Structure Determination from X-ray Scattering: Parameter extraction from cosmology for nanobiology

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Conventional medical examinations use the absorption of X-rays to yield information about the structure of biological tissues. The measurement of X-rays scattered in this process can however yield a richer wealth of structural information. Characterising molecular structures on very small scales - fractions of a micrometre - are now possible, and this can now be done repeatedly on short timescales, as short as micro- or milliseconds. This sort of experiment presents a number of challenges in analysis. One is how to characterise the structures in the first place. In typical cases the characterisation will be complex, with a fairly large numbers of components to be determined from the X-ray data. This can be very demanding computationally, and real-time processing is not generally feasible. The results of the experiment are then only determined after it has finished. A reasonable goal would be to have a fast enough analysis method that real-time processing is possible, opening up the possibility of taking further data immediately. One can certainly envisage many situations where manipulation of a sample or a change in conditions could be a great advantage. A second challenge is that the data collected may be rather poor quality in the signal may be rather small in comparison with background 'noise'; indeed in some circumstances one may wish to reduce the exposure to X-rays to avoid damage, in which case the data will become more noisy. Picking out faint signals in these circumstances can be difficult. It is essential to know how small a signal can be reliably extracted from the data, as this might allow smaller X-ray exposure which for biological samples may be critical to avoid damage. Finally, the quantity of data to be analysed can lead to a bottleneck. Conceptually similar problems are encountered in Astronomy, and are generally tackled via methods which are firmly rooted in Bayesian probability theory. In cosmology in particular, researchers strive to extract as much information as possible from their data, which in many cases are substantial in size, very noisy, and may depend on a relatively large number of model parameters. Several techniques used in this field may be applied to the materials characterisation problem. These include very rapid methods to find: the best-fitting solution; how uncertain the solution is; whether the solution is unique or not. In addition to commonly-applied tools, the PI holds a patented algorithm called MOPED, which can do this sort of task extremely rapidly indeed. For some problems, acceleration by several orders of magnitude has been achieved. If MOPED is applicable to these problems, then real-time analysis could be within our reach.