Jim in China

I have been working with two students - Zhiyou, with whom I visited Houhai on the night of the closing ceremony of the Olympics, and Hourui, our companion on our trip to Xi’an - at the nanocenter (which I now can say in Chinese: guojia nami kexue zhongxin.

We are trying to find the most economical way of representing surface plasmon resonance spectra with a simple polynomial expression. It is a tough problem in data analysis. We have had great difficulties with numerical instabilities, and we could not get consistent results. We spent two months trying to figure out the origin of the instability.

Recently, we discovered that part of the difficulty arose from limitations with Mathematica itself, so I wrote our own linear regression algorithm with arbitrary precision.

Now we have consistent results, and we have found a compact reliable method that allows us to identify the resonance position to a precision about 50 times narrower than the sampling interval. In addition, we have found that the most commonly used method has a 95 percent confidence interval that does NOT include the experimental data point closest to the resonance!