As detected by Igor Carron, this blog has reached its 1000th visit ! Well, perhaps it’s 1000th robot visit 
Yesterday I found some very funny (math) jokes on Bjørn’s maths blog about “How to catch a lion in the Sahara desert” with some … mathematical tools.
Bjørn collected there many ways to realize this task from many places on the web. There are really tons of examples. To give you an idea, here is the Schrodinger’s method:
“At any given moment there is a positive probability that there is a lion in the cage. Sit down and wait.”
or this one :
“The method of inverse geometry: We place a spherical cage in the desert and enter it. We then perform an inverse operation with respect to the cage. The lion is then inside the cage and we are outside.”
So, let’s try something about Compressed Sensing. (Note: if you have something better than my infamous suggestion, I would be very happy to read it as a comment to this post.)
“How to catch a lion in the Sahara desert”
The compressed sensing way: First you consider that only one lion in a big desert is definitely a very sparse situation by comparing lion’s size and the desert area. No need for a cage, just project randomly the whole desert into a dune of just 5 times the lion’s weight ! Since the lion obviously died in this shrinking operation, you use the RIP (!) .. and relaxed, you eventually reconstruct its best tame approximation.
Image: Wikipedia
Merci pour le Blogroll
Pedrock
De rien Pedro. Marrant que tu ai aussi migré sur WordPress !
@+,
Laurent
Good idea~
Maybe we can operate the reconstruction on the shrinked lion data in a cage, so we “catch” the lion
A lion may be sparsely represented in a basis of other lions. In that case, we can reconstruct the Lion using only very few measurements of the Lion. So no need for the whole lion, just some hairs or so. And since finding the sparsest representation of hairs of the Lion in the basis of lions is quite slow, you have plenty of time to build the cage around it while your waiting for the solver to finish…
Excellent. Thanks. Be careful, if you remove too many hairs, e.g. more than M/log(N/K), the lion becomes itself too sparse
along the lines Of Jort’s solution:
acquire CS measurements of the Lion, once it is caught it takes a long time to reconstruct. If you are fast enough, acquire an image of a cage. Since CS is linear, add the CS measurements of the Lion and that of the cage before the Lion is reconstructed and then reconstruct the new measurements of Lion + Cage.
Howw does that sound ?
Igor.
Perfect. Very handy indeed. Laurent
I would project the whole stuff onto a tight (lionlet) frame, then use a (local trigonometric) folding operator to bend the frame into a cage. If the lion is indeed sparse, the frame needs to be very very tight. Not CS enough? To deterministic? Bad bad naughty me…
So, let’s build a lion out of sand:
http://flickr.com/photos/rosemovie/2710246346/
Laurent
Cool way indeed. The only problem I could see is that there is still a lot of research in the field of the best Lionlet frame, as in any other *let field, some trying for instance to make that more directional. But after all, a frame promoting only the vertical direction of the cage bars is sufficient of course ! Thank you Laurent.
Laurent
The game of lion-hunting using mathematical methods dates back at least to the 1930s. Ralph Boas, who was famous for his mathematics, learned the game when he was a grad student at Princeton in the late 1930s. He became a great player of the game, and published some fine articles about mathematical lion-hunting. Others followed Boas’s lead, even to the extent of copying Boas’s use of pseudonyms rather than his own name. A collection of Boas’s non-technical writings is titled “Lion Hunting and other Mathematical Pursuits”. It was published by the Mathematical Association of America (http://www.maa.org) in 1995.
Thank you very much for these historical explanations Edward.
I like to read the origins of such things
(as for Matching Pursuit in one of my previous posts)
Laurent
A nice post, thanks!
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