tag:blogger.com,1999:blog-2846514233477399562.post4941757622156375988..comments2023-01-20T08:52:20.691+01:00Comments on RÉSONAANCES: Hidden Valley Revealed?Jesterhttp://www.blogger.com/profile/08947218566941608850noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2846514233477399562.post-84637223111683930202008-11-12T15:58:00.000+01:002008-11-12T15:58:00.000+01:00Thomas, true. And taking into account the fact tha...Thomas, true. And taking into account the fact that each new step in this walk is exponentially more expensive makes one feel rather depressive.<BR/><BR/>CheersAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2846514233477399562.post-86709994544255729652008-11-12T15:45:00.000+01:002008-11-12T15:45:00.000+01:00Random walk unfortunately does not reach all locat...Random walk unfortunately does not reach all locations in dimension >2... <BR/><BR/>Of course there are much more efficient ways to scan over parameter space of any given model, but if model-building is a random walk in an infinite space of new concepts or local minima, we are unlikely to predict the correct result - even if LHC is infinitely delayed.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2846514233477399562.post-66020556962119956912008-11-12T11:32:00.000+01:002008-11-12T11:32:00.000+01:00Arrh, x**2 \sim t, expectation value of x is propo...Arrh, <BR/><BR/>x**2 \sim t, expectation value of x is proportional to t.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2846514233477399562.post-47259151876339205902008-11-12T11:31:00.000+01:002008-11-12T11:31:00.000+01:00Sorry, by x I meant of course x**2 :-)Lubos, exact...Sorry, by x I meant of course x**2 :-)<BR/><BR/>Lubos, exactly, diffusive behavior of x comes from the Langevin eq., and the white noise strength in the latter is temperature. I think if you cool down too much, then quantum effects may become important - and allow something like tunneling. The tunneling time is exponentially long however, so it's probably always good to get some heat.<BR/><BR/><BR/>CheersAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2846514233477399562.post-89711852844455213462008-11-12T10:47:00.000+01:002008-11-12T10:47:00.000+01:00Dear Dmitry,there's a semicanonical compromise of ...Dear Dmitry,<BR/><BR/>there's a semicanonical compromise of these two approaches to look for the "best".<BR/><BR/>One tries to go linearly in the direction of the gradient, towards the local optimum, but adds a noise that allows one to jump from a local minimum and find a better valley elsewhere, in the case that the local minimum is not global.<BR/><BR/>The ratio of these two strategies is dictated by the temperature: the hotter the system is, the higher proportion of the Brownian motion you use. Of course, the more you're certain that you're in the ballpark of the global optimum, the cooler system you should use.<BR/><BR/>Best<BR/>LubosLuboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-2846514233477399562.post-17440812878901949162008-11-11T11:50:00.000+01:002008-11-11T11:50:00.000+01:00Hi Jester>It may well be that shooting at >r...Hi Jester<BR/><BR/>>It may well be that shooting at >random will prove more successful >than following our theoretical >prejudices.<BR/><BR/>Let x measure the amount of progress in science, by definition.<BR/>Probably, random shooting only leads to diffusive development of progress with x \sim \sqrt{t} behavior, while following theoretical prejudices will produce ballistic behavior x \sim t if prejudices are correct :-)<BR/><BR/>CheersAnonymousnoreply@blogger.com