tag:blogger.com,1999:blog-11295132.post112869679547257604..comments2015-05-20T17:18:26.607-07:00Comments on A Neighborhood of Infinity: Quantum Mechanics and the Fourier-Legendre Transform over a SemiringDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger13125tag:blogger.com,1999:blog-11295132.post-85090835577355647502009-05-20T08:49:52.375-07:002009-05-20T08:49:52.375-07:00Went to a great lecture about Tropical Math by Ber...Went to a great lecture about Tropical Math by Berndt Sturmfels, visiting Caltech from Berkeley (he was). I intend to do Tropical Math for my Latino Algebra 1 students this afternoon. Get them to think outside the box...Jonathan Vos Posthttp://magicdragon.com/math.htmlnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-89169375444387613112007-08-26T07:51:00.000-07:002007-08-26T07:51:00.000-07:00I recently tried to find the Sean Walston paper ag...I recently tried to find the Sean Walston paper again but was unable to track it down. Sorry, I don't know the title.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-21352023581604428132007-08-26T07:41:00.000-07:002007-08-26T07:41:00.000-07:00Also, the link to Sean Walston's paper is broken -...Also, the link to Sean Walston's paper is broken - do you remember the title? ThanksFrederik Eatonnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-74440885592698331392007-08-16T05:39:00.000-07:002007-08-16T05:39:00.000-07:00Are "integral" and "minimisation" swapped in the t...Are "integral" and "minimisation" swapped in the table?<BR/><BR/>Also, I think it is strange to say that integration is the "quantum" version of minimization, aren't we forgetting about classical statistical mechanics? See the previously linked section by John Baez:<BR/><BR/>http://math.ucr.edu/home/baez/qg-spring2004/discussion.html#idempotent<BR/><BR/>Does the Laplace transform deserve a mention here?Frederik Eatonnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1137599587863808442006-01-18T07:53:00.000-08:002006-01-18T07:53:00.000-08:00what you're referring to is the area of "tropical ...what you're referring to is the area of "tropical mathematics" or "idempotent mathematics". David Corfield and John Baez have a <A HREF="http://math.ucr.edu/home/baez/qg-spring2004/discussion.html#idempotent" REL="nofollow">nice discussion</A> of this.Sureshhttp://www.blogger.com/profile/16443460499476270978noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1129147952082463642005-10-12T13:12:00.000-07:002005-10-12T13:12:00.000-07:00This comment has been removed by a blog administrator.The Answer Manhttp://www.blogger.com/profile/00491221838510941304noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128972075769771662005-10-10T12:21:00.000-07:002005-10-10T12:21:00.000-07:00Just minor remark: the Fenchel transform is in fac...Just minor remark: the Fenchel transform is in fact a better name for what you quote. Legendre was working in the golden age when all functions were (infinitely) differentiable, and his original definition involved inverting the gradient of a (smooth) convex function rather than taking maxima. The modern definition allows for nonsmooth functions and was first given in the 1D by the French mathematician Mandelbrojt (an uncle of Benoit Mandelbrot) in the 1930s. It was extended to multivariate case by Fenchel in the 1940s.ansobolhttp://www.blogger.com/profile/09511696027099191902noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128890574293604922005-10-09T13:42:00.000-07:002005-10-09T13:42:00.000-07:00There is almost certainly some application of some...There is almost certainly some application of some of this stuff to feature recognition. Both convolution (eg. blurring and sharpening filters) and inf-convolution (eg. in so called 'morphological' filters) play an important role in feature recognition algorithms.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128856286257330542005-10-09T04:11:00.000-07:002005-10-09T04:11:00.000-07:00I'm wondering if there is a connection to image re...I'm wondering if there is a connection to image recognition here. Image can be recognized by it's fourier transform or by feature points. I think feature points have some realtion to Legandre transforms3dhttp://www.blogger.com/profile/12135124077632928189noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128822638377073882005-10-08T18:50:00.000-07:002005-10-08T18:50:00.000-07:00I am in fact interested in probability, but I've b...I am in fact interested in probability, but I've been coming more at the foundations, from the philosophical angle, and still need some more work on measure theory and mathematical probability before I'll understand what's going on in those papers, but thanks! (Set theory is probably the area of mathematics proper that I'm most competent in.)Kennyhttp://www.blogger.com/profile/12226268498253877151noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128718990105572712005-10-07T14:03:00.000-07:002005-10-07T14:03:00.000-07:00Or even this paper which explicitly talks about a ...Or even <A HREF="http://citeseer.csail.mit.edu/akian97duality.html" REL="nofollow">this</A> paper which explicitly talks about a 'duality'.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128718247109515892005-10-07T13:50:00.000-07:002005-10-07T13:50:00.000-07:00Oops! Mistake corrected. Thanks.I think I remember...Oops! Mistake corrected. Thanks.<BR/><BR/>I think I remember you're a probability guy. <A HREF="http://citeseer.csail.mit.edu/265498.html" REL="nofollow">This</A> paper approaches the subject from the angle of probability theory, albeit in French. Confusingly they call the Legendre transform the Fenchel transform. You can extend the table to have the rows:<BR/><BR/>Quadratic form <--> Normal distribution<BR/>inf-convolution <--> Convolutionsigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1128717475826872902005-10-07T13:37:00.000-07:002005-10-07T13:37:00.000-07:00Fascinating stuff! But I think you have a few typ...Fascinating stuff! But I think you have a few typos. In the text you say that "the positive infinity acts as the identity for +", but I think you mean for min. You have this stated correctly in the table at the bottom, but it seems that the first three rows of the table have the left and right columns switched.<BR/><BR/>I don't know too much about the physics stuff you talk about here, but it's nice that the concepts from analysis can be generalized to apply to the other semiring!Kennyhttp://www.blogger.com/profile/12226268498253877151noreply@blogger.com