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This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various structural features, including the positions of the atoms, the shapes and amplitudes of modulation functions, and possible advanced properties of the modulations, like modulation of the anisotropic displacement parameters (ADPs) and the presence anharmonic displacements. The maximum entropy method (MEM) is introduced as a model-independent method that provides a more accurate picture of the electron density than is provided by Fourier maps. The MEM can be used to determine the precise shapes of modulation functions and to study the electron density in the chemical bond.

In principle it is possible to reconstruct the reflectance function of a surface from V(z) data. This requires either that V(z) should be measured as a complex‐valued function, or that phase reconstruction techniques should be used. In practice the highest accuracy is obtained by measuring the period of oscillations in V(z), and using ray analysis. The highest accuracy is obtained from a cylindrical line‐focus‐beam lens, which also gives directionality in anisotropic surfaces. Accuracy better than one part in 10⁴ can be obtained. Stress fields can be imaged and measured. Time‐resolved techniques, enhanced if necessary by a maximum entropy method, give quantitative measurements by separating the echoes from the top and bottom of thin layers.

This chapter highlights some recent and forthcoming developments that impact on the practice of neutron powder diffraction. New and more powerful neutron sources are now in service or under construction. At the same time, there has been continuing development of critical components, such as neutron guides (supermirrors), compact collimators, focussing monochromators, and fast detection systems. These developments have been incorporated into new neutron powder diffractometers, for high resolution, high intensity, and residual stress applications. Advances in data analysis discussed include an increased focus on the use of group theory, the analysis of the total scattering, e.g., via pair distribution functions, mapping by the maximum entropy method, and rapid handling of extensive data sets. Frontier applications range from fast reaction kinetics (combustion synthesis) to the structure refinement of biological molecules. It is suggested that application of neutron powder diffraction for simultaneous investigation of structure and microstructure will assume increasing importance.

This chapter develops a statistical model for assessing financial system resilience that includes fire sale effects, network effects, and the feedback effects to/from the macroeconomy. An important innovation is that the model can be calibrated with partially available public data on banking sector exposures. The model presents stylized results largely based on data from the Bank for International Settlements in a set-up that is genuinely international—the financial network comprises domestic banks, foreign banks, and domestic firms. The aggregate system loss distributions that emerge are sensible, despite the crude calibration of the feedback effects from curtailed lending in the macroeconomy. The mode, thus, represents a first step in showing how an integrated model of systemic risk that takes complexity and realistic behavioural responses seriously can begin to be developed.