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Ab initio phasing of low-resolution Fourier syntheses
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, ch. 16.3, pp. 437-442 [ doi:10.1107/97809553602060000852 ]
... where experimental X-ray diffraction intensities are only available to a low-resolution limit, or when the standard phasing methods to ... diffraction experiments. The Monte Carlo phasing procedure includes generation of a large `population' of trial solutions, enrichment of this population by ... one to get information on the packing of particles in a crystal and on the shape (envelope) of the molecules, ...

Cluster analysis
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.5.5, p. 441 [ doi:10.1107/97809553602060000852 ]
... 1990, 1995; Buehler et al., 2009). Cluster analysis is a branch of applied mathematics aimed at classifying a set of points in a multidimensional space into several compact groups called clusters (or ...
     [more results from section 16.3.5 in volume F]

Common features of selection criteria
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.4.8, p. 439 [ doi:10.1107/97809553602060000852 ]
... Lunina, Petrova et al., 2000): (i) The best value of a target may correspond to quite a poor phase set. (ii) The target value for a good phase set may be significantly worse than the ...
     [more results from section 16.3.4 in volume F]

Low-resolution phasing
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.3, pp. 437-438 [ doi:10.1107/97809553602060000852 ]
... the true phase set. Such features can be formulated as a selection criterion (`score function', `figure of merit' etc.) that may have a qualitative or a quantitative form (Gilmore, 2000; Lunin, Lunina, Petrova et al., ...

General features of low-resolution images
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.2, p. 437 [ doi:10.1107/97809553602060000852 ]
... low-resolution images Low-resolution ab initio phasing is usually a laborious procedure. Some features of low-resolution Fourier syntheses increase the difficulties, as follows: (i) There is a common belief that low-resolution Fourier syntheses represent molecular envelopes ... the relatively small number of reflections used in the calculation, a small change in phase can significantly modify the image ...

Introduction
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.1, p. 437 [ doi:10.1107/97809553602060000852 ]
... While giving similar structural information, low-resolution crystallographic images are a more natural starting point on the way towards atomic models. ... of the crystals or the failure of standard phasing methods. A number of techniques have been suggested to estimate the phases ... structure factors using various complementary sources of information, specific to a given crystal: (i) Phasing by isomorphous replacement or anomalous ...

Conclusions and examples
Lunin, V.Y., Urzhumtsev, A.G. and Podjarny, A.  International Tables for Crystallography (2012). Vol. F, Section 16.3.6, p. 441 [ doi:10.1107/97809553602060000852 ]
... information can be combined with other imaging techniques to obtain a reliable description of the structure. The low-resolution maps for ... yet completely automated and require significant human intervention. References Fokine, A., Morales, R., Contreras-Martel, C., Carpentier, P., Renault, F., Rochu ... Chabriere, E. (2003). Direct phasing at low resolution of a protein copurified with human paraoxonase (PON1). Acta Cryst. ...

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