Nuit Blanche: Around the Blogs in 78 Summer Hours: Phase transitions, infinite CS and earliest version of phase transitions ?

Ever since the last around the blogs, we had quite a few interesting blog entries but first things first. Here are some feedbacks. Following up on the CoSeRa blog entry pointing to the presentations slides there, I felt there was a connection between those and the inifinite dimensional issues arising in a later blog entry and sent an email out to both Anders Hansen and Holger Rauhut. Holger responded with:

Dear Igor,

Thanks for your remark and for mentioning CoSeRa 2013 in your blog. There is another recent paper of Rachel Ward and myself which goes into a similar direction, see

http://arxiv.org/abs/1308.0759

Best wishes,

Holger

while Anders Hansen sent me the following:

Thanks so much for again writing about infinite-dimensional compressed sensing on your blog (you are doing a great job). This is an important topic that is getting more and more attention. Just to let you know, there will be a mini-symposium at the "8th International Conference on Curves and Surfaces (2014)" entitled "Sampling and compressive sensing over the continuum", that will focus specifically on these issues.

http://smai.emath.fr/curves2014/

Best wishes,

Anders

Yes, we all agree that in the context of dealing with field equations, the theory needs to provide as much input as possible to the hardware folks. If this issue of phase transition can be added to the current infinite dimensional CS or in the context of TV/weighted series, then we ought to witness a Donoho-Tao moment in the Radar community at the next CoSeRa meeting :-). As a reminder the Donoho-Tao moment was well put in this 2008 IPAM newsletter:

....It’s David Donoho [5] reportedly exclaiming a panel of NSF folks “You’ve got Terry Tao (a Fields medalist [6]) talking to geoscientists, what do you want?” ....

Fall 2008 UCLA Math Department Newsletter, Mark Green Ends His Remarkable Odyssey at IPAM

Also, following up on a comment I made in comment on a comment on "The Mathematical Shape of Things to Come", Emmanuel Candes reminded me that the phenomenon of phase transition was initially observed in the June 2004 Robust Uncertainty Principles:Exact Signal Reconstruction from Highly Incomplete Frequency Information specifically in Figures 2 and 3.

Which gets me to be thinking: Is this phenomenon of phase transition new provided that we already established there was a 200 year gap ? While anybody come up with signs of the phase transition in 1-D, is there an earlier version of a phase transition in 2D or 3D ?
Thanks Anders, Holger and Emmanuel for the insights and informations.
The blogs provided some very insightful subjects to read on. Here there are in no particular order. Let us note that one of them (Andrew) will be speaking at the upcoming Paris Machine Learning Meetup on Wednesday. For more, check and register here if you want to attend. In the meantime, enoy:
Dusty

Olimex