Posted by cubbybear on May 7, 2004, at 7:07:56
In reply to Re: monte carlo applied to business solutions, posted by slinky on May 7, 2004, at 4:19:47
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> > start with metropolis' article in j. chem. phys., circa 1957 or 1958 (metroplolis bias-sampling ring a bell?)...start an ensemble of random ``walkers'' with a potential function that need not be - and is not - differentiated. you randomly move each walker - here, let's assume a Cartesian space, not Minkowski 4-space, i.e,, time-independent - and you have previously computed the kinetic and potential energies for you ensemble of walkers. after the move, you evaluate the ``energy'' of each walker: if it hgher than the (new) ensemble average, discard the walker. if E_{walker} <= E_{ensemble}, keep walker but weight the contribution with a boltzmann factor, i.e., exp(-beta*E), where beta == (1/(k_b}T) (yes, i write everything in plain TeX, not LaTeX), and note that temperature here does not necessarily jibe with the traditional temperature definition (instead, market cap, P:E, trading volume, etc.). then branch for generation of new walkers to keep your ensemble constant in N, which entails weighting the already weighted walkers that survived. very quick, very precise, very easy to code, and you can actually get the *global* minimum on the PES. i use a variant - quantum diffusion monte carlo - where a change of variables from t to i(tau) (i == sqrt(-1)) in the time-dependent schrodinger equation leads to fick's second law of diffusion. problems: expectation values are very, very hard to extract (see work by ann mccoy at ohio) but you can get the quantities you need - in many cases - by following this recipe (QDMC). also, you can do quantum simmulated annealing - vary hbar from 1 to 6, usually - and for lennard-jones clusters, global minima are reached in many cases. if you define your kinetic and potential terms as functions of business solutions, the results are quite attractive....all the best, chemist
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> Am i in the right dimension? :-)You're OK. You're sane. What appears above may have come from the Twilight Zone.
poster:cubbybear
thread:344054
URL: http://www.dr-bob.org/babble/20040505/msgs/344309.html