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Considerations underlying the design of the dictionary
Fitzgerald, P. M. D., Westbrook, J. D., Bourne, P. E., McMahon, B., Watenpaugh, K. D. and Berman, H. M.  International Tables for Crystallography (2006). Vol. G, Section 3.6.2, pp. 144-145 [ doi:10.1107/97809553602060000738 ]
Considerations underlying the design of the dictionary 3.6.2. Considerations underlying the design of the dictionary From the outset, mmCIF was envisaged as a providing a more detailed description of macromolecular structures than the existing Protein Data Bank (PDB) format (Chapter 1.1 ). A number of considerations guided the development of version ...

Introduction
Fitzgerald, P. M. D., Westbrook, J. D., Bourne, P. E., McMahon, B., Watenpaugh, K. D. and Berman, H. M.  International Tables for Crystallography (2006). Vol. G, Section 3.6.1, p. 144 [ doi:10.1107/97809553602060000738 ]
... also summarized. References Bourne, P., Berman, H. M., McMahon, B., Watenpaugh, K. D., Westbrook, J. D. & Fitzgerald, P. M. D. (1997). ...

Macromolecular dictionary (mmCIF)
Fitzgerald, P. M. D., Westbrook, J. D., Bourne, P. E., McMahon, B., Watenpaugh, K. D. and Berman, H. M.  International Tables for Crystallography (2006). Vol. G, ch. 4.5, pp. 295-443 [ doi:10.1107/97809553602060000745 ]
... cell_measurement_refln _cell_measurement_refln.index_h _cell_measurement_refln.index_k _cell_measurement_refln.index_l _cell_measurement_refln.theta chem_comp _chem ... orient_refln.diffrn_id _diffrn_orient_refln.index_h _diffrn_orient_refln.index_k _diffrn_orient_refln.index_l diffrn_radiation _diffrn_radiation.collimation _diffrn_radiation.diffrn ... diffrn_refln.elapsed_time _diffrn_refln.id _diffrn_refln.index_h _diffrn_refln.index_k _diffrn_refln.index_l _diffrn_refln.intensity_net _diffrn_refln.intensity_sigma _ ...

Introduction to refinement
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, ch. 18.1, pp. 459-465 [ doi:10.1107/97809553602060000855 ]
... the next electron-density map, but this was not done. Watenpaugh et al. (1972) first showed in 1971 that [Delta]F ... from initial MIR or SIR (single isomorphous replacement) experimental phases. Watenpaugh et al. (1973) also applied least-squares techniques to the ... the structures are or are not determined. References Adams, P. D., Pannu, N. S., Read, R. J. & Brunger, A. T. ( ...

R and Rfree
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.9.3, p. 464 [ doi:10.1107/97809553602060000855 ]
R and Rfree 18.1.9.3. R and Rfree Cross validation is a powerful tool for avoiding over-interpretation of the data by a too elaborate model. The introduction of cross validation to crystallography (Brünger, 1992) has been responsible for significant improvement in the quality of structure determinations. A subset of the ...
     [more results from section 18.1.9 in volume F]

Singularity in refinement
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.8.4, p. 463 [ doi:10.1107/97809553602060000855 ]
Singularity in refinement 18.1.8.4. Singularity in refinement Unless there are more linearly independent observations than there are parameters to fit them, the system of normal equations has no solution. The inverse of the matrix does not exist. Second-order methods fail in these circumstances by doing the matrix equivalent of dividing ...
     [more results from section 18.1.8 in volume F]

Models
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.7, pp. 461-462 [ doi:10.1107/97809553602060000855 ]
... 350. Murshudov, G. N., Vagin, A. A., Lebedev, A., Wilson, K. S. & Dodson, E. J. (1999). Efficient anisotropic refinement of ... structure refinement. Proteins Struct. Funct. Genet. 19, 277-290. Tronrud, D. E. (1996). Knowledge-based B-factor restraints for the ... refinement of proteins. J. Appl. Cryst. 29, 100-104. Tronrud, D. E. (1997). The TNT refinement package. Methods Enzymol. ...

Data
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.6, p. 460 [ doi:10.1107/97809553602060000855 ]
Data 18.1.6. Data Resolution, accuracy, completeness and weighting of data all have an impact on the refinement process. Small-molecule crystals usually, but not always, diffract to well beyond atomic resolution. Macromolecular crystals do not generally diffract to atomic resolution. Macromolecular structures are by definition large, which in turn means that ...

Optimization
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.5, p. 460 [ doi:10.1107/97809553602060000855 ]
Optimization 18.1.5. Optimization Once the choice of criteria for agreement has been made, the next step is to adjust the parameters of the model to minimize the disagreement (or maximize the agreement) between the model and the data. The literature on optimization in numerical analysis and operations research, discussed in IT ...

Least squares and maximum likelihood
Ten Eyck, L. F. and Watenpaugh, K. D.  International Tables for Crystallography (2012). Vol. F, Section 18.1.4, p. 460 [ doi:10.1107/97809553602060000855 ]
Least squares and maximum likelihood 18.1.4. Least squares and maximum likelihood `Improving the agreement' between the observed and calculated data can only be done if one first decides the criteria to be used to measure the agreement. The most commonly used measure is the norm of the residuals, which is simply ...

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