They didn’t set out to find the key to the popular number puzzles called Sudoku, but this was an extra bonus for researchers whose loftier purpose was to resolve a biological imaging problem concerning x-ray diffraction microscopy.
What they came up with was a difference-map algorithm that can resolve noisy and incomplete data from an x-ray diffraction microscope and that can reconstruct detailed images of minuscule and delicate biological specimens such as yeast cells. This allows precise imaging without staining the sample or endangering it by exposure to radiation.
The researchers, from Stony Brook University, State University of New York, from Cornell University and from Brookhaven and Lawrence Berkeley national laboratories, reported their results in the Oct.11, 2005, issue of PNAS. They figured out two constraints — establishing a bounded imaging area and matching wave amplitudes for the Fourier synthesis to those in the experiment — that enabled the computer to factor the wave phase data and do the reconstructions. They expect that their method will eventually enable imaging of specimens at 10-nm resolution in three dimensions.
Meanwhile, the algorithm that can handle these complex constraints finds the simpler constraints of Sudoku — using nine numbers nine times in a grid, but only once per row or column and having all nine numbers appear in blocks in the grid — to be a no-brainer. Or at least not the tease that it is for us puzzle addicts.