow is to draw this sort of thing in Adobe Illustrator, but one drawback of doing things this way is huge files: as a PDF file suitable for inclusion in LaTeX, these...

Linkage

Telemetry: Tessellated paper sculptures by Matthew Shlian (G+)Polygonal billiard paths, after the work of Iranian-American Fields medalist Maryam Mirzakhani (G+)We are all Iranians: Lance Fortnow speaks out about the travel ban and its affect on his colleagues (G+)David Wood shares the saga of the journal publication of one of his papers, highlighting...

Complete bipartite polyhedra

The tetrahedron and the Császár polyhedron are polyhedra whose edges and vertices form complete graphs; it is unknown whether any others exist. At the tutorial session for Graph Drawing 2015, I asked whether there are any complete bipartite polyhedra.As the definition of non-convex polyhedra can be the subject of heated debate (check out Wikipedia:Talk:Polyhedron...

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