QMC wiki

Check out the QMC wiki at http://www.qmcwiki.org

It looks like a promising resource for the QMC research community.

Optimal histogram bin width

Kevin Knuth wrote a paper about finding the optimal number of bins to represent data in a histogram (Optimal Data-Based Binning for Histograms). He starts from a piecewise constant density model and finds the (Bayesian) posterior probability from this model (equation 36, which is actually the log of the posterior). The posterior function is then maximized to find the number of bins that best models the data.

The article also investigates the number of data points for a reliable estimation of the density. The recommendation is 100-150 points, if the distribution is Gaussian.

It would be interesting to apply this method to radial distribution functions. However the assumption of a constant volume for each bin is not met in this case. There are several ways this could be adjusted, but I'm not sure they are valid (scale each bin count by the volume, or use non-uniform bin spacing to maintain constant volume)

Alternately, the discussion references other algorithms for dealing with variable bin-width models (which may be better for resolving multiple peaks anyway).

QMC derivation notes

I posted a document I wrote in grad school, Notes on the wavefunction and local energy. It contains derivations of various QMC formulas, particularly the first and second derivatives for several forms of wavefunctions.

I'm posting this for two reasons. The first is in case anyone finds the formulas useful when working on a QMC code.

The second is related to the process of scientific programming. When writing a QMC code, I found it useful to record the formulas and derivations in a neatly typset form. Then the next step involved turning the equations into computer code. (Then, of course, testing and debugging).

This workflow is what I would like to capture with the Progamming in Mathematical Notation work. The document with derivations could be written in content MathML (or something more amenable to human manipulation). Ideally the computer could then assist with verifying the derivations for correctness, and with converting the equations into computer code.

And as long as I'm dreaming, I'd really like a wiki-like interface for creating and editing such a document (making a set of hyperlinked pages rather than a single linear document)

Interesting article studying writing journal articles

Last fall I looked at methods for improving the efficiency of MC simulations, and was pointed to the article, Efficient Monte Carlo methods for the computer simulation of biological molecules by Djamal Bouzida, Shankar Kumar, and Robert Swendsen.

A search of the author's names on Yahoo turned up a fascinating article by Ann Beakeslee, who studied the process of writing this paper. The article examines the interaction of the graduate student (Bouzida) and the advisor (Swendsen), covers the process of learning to write scientific papers, and looks at difficulties Bouzida faced as a novice.

Search for chemicals

Check out chmoogle, the search engine for chemicals. Many of the results are for suppliers (not so useful for theoreticians), but some of the results contain more information about the chemical.

The "details" link by the chemical structure picture also has alternate names, along with links to search Google or Yahoo.

[APS] First Principles Molecular Dynamics on Blue Gene

Francois Gygi gave a talk about scaling a first principles molecular dynamics code to 65,536 processors on the Blue Gene/L at LLNL.
The core numerical algorithms that need to scale are the FFT and dense linear algebra. The FFT is limited in scalability to 512 processors per k-point. Fortunately, there are many k-points and they can be computed independently.

Modifying the assignment of tasks to processors increased the performance by 64%! FLOPS are free, it's the communication patterns that are determine performance.

One research problem is improving the scalability of computations for small systems (ie, 32 water molecules), so they can be simulated for longer times.

[APS] Solar Power

David Carlson (from BP Solar) gave a talk titled, The Status and Outlook for the Photovoltaics Industry. His presentation slides are also available online.

Some random facts I found interesting

• The photovoltaic industry has been growing at 35% per year.


• This year, the PV industry will use as much or more silicon than the semiconductor industry. This may cause problems with the growth curve, as suppliers ramp up to supply the PV industry.


• The current cost per kWh is $0.18. Less than half of the cost is due to the PV module. (Slide 30)


• Given the cost of PV electricity, the cost of conventional electricity, and the availability of sun, Spain is almost to the point of cost-competetive PV electricity. (Slide 31)