578 karma · joined May 9, 2015
https://www.cl.cam.ac.uk/research/hvg/Isabelle//dist/library...
Many thanks for sharing this though. It is very easy and convenient to create simple diagrams with tikzcd, but I often struggle to make larger and more complex diagrams look nice.
It sadly also depends a lot on the solver used and the way the problem was encoded in SMT. For a class in college I once tried to solve Fillomino puzzles using SMT. I programmed two solutions, one used a SAT encoding of Warshall's algorithm and another constructed spanning trees. One some puzzles the first solver required multiple hours whereas the second only needed a few seconds, while on other puzzles it was the complete opposite. My second encoding needed on hours for a puzzle which I could solve by hand in literally a few seconds. SAT and SMT solvers are extremely cool, but way incredibly unpredictable.
https://obamawhitehouse.archives.gov
All pages about president Obama's policies have been removed. Just like how white house website from during the Bush administration is archived here:
https://georgewbush-whitehouse.archives.gov
Trump might be a climate change denier, but removing all policy related webpages is business as usual.
I'm not aware of articles treating graphs as Kleene algebras (I haven't looked for them though). Conway's "Regular Algebra and Finite Machines" [1] and Kozen's "A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events" [2] are interesting texts to read on Kleene algebra.
[1] https://www.amazon.com/Regular-Algebra-Finite-Machines-Mathe...
Another interesting way to represent directed graphs is using matrices over boolean matrices (also forming an idempotent semiring). Matrices over min, + algebra (also a Kleene algebra) allow us to represent direct graphs with weighted edges and allow us to derive many interesting algorithms, such as the Floyd-Warshall (if we replace the min, + algebra by regular sets we get Kleene's algorithm instead).
The numbers of billionaires, and especially percentages of those, are a worthless metric. Billionaires are about as rare unicorns, especially here in the Netherlands (pop. 17 million) where we only have 9 billionaires in total. Due to the high taxes here in Europe it's incredibly difficult to become very rich, so it's not strange that a lot of our billionaires have inherited their wealth. We also lack the tech scene which created a lot of self-made billionaires in the US.
[1] http://pbrt.org/
[2] https://www.cbs.nl/en-gb/news/2015/11/9-in-10-people-access-...
http://www.visualcapitalist.com/chart-epic-collapse-deutsche...
Edit: source: https://twitter.com/samcoatestimes/status/751682424405430272