The maximum entropy method (MEM) is used to analyze time-resolved pulse-fluorescence spectrometry. The central problem in such analyses is the recovery of the distribution of exponentials describing the decay of the fluorescence (i.e., inverting the Laplace transform) which is, in turn, convolved by the shape of the excitation flash. MEM is shown to give high quality results from both computer-generated "noisy" data and experimental data from chemical and biological molecules.The use of the Shannon-Jaynes entropy function is justified and both the theoretical and practical advantages of MEM are presented. The MEM results are easy to interpret and can help to overcome some experimental limitations. In particular MEM could be a powerful tool to analyze the heterogeneity of fluorescent emission of biological macromolecules which can be correlated with their conformational dynamics in solution.

A maximum entropy method (MEM) map of electron density is obtained by maximizing S=-~p log p subject to whatever data are available. MEM is derived as the only reconstruction technique that is consistent with simple and general requirements. The method is very widely applicable, but, in this paper, attention is focused on the problem of producing electron density maps in crystallography. The entropy formula can also be derived by analogy with a thermodynamic system of quanta, but it is shown that this model can be misleading, and can break down in practice. MEM applied to a different problem related to quantum fluctuations in the thermodynamic model is shown to lead to formulae equivalent to the maximum determinant method. It is argued that direct MEM will produce superior maps. AbstractTwo independent determinations of the same structure may be compared by means of statistical techniques such as normal probability plots and X 2 hypothesis tests. Computer simulations show that errors may arise in the application of these techniques 0108-7673/85/020122-07501.50 if rounded estimates of structural parameters and their e.s.d.s are used in the calculations. Round-off errors are particularly serious in goodness-of-fit hypothesis tests, since they increase the probability of making type I errors, i.e. falsely rejecting the null hypothesis.

The application of the maximum entropy method to nondestructive depth profiling by angle-dependent XPS is described. The algorithm gives the set of depth profiles that has maximum SkillingJaynes entropy, subject to the condition that the calculated data agree with the measured data within the experimental precision. The method does not require an inverse transform, is robust to experimental noise and is not restricted to small numbers of components. The programme can determine which of a set of prior estimates for the depth profiles is most probable; however, the reconstruction near the surface is virtually independent of this choice. Further, the method also estimates the accuracy of the reconstruction from a single data set. It is illustrated using model data and by a re-analysis of angleresolved XPS data sets available in the literature.

Upon the application of cumulant analysis to the interpretation of quasielastic light scattering spectra J. Chem. Phys. 89, 91 (1988); 10.1063/1.455465 Bispectral analysis as a probe of quasielastic light scattering intensity fluctuationsThe maximum entropy method (MEM) is used to analyze quasielastic light scattering correlation functions. The central problem, in such data analysis, is the recovery of the distribution of exponentials describing the decay of the correlation function (i.e., inverting the Laplace transform). MEM is shown to give a high-quality reconstruction ofthese distributions. The success of the method is illustrated with results from computer-generated "noisy" data and with experimental data from colloidal dispersions. Both the theoretical properties, and practical advantages of MEM are presented and compared with current data analysis techniques.

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