Jungfraujoch/docs/CPU_DATA_ANALYSIS.md

# CPU-side crystallographic data analysis (Jungfraujoch)

This document describes the crystallographic algorithms implemented in Jungfraujoch for **CPU**- and **GPU**-side real‑time and near‑real‑time data analysis.

**Scope.** The pipeline covered here comprises:

1. geometry mapping and corrections,
2. azimuthal integration (powder/radial profiles),
3. Bragg spot finding (strong pixels → connected components → spot descriptors),
4. indexing (still and rotation modes),
5. Bravais lattice / centering inference,
6. geometry and lattice refinement,
7. reflection prediction (still and rotation),
8. Bragg integration by either 2D box summation or profile fitting (Kabsch, reference-free),
9. scaling and merging,
10. merge-level error modelling, outlier rejection and the resolution cutoff,
11. space-group determination from the merged intensities (Laue group, screw axes, glide planes, centering, the centre of symmetry), the twinning check and the translational pseudo-symmetry check,
12. auxiliary statistics (Wilson plot, ⟨I/σ(I)⟩, CC1/2, CCref),
13. amplitude estimation (French–Wilson) and R-free test-set flagging,
14. optional model-based validation: rigid-body placement of a supplied model (molecular replacement where the rigid body does not place it, or for a predicted model), R-free against it, sigma_A-weighted 2mFo−DFc / mFo−DFc electron-density maps, and an anomalous difference map with the strongest anomalous sites named.


The reference is split into four parts, in pipeline order; the section numbers run continuously
across them and are the ones the rest of the documentation cites.

- [From images to spots (§0–§3)](CPU_DATA_ANALYSIS_IMAGE.md) — device-side decoding, geometry and
  reciprocal-space mapping, azimuthal integration, spot finding.
- [Indexing and geometry refinement (§4–§7)](CPU_DATA_ANALYSIS_INDEXING.md) — FFT and fast-feedback
  indexing, the lattice search, geometry refinement, post-refinement and powder calibration.
- [Prediction, integration, scaling and merging (§8–§12)](CPU_DATA_ANALYSIS_INTEGRATION.md) —
  reflection prediction, profile-fitted integration, scaling, merging, mosaicity and the auxiliary
  statistics.
- [Space group and validation (§13–§14)](CPU_DATA_ANALYSIS_DECISIONS.md) — the space-group search,
  twinning and translational pseudo-symmetry, the resolution cutoff, diffraction anisotropy,
  model-based validation and molecular replacement.

## References

The methods draw on, and in places reimplement, solutions from:

- W. Kabsch, “XDS”, *Acta Cryst.* **D66** (2010), 125–132 and related XDS papers (rotation geometry, partiality, scaling concepts).
- W. Kabsch, “Integration, scaling, space-group assignment and post-refinement”, *Acta Cryst.* **D66** (2010), 133–144 (mosaicity/partiality likelihood treatment; notation such as ζ and rotation factors).
- T. A. White et al., CrystFEL method papers (spot finding, three‑ring integration, serial/still diffraction processing concepts).
- J. Kieffer & J. P. Wright, "PyFAI: a Python library for high performance azimuthal integration on GPU", *Powder Diffraction* **28** (2013), S339-S350 (detector geometry definition, azimuthal integration)
- G. Bricogne, *Proceedings of the EEC Cooperative Workshop on Position-Sensitive Detector Software (Phase III)*, LURE, Paris (1986), p. 28 (Fourier-transform indexing, proposed as a three-dimensional transform; §5 uses its one-dimensional projection form).
- I. Steller, R. Bolotovsky & M. G. Rossmann, "An algorithm for automatic indexing of oscillation images using Fourier analysis", *J. Appl. Cryst.* **30** (1997), 1036-1040 (the projection/1D-FFT autoindexing algorithm of §5).
- H. Powell, "The Rossmann Fourier autoindexing algorithm in MOSFLM", *Acta Cryst.* **D55** (1999), 1690-1695 (the MOSFLM implementation of it, whose practice is followed)
- P. Gasparotto, L. Barba, H.-C. Stadler et al., "TORO Indexer: a PyTorch-based indexing algorithm for kilohertz serial crystallography", *J. Appl. Cryst.* **57** (2024), 931-944 (the algorithm of the `ffbidx` fast-feedback indexer, §4).
- I. Křivý & B. Gruber, "A unified algorithm for determining the reduced (Niggli) cell", *Acta Cryst.* **A32** (1976), 297-298, and International Tables for Crystallography Vol. A, Table 9.2.5.1 (the Niggli reduction and the lattice-character table of §5.3/§6).
- J. E. Padilla & T. O. Yeates, "A statistic for local intensity differences: robustness to anisotropy and pseudo-centering and utility for detecting twinning", *Acta Cryst.* **D59** (2003), 1124-1130 (the L test, §13.2).
- T. O. Yeates, "Detecting and overcoming crystal twinning", *Methods Enzymol.* **276** (1997), 344-358 (the twinned intensity model and the $H$ statistic behind the twin fraction of the twin hypothesis, §13.2, §14.9).
- A. J. C. Wilson, "The probability distribution of X-ray intensities", *Acta Cryst.* **2** (1949), 318-321, and E. R. Howells, D. C. Phillips & D. Rogers, "The probability distribution of X-ray intensities. II. Experimental investigation and the X-ray detection of centres of symmetry", *Acta Cryst.* **3** (1950), 210-214 (the acentric and centric intensity distributions behind the centre-of-symmetry statistics of §13.1 and the Wilson outlier test of §13.3).
- W. H. Baur & D. Kassner, "The perils of Cc: comparing the frequencies of falsely assigned space groups with their general population", *Acta Cryst.* **B48** (1992), 356-369 (writing the centrosymmetric group where the absences cannot decide the centre, §13.1).
- R. J. Read, P. D. Adams & A. J. McCoy, "Intensity statistics in the presence of translational noncrystallographic symmetry", *Acta Cryst.* **D69** (2013), 176-183 (the native-Patterson detection of translational pseudo-symmetry, and the intensity modulation it produces, which the axial-zone screw-absence test scores against).
- A. Barty, R. A. Kirian, F. R. N. C. Maia et al., "Cheetah: software for high-throughput reduction and analysis of serial femtosecond X-ray diffraction data", *J. Appl. Cryst.* **47** (2014), 1118-1131 (peakfinder8: the per-resolution-ring background statistics of §3.2).
- A. Hennequin, B. Couturier, V. V. Gligorov & L. Lacassagne, "SparseCCL: Connected Components Labeling and Analysis for sparse images", DASIP 2019, 65-70 (the connected-component labelling of §3.4, used via ACTS/traccc).
- S. French & K. Wilson, "On the treatment of negative intensity observations", *Acta Cryst.* **A34** (1978), 517-525 (Bayesian amplitude estimation from intensities), and CCP4's ctruncate (C. Ballard & N. Stein), whose anisotropic Wilson prior §10.8 follows, cited through M. D. Winn et al., "Overview of the CCP4 suite and current developments", *Acta Cryst.* **D67** (2011), 235-242.
- A. T. Brünger, "Free R value: a novel statistical quantity for assessing the accuracy of crystal structures", *Nature* **355** (1992), 472-475 (R-free cross-validation).
- P. H. C. Eilers, "A perfect smoother", *Anal. Chem.* **75** (2003), 3631-3636, after E. T. Whittaker, "On a new method of graduation", *Proc. Edinburgh Math. Soc.* **41** (1923), 63-75 (the penalised smoother of the fulls' per-frame scale, §10.6).
- H. F. Walker & P. Ni, "Anderson acceleration for fixed-point iterations", *SIAM J. Numer. Anal.* **49** (2011), 1715-1735, after D. G. Anderson, "Iterative procedures for nonlinear integral equations", *J. ACM* **12** (1965), 547-560 (the acceleration of the per-frame scaling loops, §10.6).
- R. A. Fisher, "Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population", *Biometrika* **10** (1915), 507-521 (the z-transformation on which the correction surfaces' held-out half-set CC1/2 is compared).
- M. Wojdyr, "GEMMI: A library for structural biology", *J. Open Source Softw.* **7** (2022), 4200 (model / structure-factor / map machinery used in §14).
- J. P. Wright, "Experiences with GPU decompression for bitshuffle + LZ4 data", HDF5 User Group meeting (2021), and [github.com/jonwright/bslz4decoders](https://github.com/jonwright/bslz4decoders) (device-side decoding of bitshuffle+LZ4 images, §0).
- A. Thorn & G. M. Sheldrick, "ANODE: anomalous and heavy-atom density calculation", *J. Appl. Cryst.* **44** (2011), 1285-1287 (anomalous difference density read at the model's sites).
- R. Kahn, R. Fourme, A. Gadet, J. Janin, C. Dumas & D. Andre, "Macromolecular crystallography with synchrotron radiation: photographic data collection and polarization correction", *J. Appl. Cryst.* **15** (1982), 330-337 (the azimuthal polarization factor of §2.2, applied to the azimuthal profile, the Bragg intensities and the ring background the beam-stop shadow test compares against).
- R. J. Read, "Improved Fourier coefficients for maps using phases from partial structures with errors", *Acta Cryst.* **A42** (1986), 140-149 (the sigma_A formalism and the m, D weighting of the map coefficients of §14.4).
- A. Fokine & A. Urzhumtsev, "Flat bulk-solvent model: obtaining optimal parameters", *Acta Cryst.* **D58** (2002), 1387-1392 (the flat bulk-solvent model, its optimal parameters and the range they are physically meaningful over, used when scaling a model to the data in §14).
- P. V. Afonine, R. W. Grosse-Kunstleve & P. D. Adams, "A robust bulk-solvent correction and anisotropic scaling procedure", *Acta Cryst.* **D61** (2005), 850-855 (the grid search over that range that fits k_sol and b_sol, with the overall scale and anisotropic B refitted at each grid point).
- K. Shoemake, "Uniform Random Rotations", in *Graphics Gems III*, ed. D. Kirk, Academic Press (1992), 124-132 (the uniform random rotations the model-fit null of §14.5 is built from).
- G. H. Golub & V. Pereyra, "The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate", *SIAM J. Numer. Anal.* **10** (1973), 413-432, and L. Kaufman, "A variable projection method for solving separable nonlinear least squares problems", *BIT* **15** (1975), 49-57 (the scale re-fit folded into the rigid-body Jacobian of §14.8).
- Z. Otwinowski & W. Minor, "Processing of X-ray diffraction data collected in oscillation mode", *Methods Enzymol.* **276** (1997), 307-326 (reweighted, de-biased profile-fit variances).
- G. Winter et al., "DIALS: implementation and evaluation of a new integration package", *Acta Cryst.* **D74** (2018), 85-97, and J. Beilsten-Edmands et al., *Acta Cryst.* **D76** (2020), 385-399 (CC1/2 resolution cutoff, merge outlier rejection, scaling error model).
- R. H. Blessing, "An empirical correction for absorption anisotropy", *Acta Cryst.* **A51** (1995), 33-38 (absorption as spherical harmonics of the beam directions).
- P. Evans, "Scaling and assessment of data quality", *Acta Cryst.* **D62** (2006), 72-82, and P. R. Evans, *Acta Cryst.* **D67** (2011), 282-292 (POINTLESS: operator-by-operator point-group scoring, and the axial-zone screw-absence test).
- A. G. W. Leslie & H. R. Powell, "Processing diffraction data with MOSFLM" (2007), NATO Science Series II **245**, 41-51 (post-refinement practice: what is refined per image and what over a wedge).
- D. W. Moreau, H. Atakisi & R. E. Thorne, "Ice in biomolecular cryocrystallography", *Acta Cryst.* **D77** (2021), 540-554 (measured hexagonal-ice ring positions, used by the ice-ring score, the ice flagging and the ice calibrant).
- K. Röttger, A. Endriss, J. Ihringer, S. Doyle & W. F. Kuhs, "Lattice constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K", *Acta Cryst.* **B50** (1994), 644-648 (the ice Ih cell the ring positions below 1.522 Å are calculated from).
- S. Sheriff & W. A. Hendrickson, "Description of overall anisotropy in diffraction from macromolecular crystals", *Acta Cryst.* **A43** (1987), 118-121 (the overall anisotropic B tensor and its symmetry constraints), and A. N. Popov & G. P. Bourenkov, "Choice of data-collection parameters based on statistic modelling", *Acta Cryst.* **D59** (2003), 1145-1153 (the sigma-aware estimation of the anisotropy of the observed intensity distribution, part of that paper's statistic modelling).
- I. J. Tickle, C. Flensburg, P. Keller, W. Paciorek, A. Sharff, C. Vonrhein & G. Bricogne, STARANISO (2016), Global Phasing Ltd, [staraniso.globalphasing.org](https://staraniso.globalphasing.org/cgi-bin/staraniso.cgi) (the inspiration for analysing and reporting diffraction anisotropy on every run, §13.5).
- C. Vonrhein, C. Flensburg, P. Keller et al., "Data processing and analysis with the autoPROC toolbox", *Acta Cryst.* **D67** (2011), 293-302 (the inspiration for not trusting header geometry and for finding the beam centre from the images, §1.4).
- P. R. Evans & G. N. Murshudov, "How good are my data and what is the resolution?", *Acta Cryst.* **D69** (2013), 1204-1214 (AIMLESS: the anisotropic deltaB as the range of the principal components, and diffraction limits from a cone about each principal direction).
- G. Assmann, W. Brehm & K. Diederichs, "Identification of rogue datasets in serial crystallography", *J. Appl. Cryst.* **49** (2016), 1021-1028, and G. M. Assmann, M. Wang & K. Diederichs, *Acta Cryst.* **D76** (2020), 636-652 (XDSCC12: sigma-tau CC1/2, delta-CC1/2, the Fisher transformation and the rejection discipline the frame disposition follows).
- K. Diederichs & P. A. Karplus, *Nat. Struct. Biol.* **4** (1997), 269-275, and P. A. Karplus & K. Diederichs, *Science* **336** (2012), 1030-1033 (R_meas / R_pim, CC1/2 and CC\*).
- M. S. Weiss, "Global indicators of X-ray data quality", *J. Appl. Cryst.* **34** (2001), 130-135 (R_pim).
- IUCr Commission on Crystallographic Nomenclature, "Statistical descriptors in crystallography", *Acta Cryst.* **A45** (1989), 63-75, and *Acta Cryst.* **A51** (1995), 565-569 (uncertainty conventions).
- J. Navaza, "AMoRe: an automated package for molecular replacement", *Acta Cryst.* **A50** (1994), 157-163 (the rotation function on an interpolated molecular transform, §14.10).
- R. A. Crowther & D. M. Blow, "A method of positioning a known molecule in an unknown crystal structure", *Acta Cryst.* **23** (1967), 544-548 (the full-symmetry translation function, §14.10).
- B. W. Matthews, "Solvent content of protein crystals", *J. Mol. Biol.* **33** (1968), 491-497, and K. A. Kantardjieff & B. Rupp, "Matthews coefficient probabilities", *Protein Sci.* **12** (2003), 1865-1871 (how many copies the cell holds, §14.10).
- R. J. Read, "Pushing the boundaries of molecular replacement with maximum likelihood", *Acta Cryst.* **D57** (2001), 1373-1382; A. J. McCoy, R. W. Grosse-Kunstleve, L. C. Storoni & R. J. Read, "Likelihood-enhanced fast translation functions", *Acta Cryst.* **D61** (2005), 458-464; A. J. McCoy et al., "Phaser crystallographic software", *J. Appl. Cryst.* **40** (2007), 658-674; A. J. McCoy et al., *Proc. Natl. Acad. Sci. USA* **114** (2017), 3637-3641 (the likelihood target, the solution criterion and the expected gain of molecular replacement, §14.10).
- R. D. Oeffner, T. Croll, C. Millán et al., "Putting AlphaFold models to work with phenix.process_predicted_model and ISOLDE", *Acta Cryst.* **D78** (2022), 1303-1314, and J. Jumper et al., "Highly accurate protein structure prediction with AlphaFold", *Nature* **596** (2021), 583-589 (preparing a predicted model for molecular replacement, §14.10).

(list is not exhaustive; the full citations, with DOIs, are in [ACKNOWLEDGEMENT.md](ACKNOWLEDGEMENT.md))