Jungfraujoch/docs/ACKNOWLEDGEMENT.md

# Acknowledgements

How to cite Jungfraujoch and Rugnux, and the papers that describe them, is on the
[Publications](PUBLICATIONS.md) page. In short:

- **Rugnux**: F. Leonarski and M. Wang, "Rugnux: from diffraction images to structure at synchrotrons
  and XFELs in one program" (2026), bioRxiv
  [doi:10.64898/2026.10.24.761522](https://doi.org/10.64898/2026.10.24.761522).
- **Jungfraujoch**: F. Leonarski, M. Brückner, C. Lopez-Cuenca, A. Mozzanica, H.-C. Stadler,
  Z. Matěj, A. Castellane, B. Mesnet, J. Wojdyla, B. Schmitt and M. Wang, "Jungfraujoch:
  hardware-accelerated data-acquisition system for kilohertz pixel-array X-ray detectors" (2023),
  J. Synchrotron Rad. 30, 227-234 [doi:10.1107/S1600577522010268](https://doi.org/10.1107/S1600577522010268);
  for real-time serial crystallography and live indexing feedback also J. Duan, H.-C. Stadler,
  J. Nan et al., "Jungfraujoch: 38 GB s⁻¹ real-time serial crystallography – data acquisition and
  live indexing feedback" (2026), J. Appl. Cryst. 59, 1668-1677
  [doi:10.1107/S1600576726008083](https://doi.org/10.1107/S1600576726008083).

## Funding and support

The project is supported by:
* Innosuisse via Innovation Project "NextGenDCU high data rate acquisition system for X-ray detectors in structural biology applications" (101.535.1 IP-ENG; Apr 2023 - Sep 2025).
* ETH Domain via Open Research Data Contribute project (Jan - Dec 2023).
* AMD University Program with donation of licenses of Ethernet IP cores and Vivado software.

## Automatic processing as an expert system

**Global Phasing Ltd** — much of what rugnux tries to do was inspired by the work of Gérard Bricogne
and his colleagues at [Global Phasing](https://www.globalphasing.com/): the Fourier-transform
indexing its de-novo indexers descend from, which Bricogne proposed in 1986 (see
[Indexing](#indexing) below), the view of data processing as an expert system, the distrust of
image-header metadata, and the attention paid to diffraction anisotropy, each described below.

**[autoPROC](https://www.globalphasing.com/autoproc/)** — rugnux's goal is a fully automatic
pipeline that takes the decisions an experienced crystallographer would take while processing a
dataset, and reports each decision together with the evidence it rests on, so that a bare
invocation gives the best answer available. autoPROC is the inspiration and the target for that
behaviour, and two of rugnux's working principles come from it. The first, and the one that has
guided rugnux most, we owe to Clemens Vonrhein: a processing pipeline should not take the
experimental metadata it is given - the beam centre, the detector geometry, the goniometer and its
rotation axis - on trust, but verify it against the images and, where it is wrong, correct it. We
are grateful to him for arguing this so clearly and for so long. The second follows from it: the
beam centre should be determined from the images themselves; rugnux does this in its own way,
described in §1.4 of the [data-analysis reference](CPU_DATA_ANALYSIS_IMAGE.md). The
reasons rugnux gives for a weak stretch of a sweep also use autoPROC's wording ("loss of centring
during crystal rotation"). C. Vonrhein, C. Flensburg, P. Keller, A. Sharff, O. Smart, W. Paciorek,
T. Womack and G. Bricogne, "Data processing and analysis with the autoPROC toolbox" (2011),
Acta Cryst. D67, 293-302
[doi:10.1107/S0907444911007773](https://doi.org/10.1107/S0907444911007773).

**[STARANISO](https://staraniso.globalphasing.org/)** — the understanding that diffraction
anisotropy matters, and that every run should analyse and report it, was inspired by STARANISO.
The estimators rugnux uses for it are those credited under
[Scaling, merging and data quality](#scaling-merging-and-data-quality) below. I. J. Tickle,
C. Flensburg, P. Keller, W. Paciorek, A. Sharff, C. Vonrhein and G. Bricogne (2016), STARANISO
([staraniso.globalphasing.org/cgi-bin/staraniso.cgi](https://staraniso.globalphasing.org/cgi-bin/staraniso.cgi)),
Cambridge, United Kingdom: Global Phasing Ltd.

## Crystallographic methods adopted from other packages

The analysis pipeline builds on methods first published, and in most cases first implemented, by
other crystallographic software. The code below is Jungfraujoch's own; the methods are theirs, and
are acknowledged here. Where a package's source was consulted this is said explicitly. Most of these
packages are neither linked nor vendored; the three that are - GEMMI, traccc and
fast-feedback-indexer - also carry a licence obligation, recorded in
[THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md).

### Spot finding

**[CrystFEL](https://www.desy.de/~twhite/crystfel/)** — spot finding, the three-ring integration
region, the serial/stills processing model, and the per-frame indexing acceptance test
(`indexing_peak_check()` in `peaks.c`). T. A. White, R. A. Kirian, A. V. Martin, A. Aquila, K. Nass,
A. Barty and H. N. Chapman, "CrystFEL: a software suite for snapshot serial crystallography" (2012),
J. Appl. Cryst. 45, 335-341 [doi:10.1107/S0021889812002312](https://doi.org/10.1107/S0021889812002312).
The self-calibrating spot finder's per-resolution-ring background statistics, with the Bragg peaks
excluded by iterated clipping, follow Cheetah's peakfinder8: A. Barty, R. A. Kirian,
F. R. N. C. Maia, M. Hantke, C. H. Yoon, T. A. White and H. N. Chapman, "Cheetah: software for
high-throughput reduction and analysis of serial femtosecond X-ray diffraction data" (2014),
J. Appl. Cryst. 47, 1118-1131
[doi:10.1107/S1600576714007626](https://doi.org/10.1107/S1600576714007626).

**Per-crystal post-refinement of serial stills** - refining, for each still, the partiality
parameters the spot positions cannot pin (a small reorientation, the crystal's own rocking width and the
radial scale of its reciprocal lattice, which a shot's photon energy or a crystal's cell moves) against
the merged intensities follows the post-refinement of PRIME and the mosaic-block model of Sauter et al.:
M. Uervirojnangkoorn, O. B. Zeldin, A. Y. Lyubimov, J. Hattne, A. S. Brewster, N. K. Sauter, A. T. Brunger
and W. I. Weis, "Enabling X-ray free electron laser crystallography for challenging biological systems
from a limited number of crystals" (2015), eLife 4, e05421; N. K. Sauter, J. Hattne, A. S. Brewster,
N. Echols, P. H. Zwart and P. D. Adams, "Improved crystal orientation and physical properties from
single-shot XFEL stills" (2014), Acta Cryst. D70, 3299-3309 (DOIs not verified here, so not given).

Spot extraction groups strong pixels into spots with the sparse connected-component labelling of the
ACTS traccc project: P. Gessinger, H. M. Gray, A. Krasznahorkay, C. Leggett, J. Niermann,
A. Salzburger, S. N. Swatman and B. Yeo, "traccc: GPU track reconstruction library for HEP
experiments" (2025), [arXiv:2505.22822](https://arxiv.org/abs/2505.22822);
[traccc](https://github.com/acts-project/traccc). The CPU spot extractor adapts its SparseCCL source,
and the CUDA spot extractor follows the design of its GPU counterpart - a backward-neighbour graph
over a sorted hit list, resolved by a parallel union-find. traccc is MPL-2.0; see
[THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md). The SparseCCL algorithm itself is A. Hennequin,
B. Couturier, V. V. Gligorov and L. Lacassagne, "SparseCCL: Connected Components Labeling and
Analysis for sparse images" (2019), DASIP 2019, 65-70
[doi:10.1109/DASIP48288.2019.9049184](https://doi.org/10.1109/DASIP48288.2019.9049184).

**XDS and DISTL** — a spot is bounded by its shape (how much of its bounding box it fills) rather than
by its size alone, as XDS (cited under [Integration and rotation geometry](#integration-and-rotation-geometry)) and DISTL bound theirs; the statistic
is rugnux's own, the choice of shape over size is theirs. Z. Zhang, N. K. Sauter, H. van den Bedem,
G. Snell and A. M. Deacon, "Automated diffraction image analysis and spot searching for high-throughput
crystal screening" (2006), J. Appl. Cryst. 39, 112-119
[doi:10.1107/S0021889805040677](https://doi.org/10.1107/S0021889805040677).

### Indexing

**Fourier-transform indexing** — indexing a diffraction pattern, with no prior knowledge of the
cell, by Fourier-transforming the reciprocal-space positions of its spots was proposed by Gérard
Bricogne as a three-dimensional transform; the de-novo FFT indexers (`-X fft`, `-X fftw`) use the
one-dimensional projection form of that idea described in the next paragraph. G. Bricogne (1986),
in *Proceedings of the EEC Cooperative Workshop on Position-Sensitive Detector Software
(Phase III)*, LURE, Paris, p. 28 (a workshop proceedings without a DOI).

**[MOSFLM](https://www.mrc-lmb.cam.ac.uk/mosflm/mosflm/)** — the Rossmann FFT autoindexing algorithm and
post-refinement practice, including which parameters are safe to refine per image and which must be
refined over a wedge. The autoindexing algorithm itself — projecting the reciprocal-space points
onto many directions and Fourier-transforming the 1D projection histograms — is I. Steller,
R. Bolotovsky and M. G. Rossmann, "An algorithm for automatic indexing of oscillation images using
Fourier analysis" (1997), J. Appl. Cryst. 30, 1036-1040
[doi:10.1107/S0021889897008777](https://doi.org/10.1107/S0021889897008777); MOSFLM is the
implementation whose practice is followed, described in H. R. Powell, "The Rossmann Fourier
autoindexing algorithm in MOSFLM" (1999), Acta Cryst. D55, 1690-1695
[doi:10.1107/S0907444999009506](https://doi.org/10.1107/S0907444999009506). A. G. W. Leslie and H. R. Powell, "Processing diffraction data with MOSFLM"
(2007), in *Evolving Methods for Macromolecular Crystallography*, NATO Science Series II, vol. 245,
41-51 [doi:10.1007/978-1-4020-6316-9_4](https://doi.org/10.1007/978-1-4020-6316-9_4);
T. G. G. Battye, L. Kontogiannis, O. Johnson, H. R. Powell and A. G. W. Leslie, "iMOSFLM: a new
graphical interface for diffraction-image processing with MOSFLM" (2011), Acta Cryst. D67, 271-281
[doi:10.1107/S0907444910048675](https://doi.org/10.1107/S0907444910048675); H. R. Powell,
T. G. G. Battye, L. Kontogiannis, O. Johnson and A. G. W. Leslie, "Integrating macromolecular X-ray
diffraction data with the graphical user interface iMosflm" (2017), Nat. Protoc. 12, 1310-1325
[doi:10.1038/nprot.2017.037](https://doi.org/10.1038/nprot.2017.037).

**[fast-feedback-indexer](https://github.com/paulscherrerinstitute/fast-feedback-indexer)** — the
known-cell indexer for serial stills (`-X ffbidx`) is PSI's fast-feedback-indexer library, linked at
build time (BSD-3-Clause; see [THIRD_PARTY_NOTICES.md](THIRD_PARTY_NOTICES.md)), which implements
the TORO algorithm: P. Gasparotto, L. Barba, H.-C. Stadler, G. Assmann, H. Mendonça, A. W. Ashton,
M. Janousch, F. Leonarski and B. Béjar, "TORO Indexer: a PyTorch-based indexing algorithm for
kilohertz serial crystallography" (2024), J. Appl. Cryst. 57, 931-944
[doi:10.1107/S1600576724003182](https://doi.org/10.1107/S1600576724003182). The CPU implementation
used without a GPU (`image_analysis/indexing/FFBIDXIndexerCPU.cpp`) is a port of the library's CUDA
kernels by H.-C. Stadler (PSI): the same samples and scores, with the loops reorganised for a CPU.

### Cell reduction and lattice symmetry

**[GEMMI](https://github.com/project-gemmi/gemmi)** — symmetry operations, unit-cell and
structure-factor machinery, and MTZ / XDS_ASCII I/O. Vendored in `gemmi_gph/`, so it also carries a
licence obligation. M. Wojdyr, "GEMMI: A library for structural biology" (2022), J. Open Source
Softw. 7, 4200 [doi:10.21105/joss.04200](https://doi.org/10.21105/joss.04200).

**Křivý & Gruber's Niggli reduction, and the lattice-character table** — the reduction that puts
every candidate cell in a comparable form is I. Křivý and B. Gruber, "A unified algorithm for
determining the reduced (Niggli) cell" (1976), Acta Cryst. A32, 297-298
[doi:10.1107/S0567739476000636](https://doi.org/10.1107/S0567739476000636), used through GEMMI's
implementation; the table of lattice characters that maps a reduced cell to Bravais lattices and
centrings follows International Tables for Crystallography Vol. A, Table 9.2.5.1.

**Grosse-Kunstleve, Sauter & Adams's numerically stable cell reduction** - the magnitude-scaled
tolerance that decides the sign of a structurally-zero scalar product, and with it the Niggli type a
reduced cell is presented in. R. W. Grosse-Kunstleve, N. K. Sauter and P. D. Adams, "Numerically
stable algorithms for the computation of reduced unit cells" (2004), Acta Cryst. A60, 1-6
[doi:10.1107/S010876730302186X](https://doi.org/10.1107/S010876730302186X).

**Le Page's metric-symmetry search** - the obliquity of each of the 81 candidate two-folds of a
reduced cell, which is what tells a run that its lattice metric hosts more rotational symmetry than
the group its intensities supported, and the derivation of the conventional axes from that
rotation group, which is what the run then offers to the space-group search as a second lattice
candidate. The two-fold search is used through GEMMI's implementation of it. Y. Le Page, "The
derivation of the axes of the conventional unit cell from the dimensions of the Buerger-reduced
cell" (1982), J. Appl. Cryst. 15, 255-259
[doi:10.1107/S0021889882011959](https://doi.org/10.1107/S0021889882011959).

### Integration and rotation geometry

**[XDS](https://xds.mr.mpg.de/)** — rotation geometry and notation, the reciprocal Lorentz and
partiality treatment, the maximum-likelihood mosaicity estimate, the `MINPK` criterion for rejecting
a reflection whose predicted profile is not cleanly its own, the intensity-based test for a
centred lattice, the recognition of shaded detector regions by comparing a pixel's background
against the background at its own resolution (`DEFPIX`), and the scaling correction surfaces
indexed by image number and detector region. W. Kabsch, "XDS" (2010), Acta Cryst. D66, 125-132
[doi:10.1107/S0907444909047337](https://doi.org/10.1107/S0907444909047337); W. Kabsch, "Integration,
scaling, space-group assignment and post-refinement" (2010), Acta Cryst. D66, 133-144
[doi:10.1107/S0907444909047374](https://doi.org/10.1107/S0907444909047374).

**Profile fitting** with reweighted, de-biased variances is the Kabsch/Otwinowski iteration, from the
second XDS paper above and from Z. Otwinowski and W. Minor, "Processing of X-ray diffraction data
collected in oscillation mode" (1997), Methods Enzymol. 276, 307-326
[doi:10.1016/S0076-6879(97)76066-X](https://doi.org/10.1016/S0076-6879%2897%2976066-X).

**The two-dimensional integration architecture** — integrating each image in the detector plane
and only afterwards assembling a reflection's partials into a full across images, as against
three-dimensional profile fitting through the image stack — is the architecture of DENZO/SCALEPACK
and MOSFLM, and it is the one Rugnux's rotation pipeline follows (per-image profile-fitted
integration, then partials combined into fulls; §9 and §10.6 of the [data-analysis reference](CPU_DATA_ANALYSIS.md)). The
Otwinowski & Minor citation above and the MOSFLM citations below carry the credit for the paradigm
as well as for the specifics taken from each.

### Space group, twinning and pseudo-symmetry

**[POINTLESS](https://www.ccp4.ac.uk/)** (CCP4) — the space-group search. Stage A scores each
candidate rotation operator by the correlation of I(h) with I(Rh) on **resolution-normalised**
intensities (E²), as POINTLESS does — both arms of a symmetry pair sit at the same |s|, so on raw
intensities the resolution fall-off is variance shared between them and lifts a false operator's
correlation as much as a true one's; the screw-axis test scores a
predicted-absent class against the rest of its own axial row rather than against a global mean or a
fixed cut, and lets confidence fall away with the number of axial reflections instead of refusing
below a count; the glide-plane test is that same test applied to a zone, scoring the extinguished
class against the rest of its own plane, as POINTLESS scores zonal absences. P. Evans, "Scaling and assessment of data quality" (2006), Acta Cryst. D62, 72-82
[doi:10.1107/S0907444905036693](https://doi.org/10.1107/S0907444905036693); P. R. Evans, "An
introduction to data reduction: space-group determination, scaling and intensity statistics" (2011),
Acta Cryst. D67, 282-292 [doi:10.1107/S090744491003982X](https://doi.org/10.1107/S090744491003982X);
P. R. Evans and G. N. Murshudov, "How good are my data and what is the resolution?" (2013), Acta
Cryst. D69, 1204-1214 [doi:10.1107/S0907444913000061](https://doi.org/10.1107/S0907444913000061);
J. Agirre, M. Atanasova, H. Bagdonas et al., "The CCP4 suite: integrative software for macromolecular
crystallography" (2023), Acta Cryst. D79, 449-461
[doi:10.1107/S2059798323003595](https://doi.org/10.1107/S2059798323003595).

**Baur and Kassner** — the convention for which of two absence-equivalent glide groups the space-group
search writes (P2/c over Pc, C2/c over Cc): the centrosymmetric one, because a missed inversion centre is
the common error among published small-molecule space-group assignments. W. H. Baur and D. Kassner,
"The perils of Cc: comparing the frequencies of falsely assigned space groups with their general
population" (1992), Acta Cryst. B48, 356-369
[doi:10.1107/S0108768191014726](https://doi.org/10.1107/S0108768191014726).

**The centre-of-symmetry statistics** are Wilson's and Howells, Phillips & Rogers's: the intensity
distributions of acentric and centric structures and the cumulative N(z) test built on them, read here
on the general reflections of the Laue class beside <|E^2-1|> and Padilla and Yeates's L test (taken at
its centric value, 2/pi). A. J. C. Wilson, "The probability distribution of X-ray intensities" (1949),
Acta Cryst. 2, 318-321 [doi:10.1107/S0365110X49000813](https://doi.org/10.1107/S0365110X49000813);
E. R. Howells, D. C. Phillips and D. Rogers, "The probability distribution of X-ray intensities. II.
Experimental investigation and the X-ray detection of centres of symmetry" (1950), Acta Cryst. 3,
210-214 [doi:10.1107/S0365110X50000513](https://doi.org/10.1107/S0365110X50000513).

**The twinning L test** is Padilla and Yeates's: pairing each acentric reflection with a
symmetry-independent neighbour and reading the first and second moments of
L = (I1−I2)/(I1+I2) against their untwinned and perfect-twin values. J. E. Padilla and
T. O. Yeates, "A statistic for local intensity differences: robustness to anisotropy and
pseudo-centering and utility for detecting twinning" (2003), Acta Cryst. D59, 1124-1130
[doi:10.1107/S0907444903007947](https://doi.org/10.1107/S0907444903007947). Their title claims
robustness to pseudo-centering, and this program's partner steps deliver it: a step of 2 along an
axis preserves the class of a half-integer pseudo-translation, which is what a pseudo-centering is.
That robustness does not extend to a pseudo-translation which is not half-integer, and the partner
steps are restricted when one is detected - see the translational-pseudo-symmetry note below.

**The twin fraction of the twin hypothesis, and the twinned model it is scored with**, follow Yeates:
the intensity a twinned crystal records is (1−α) I(h) + α I(Th), and the disagreement
H = |I(h) − I(Th)|/(I(h) + I(Th)) of the pairs a law relates is uniform on [0, 1−2α], so the median
gives the fraction. T. O. Yeates, "Detecting and overcoming crystal twinning" (1997), Methods Enzymol.
276, 344-358 [doi:10.1016/S0076-6879(97)76068-3](https://doi.org/10.1016/S0076-6879%2897%2976068-3).

**The symmetry hypotheses a refused promotion leaves** - the adopted group and every other index-2 subgroup
of the refused group perfectly twinned by a law of its coset, all merging alike, carried to the model and
decided by placing and refining it in each - follow the advice to refine in the candidate groups and compare,
rather than decide from intensity statistics, that pseudo-symmetry and twinning call for:
P. H. Zwart, R. W. Grosse-Kunstleve, A. A. Lebedev, G. N. Murshudov and P. D. Adams, "Surprises and pitfalls
arising from (pseudo)symmetry" (2008), Acta Cryst. D64, 99-107
[doi:10.1107/S090744490705531X](https://doi.org/10.1107/S090744490705531X); A. A. Lebedev and M. N. Isupov,
"Space-group and origin ambiguity in macromolecular structures with pseudo-symmetry and its treatment with the
program Zanuda" (2014), Acta Cryst. D70, 2430-2443
[doi:10.1107/S1399004714014795](https://doi.org/10.1107/S1399004714014795).

**Twin refinement** (§15.12) refines the model against Yeates's twinned intensity, (1−α) I(h) + α I(Th), with the
twin fraction refined beside it as SHELXL refines BASF: R. Herbst-Irmer and G. M. Sheldrick, "Refinement of twinned
structures with SHELXL97" (1998), Acta Cryst. B54, 443-449
[doi:10.1107/S0108768197018454](https://doi.org/10.1107/S0108768197018454). The twin laws come from the lattice's
metric as A. A. Lebedev, A. A. Vagin and G. N. Murshudov describe, "Intensity statistics in twinned crystals with
examples from the PDB" (2006), Acta Cryst. D62, 83-95
[doi:10.1107/S0907444905036759](https://doi.org/10.1107/S0907444905036759), and the fractions are refined by
least squares at every cycle, as REFMAC5 refines them (Murshudov et al. 2011, Acta Cryst. D67, 355-367, cited
above). REFMAC5's target is a twinned-intensity likelihood; ours keeps the amplitude likelihood with the twinned
model amplitude in it, a simplification of that.

**A first-pass cell that is the coincidence lattice of two twin domains** (twinning by reticular
merohedry of index 2 or 3, e.g. obverse/reverse rhombohedral domains or a cubic crystal twinned about
[111]) is recognised by the nodes that belong to neither domain being empty. The twin index is
Friedel's (G. Friedel, *Leçons de cristallographie*, 1926; no DOI); the split of the reflections into
those of one domain, of the other, of both and of neither is the one Herbst-Irmer and Sheldrick use
for obverse/reverse twins: R. Herbst-Irmer and G. M. Sheldrick, "Refinement of obverse/reverse twins"
(2002), Acta Cryst. B58, 477-481
[doi:10.1107/S0108768102001039](https://doi.org/10.1107/S0108768102001039).

**Translational pseudo-symmetry** is detected from the native Patterson computed from the merged
intensities, and the interpretation of an off-origin peak as a pseudo-translation between copies of
the contents of the asymmetric unit - together with the modulation it puts on the intensities, which
is the second half of the test here - is Read, Adams and McCoy's. Their fitted peak-height table is
not used: the peak is scored against a per-dataset within-shell permutation null instead, because the
noise floor of the statistic depends strongly on how many reflections a dataset has. The same
modulation is what the axial systematic-absence test scores against, so that a reflection class a
pseudo-translation merely suppresses is not read as extinct and does not buy a screw axis; the
estimate of its depth there is our own, measured per axial row from the merged intensities rather
than from the Patterson vector. Where a symmetry operator or a twin law carries the vector to one
that is not ±itself, the modulation is also read on classes averaged over the lattice's rotations -
their modulation model summed over the copy pairs each rotation relates, as the measured intensity
sums them; that averaging is our own construction. R. J. Read,
P. D. Adams and A. J. McCoy, "Intensity statistics in the presence of translational
noncrystallographic symmetry" (2013), Acta Cryst. D69, 176-183
[doi:10.1107/S0907444912045374](https://doi.org/10.1107/S0907444912045374).

### Scaling, merging and data quality

**[DIALS](https://dials.github.io/)** — the resolution cutoff from the CC1/2 fall-off, per-observation
outlier rejection at merge, the scaling error model, and the treatment of a reflection whose
background is contaminated. Its published behaviour, and in places its source, settled several
choices here. G. Winter, D. G. Waterman, J. M. Parkhurst et al., "DIALS: implementation and
evaluation of a new integration package" (2018), Acta Cryst. D74, 85-97
[doi:10.1107/S2059798317017235](https://doi.org/10.1107/S2059798317017235); D. G. Waterman,
G. Winter, R. J. Gildea et al., "Diffraction-geometry refinement in the DIALS framework" (2016),
Acta Cryst. D72, 558-575 [doi:10.1107/S2059798316002187](https://doi.org/10.1107/S2059798316002187);
J. Beilsten-Edmands, G. Winter, R. Gildea et al., "Scaling diffraction data in the DIALS software
package: algorithms and new approaches for multi-crystal scaling" (2020), Acta Cryst. D76, 385-399
[doi:10.1107/S2059798320003198](https://doi.org/10.1107/S2059798320003198); J. M. Parkhurst,
G. Winter, D. G. Waterman et al., "Robust background modelling in DIALS" (2016), J. Appl. Cryst. 49,
1912-1921 [doi:10.1107/S1600576716013595](https://doi.org/10.1107/S1600576716013595).

**Wilson outlier test** — judging an observation that has no symmetry mates against the acentric and
centric intensity distributions of its resolution shell, with the symmetry enhancement factor, is
Wilson's statistics; rejecting only observations that are also significant, and keeping a reflection
whose observations are all large, follows AIMLESS's EMAX test. A. J. C. Wilson, "The probability
distribution of X-ray intensities" (1949), Acta Cryst. 2, 318-321
[doi:10.1107/S0365110X49000813](https://doi.org/10.1107/S0365110X49000813);
P. Evans, "Scaling and assessment of data quality" (2006), Acta Cryst. D62, 72-82
[doi:10.1107/S0907444905036693](https://doi.org/10.1107/S0907444905036693).

**Amplitudes from intensities** — the posterior-mean amplitude of each merged intensity under the
acentric and centric Wilson priors is French and Wilson's; giving no amplitude to an intensity more
than 3.7 sigma below zero, and leaving such intensities out of the prior, follows CCP4's
[ctruncate](https://www.ccp4.ac.uk/) (C. Ballard and N. Stein). So does scaling each reflection's
Wilson prior by the anisotropy tensor along its direction, which ctruncate has done by default since
its version 1.7 ("use anisotropy in prior for truncate procedure"); rugnux uses its own tensor for it
(see Diffraction anisotropy below). S. French and K. Wilson, "On the treatment of negative intensity
observations" (1978), Acta Cryst. A34, 517-525
[doi:10.1107/S0567739478001114](https://doi.org/10.1107/S0567739478001114); ctruncate is cited through
the CCP4 suite: M. D. Winn, C. C. Ballard, K. D. Cowtan et al.,
"Overview of the CCP4 suite and current developments" (2011), Acta Cryst. D67, 235-242
[doi:10.1107/S0907444910045749](https://doi.org/10.1107/S0907444910045749).

**Absorption as spherical harmonics** — describing an empirical absorption correction as a series of
real spherical harmonics of the beam directions in the crystal frame is Blessing's; its use as a
restrained scaling surface of the diffracted-beam direction follows SCALA and AIMLESS. R. H. Blessing,
"An empirical correction for absorption anisotropy" (1995), Acta Cryst. A51, 33-38
[doi:10.1107/S0108767394005726](https://doi.org/10.1107/S0108767394005726); P. Evans, "Scaling and
assessment of data quality" (2006), Acta Cryst. D62, 72-82
[doi:10.1107/S0907444905036693](https://doi.org/10.1107/S0907444905036693).

**Diffraction anisotropy** — the description of the overall fall-off by a single anisotropic
displacement tensor, its symmetry constraints, and the fact that only its deviatoric part is
determined (the isotropic part being degenerate with the overall scale) are Sheriff and Hendrickson's.
The estimator fits that tensor to the observed intensity distribution, taking sigma(I) into account,
in the sense of Popov and Bourenkov. The directional diffraction limits - <I/sigma(I)> in a cone about
each principal direction, and the reporting of the anisotropic deltaB as the range of the principal
components - follow AIMLESS. Rugnux reports these; it corrects no intensity and removes no reflection
on a directional criterion. S. Sheriff and W. A. Hendrickson, "Description of overall anisotropy in
diffraction from macromolecular crystals" (1987), Acta Cryst. A43, 118-121
[doi:10.1107/S010876738709977X](https://doi.org/10.1107/S010876738709977X); A. N. Popov and
G. P. Bourenkov, "Choice of data-collection parameters based on statistic modelling" (2003), Acta
Cryst. D59, 1145-1153 [doi:10.1107/S0907444903008163](https://doi.org/10.1107/S0907444903008163);
P. R. Evans and G. N. Murshudov, "How good are my data and what is the resolution?" (2013), Acta
Cryst. D69, 1204-1214 [doi:10.1107/S0907444913000061](https://doi.org/10.1107/S0907444913000061).

**Data-quality statistics** follow the established conventions rather than any one program: R_meas
and R_pim, CC1/2 and CC\*, the per-shell CC(model, data) between F^2_calc and F^2_obs, and the
reporting of I/sigma(I). K. Diederichs and P. A. Karplus, "Improved
R-factors for diffraction data analysis in macromolecular crystallography" (1997), Nat. Struct. Biol.
4, 269-275 [doi:10.1038/nsb0497-269](https://doi.org/10.1038/nsb0497-269); P. A. Karplus and
K. Diederichs, "Linking crystallographic model and data quality" (2012), Science 336, 1030-1033
[doi:10.1126/science.1218231](https://doi.org/10.1126/science.1218231) (CC\* is also what a joint merge of
several sweeps tests their isomorphism against: CC_AB / (CC\*_A CC\*_B) is the cosine of the angle between
two data sets, their systematic difference apart from their noise, as K. Diederichs, "Dissecting random and
systematic differences between noisy composite data sets" (2017), Acta Cryst. D73, 286-293
[doi:10.1107/S2059798317000699](https://doi.org/10.1107/S2059798317000699) shows - which is why the join is
decided on the size of that ratio, and a doubtful sweep by the merge with and without it, the idea of
delta-CC1/2 by Assmann, Brehm and Diederichs (2016), below); M. S. Weiss, "Global
indicators of X-ray data quality" (2001), J. Appl. Cryst. 34, 130-135
[doi:10.1107/S0021889800018227](https://doi.org/10.1107/S0021889800018227) (R_pim beside R_meas and
R_merge); K. Diederichs and
P. A. Karplus, "Better models by discarding data?" (2013), Acta Cryst. D69, 1215-1222
[doi:10.1107/S0907444913001121](https://doi.org/10.1107/S0907444913001121).

**The Whittaker smoother** — the per-frame scale of the rotation fulls is a penalised least-squares
curve (a second-difference penalty, the smoothness chosen by cross-validation)
in the form P. H. C. Eilers gave Whittaker's graduation: P. H. C. Eilers, "A perfect smoother" (2003),
Anal. Chem. 75, 3631-3636 [doi:10.1021/ac034173t](https://doi.org/10.1021/ac034173t); E. T. Whittaker,
"On a new method of graduation" (1923), Proc. Edinburgh Math. Soc. 41, 63-75
[doi:10.1017/S0013091500077853](https://doi.org/10.1017/S0013091500077853).

**Fisher's z-transformation** — the cross-validation of the scaling correction surfaces averages the
change of the half-set CC1/2 over resolution shells on atanh(CC), so that the shells near CC = 1, where
a multiplicative error shows, are not outweighed by the noise of the shells without signal. R. A.
Fisher, "Frequency distribution of the values of the correlation coefficient in samples from an
indefinitely large population" (1915), Biometrika 10, 507-521
[doi:10.2307/2331838](https://doi.org/10.2307/2331838).

**The frame disposition** - which stretches of a rotation sweep are kept, carried at reduced weight or
dropped from the merge - decides every exclusion on delta-CC1/2, the change in the overall CC1/2 when a
group of images is left out, measured in the sigma-tau form so that no random half-dataset split is
involved. The statistic, the Fisher transformation used to compare it across CC1/2 values, its standard
error going as the inverse square root of the reflection count, and the rejection discipline (never
remove a group whose delta-CC1/2 is positive or near zero; remove a little, re-form the reference and
repeat) are all taken from its authors, whose XDSCC12 is the reference implementation.
G. Assmann, W. Brehm and K. Diederichs, "Identification of rogue datasets in serial crystallography"
(2016), J. Appl. Cryst. 49, 1021-1028
[doi:10.1107/S1600576716005471](https://doi.org/10.1107/S1600576716005471); G. M. Assmann, M. Wang and
K. Diederichs, "Making a difference in multi-data-set crystallography: simple and deterministic
data-scaling/selection methods" (2020), Acta Cryst. D76, 636-652
[doi:10.1107/S2059798320006348](https://doi.org/10.1107/S2059798320006348). That the same statistic
belongs at scaling, applied to groups of images rather than to whole datasets, follows
[DIALS](https://dials.github.io/) (`dials.scale`, delta-CC1/2 image-group filtering):
J. Beilsten-Edmands, G. Winter, R. Gildea et al., "Scaling diffraction data in the DIALS software
package: algorithms and new approaches for multi-crystal scaling" (2020), Acta Cryst. D76, 385-399
[doi:10.1107/S2059798320003198](https://doi.org/10.1107/S2059798320003198).

**Several sweeps merged as one** - each sweep's partials combined into fulls on their own, and the
fulls of all the sweeps then scaled together, every sweep with its own frame scales and a relative B
against the joint merge, is how XSCALE merges several data sets (W. Kabsch, "Integration, scaling,
space-group assignment and post-refinement" (2010), above). Reading the radiation dose a sweep was taken
at from its relative B, which orders the sweeps by dose from the data rather than from the order they
were given in, follows K. Diederichs, "Some aspects of quantitative analysis and correction of radiation
damage" (2006), Acta Cryst. D62, 96-101
[doi:10.1107/S0907444905031537](https://doi.org/10.1107/S0907444905031537).

**Uncertainty conventions** follow the IUCr Commission on Crystallographic Nomenclature:
D. Schwarzenbach, S. C. Abrahams, H. D. Flack et al., "Statistical descriptors in crystallography:
Report of the IUCr Subcommittee on Statistical Descriptors" (1989), Acta Cryst. A45, 63-75
[doi:10.1107/S0108767388009596](https://doi.org/10.1107/S0108767388009596); D. Schwarzenbach,
S. C. Abrahams, H. D. Flack, E. Prince and A. J. C. Wilson, "Statistical descriptors in
crystallography. II. Report of a Working Group on Expression of Uncertainty in Measurement" (1995),
Acta Cryst. A51, 565-569 [doi:10.1107/S0108767395002340](https://doi.org/10.1107/S0108767395002340).

**Unit-cell e.s.d.s** — that the e.s.d.s of a least-squares cell fit are too small, seeing only the
scatter of the centroids, is Herbstein's survey; rugnux therefore also fits the cell on blocks of
consecutive frames and writes the larger of the two estimates: F. H. Herbstein, "How precise are
measurements of unit-cell dimensions from single crystals?" (2000), Acta Cryst. B56, 547-557
[doi:10.1107/S010876810000269X](https://doi.org/10.1107/S010876810000269X).

**Indexing ambiguity of serial data without a reference** — where a serial run's lattice is more
symmetric than its crystals and no reference or model is given, each crystal is put into the indexing in
which its intensities agree best with those of all the other crystals, crystal by crystal until none
changes. The objective - the summed agreement between every pair of crystals - and the iteration that
maximises it are taken from Brehm and Diederichs, whose method CrystFEL's `ambigator` also implements;
rugnux measures the agreement as a product of standardised amplitudes (square roots of the intensities)
rather than a correlation, which lets the sum over all partners be taken against one running sum instead
of pair by pair.
W. Brehm and K. Diederichs, "Breaking the indexing ambiguity in serial crystallography" (2014),
Acta Cryst. D70, 101-109 [doi:10.1107/S1399004713025431](https://doi.org/10.1107/S1399004713025431).
The same objective settles which twin law puts each sweep of a joint merge of several sweeps on the
reference's indexing - decided over all pairs of sweeps at once, as dials.cosym does for its data sets:
R. J. Gildea and G. Winter, "Determination of Patterson group symmetry from sparse multi-crystal data sets
in the presence of an indexing ambiguity" (2018), Acta Cryst. D74, 405-410
[doi:10.1107/S2059798318002978](https://doi.org/10.1107/S2059798318002978).

**Reference sweep of a joint merge** — the sweep the others are put on the axes of is the one whose own
merge reaches the finest resolution, as KAMO takes the data set of the smallest Wilson B as its reference:
K. Yamashita, K. Hirata and M. Yamamoto, "KAMO: towards automated data processing for microcrystals"
(2018), Acta Cryst. D74, 441-449 [doi:10.1107/S2059798318004576](https://doi.org/10.1107/S2059798318004576).

### Physical corrections and calibration

**Sensor absorption at oblique incidence, and the flight path** — the angle-dependent quantum
efficiency of a flat sensor, the radial parallax variance that comes from the same integral, and the
attenuation of a reflection in the air between the sample and its pixel are all the Beer-Lambert law
taken along a ray that crosses t/cos(alpha) of sensor, or D/cos(alpha) of air, and converts at a
random depth. The attenuation coefficients, for silicon, CdTe, dry air and helium alike, are the
NIST tabulation: J. H. Hubbell and S. M. Seltzer, "Tables of X-Ray
Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients from 1 keV to 20 MeV for
Elements Z = 1 to 92 and 48 Additional Substances of Dosimetric Interest" (1995, data updated 2004),
NIST Standard Reference Database 126
[doi:10.18434/T4D01F](https://doi.org/10.18434/T4D01F).

**Polarization correction** — the azimuthal polarization factor applied to the azimuthally
integrated profile, to the integrated Bragg intensities and to the ring background the beam-stop
shadow test compares a pixel against is the one derived for a partially polarized
synchrotron source by R. Kahn, R. Fourme, A. Gadet, J. Janin, C. Dumas and D. Andre, "Macromolecular
crystallography with synchrotron radiation: photographic data collection and polarization
correction" (1982), J. Appl. Cryst. 15, 330-337
[doi:10.1107/S0021889882012060](https://doi.org/10.1107/S0021889882012060).

**Hexagonal-ice ring positions** — the eleven ring $d$ spacings from 3.895 to 1.522 Å that the
ice-ring score, the ice-ring flagging and the ice calibrant are all built on are taken from the
measurements of Moreau and co-workers, not enumerated from a cell. D. W. Moreau, H. Atakisi and R. E. Thorne, "Ice in
biomolecular cryocrystallography" (2021), Acta Cryst. D77, 540-554
[doi:10.1107/S2059798321001170](https://doi.org/10.1107/S2059798321001170).

That list ends at 1.522 Å by its own scope, so the eight bands below it are calculated here rather
than taken from anyone: ice Ih structure factors on the oxygen sublattice, kept where they reach 3% of
the strongest line, which reproduces the eleven measured positions exactly. The lattice constants are
Röttger and co-workers'. K. Röttger, A. Endriss, J. Ihringer, S. Doyle and W. F. Kuhs, "Lattice
constants and thermal expansion of H2O and D2O ice Ih between 10 and 265 K" (1994), Acta Cryst. B50,
644-648 [doi:10.1107/S0108768194004933](https://doi.org/10.1107/S0108768194004933).

### Model-based analysis and maps

**Bulk-solvent correction and overall scaling** — the model's structure factors are put on the
observed scale with an overall factor, an anisotropic B and a flat bulk-solvent term, the flat-mask
model of A. Fokine and A. Urzhumtsev, "Flat bulk-solvent model: obtaining optimal parameters"
(2002), Acta Cryst. D58, 1387-1392
[doi:10.1107/S0907444902010284](https://doi.org/10.1107/S0907444902010284), which is also the source
of the starting values and of the range those two parameters are physically meaningful over. The mask itself -
the region a probe cannot reach from the atoms, shrunk back - is J.-S. Jiang and A. T. Brünger's, "Protein
hydration observed by X-ray diffraction: solvation properties of penicillopepsin and neuraminidase crystal
structures" (1994), J. Mol. Biol. 243, 100-115
[doi:10.1006/jmbi.1994.1633](https://doi.org/10.1006/jmbi.1994.1633), drawn with the radii REFMAC5 uses. The
procedure that fits them — a grid search over that range for the solvent pair, with the overall
scale and the anisotropic B refitted at every grid point — follows P. V. Afonine,
R. W. Grosse-Kunstleve and P. D. Adams, "A robust bulk-solvent correction and anisotropic scaling
procedure" (2005), Acta Cryst. D61, 850-855
[doi:10.1107/S0907444905007894](https://doi.org/10.1107/S0907444905007894). The fit is unweighted,
as in both that procedure and REFMAC5: G. N. Murshudov, P. Skubak, A. A. Lebedev, N. S. Pannu,
R. A. Steiner, R. A. Nicholls, M. D. Winn, F. Long and A. A. Vagin, "REFMAC5 for the refinement of
macromolecular crystal structures" (2011), Acta Cryst. D67, 355-367
[doi:10.1107/S0907444911001314](https://doi.org/10.1107/S0907444911001314).

**sigma_A map coefficients** — the maps written by `--model` are weighted by a maximum-likelihood
sigma_A estimated per resolution shell, giving 2mFo-DFc and mFo-DFc rather than 2Fo-Fc and Fo-Fc.
What is taken is the formalism itself: the Rice and Woolfson likelihoods of |Fo| given |Fc| and
sigma_A, the figure of merit m and the scale D that follow from it, and the result that the
bias-corrected coefficient is 2mFo-DFc for an acentric reflection and mFo for a centric one.
R. J. Read, "Improved Fourier coefficients for maps using phases from partial structures with
errors" (1986), Acta Cryst. A42, 140-149
[doi:10.1107/S0108767386099622](https://doi.org/10.1107/S0108767386099622).

**[ANODE](https://doi.org/10.1107/S0021889811041768)** — reading the anomalous difference map at the
atoms of a supplied model and reporting the strongest sites by name, instead of searching the map for
blobs. The map itself is the textbook anomalous difference Fourier; what is taken from ANODE is that
reading: A. Thorn and G. M. Sheldrick, "ANODE: anomalous and heavy-atom density calculation" (2011),
J. Appl. Cryst. 44, 1285-1287
[doi:10.1107/S0021889811041768](https://doi.org/10.1107/S0021889811041768).

**Uniform random rotations** — the null a supplied model is scored against re-orients that model at
random about its own centroid, and the rotations are drawn uniformly from SO(3) through a uniform
random unit quaternion. K. Shoemake, "Uniform Random Rotations", in *Graphics Gems III*, ed. D. Kirk,
Academic Press (1992), 124-132 (no DOI).

**Variable projection** — the rigid-body placement of a supplied model re-fits the overall scale at
every step, and its Jacobian folds that re-fit in by projecting the scale's own derivatives out of the
placement's, in Kaufman's simplified form of Golub and Pereyra's derivative of the reduced problem.
G. H. Golub and V. Pereyra, "The Differentiation of Pseudo-Inverses and Nonlinear Least Squares
Problems Whose Variables Separate" (1973), SIAM J. Numer. Anal. 10, 413-432
[doi:10.1137/0710036](https://doi.org/10.1137/0710036). L. Kaufman, "A variable projection method
for solving separable nonlinear least squares problems" (1975), BIT 15, 49-57
[doi:10.1007/BF01932995](https://doi.org/10.1007/BF01932995).

**Predicted models** — `--model` (and `--mr`) place an AlphaFold prediction (or any model the rigid
body does not place) by molecular replacement. J. Jumper, R. Evans, A. Pritzel et al., "Highly accurate protein structure prediction
with AlphaFold" (2021), Nature 596, 583-589
[doi:10.1038/s41586-021-03819-2](https://doi.org/10.1038/s41586-021-03819-2); the models are those of
the AlphaFold Protein Structure Database: M. Varadi, S. Anyango, M. Deshpande et al., "AlphaFold
Protein Structure Database: massively expanding the structural coverage of protein-sequence space
with high-accuracy models" (2022), Nucleic Acids Res. 50, D439-D444
[doi:10.1093/nar/gkab1061](https://doi.org/10.1093/nar/gkab1061). The model is prepared as
phenix.process_predicted_model prepares one - residues below pLDDT 70 removed, B-factors from the
coordinate error the pLDDT predicts: R. D. Oeffner, T. Croll, C. Millán et al., "Putting AlphaFold
models to work with phenix.process_predicted_model and ISOLDE" (2022), Acta Cryst. D78, 1303-1314
[doi:10.1107/S2059798322010026](https://doi.org/10.1107/S2059798322010026).

**Molecular replacement** — the search scores each orientation of the model against the data by
interpolating its molecular transform, computed once by FFT, as Navaza's AMoRe does: J. Navaza,
"AMoRe: an automated package for molecular replacement" (1994), Acta Cryst. A50, 157-163
[doi:10.1107/S0108767393007597](https://doi.org/10.1107/S0108767393007597). The translation
function is the full-symmetry one, all pairs of symmetry copies on one Fourier synthesis:
R. A. Crowther and D. M. Blow, "A method of positioning a known molecule in an unknown crystal
structure" (1967), Acta Cryst. 23, 544-548
[doi:10.1107/S0365110X67003172](https://doi.org/10.1107/S0365110X67003172). A placement is called
a solution, as Phaser calls one, where its translation-function Z-score reaches 8: A. J. McCoy,
R. W. Grosse-Kunstleve, P. D. Adams, M. D. Winn, L. C. Storoni and R. J. Read, "Phaser
crystallographic software" (2007), J. Appl. Cryst. 40, 658-674
[doi:10.1107/S0021889807021206](https://doi.org/10.1107/S0021889807021206). Whether one copy fits
the cell is read off the Matthews coefficient: B. W. Matthews, "Solvent content of protein
crystals" (1968), J. Mol. Biol. 33, 491-497
[doi:10.1016/0022-2836(68)90205-2](https://doi.org/10.1016/0022-2836%2868%2990205-2). How many copies
to search for is weighed by a distribution of the Matthews coefficient over protein crystals made from
the mode and mean of Kantardjieff and Rupp's: K. A. Kantardjieff and B. Rupp, "Matthews coefficient
probabilities: Improved estimates for unit cell contents of proteins, DNA, and protein-nucleic acid
complex crystals" (2003), Protein Sci. 12, 1865-1871
[doi:10.1110/ps.0350503](https://doi.org/10.1110/ps.0350503). A copy refined beside the others has the
others' placements read off by least-squares superposition: W. Kabsch, "A solution for the best rotation
to relate two sets of vectors" (1976), Acta Cryst. A32, 922-923
[doi:10.1107/S0567739476001873](https://doi.org/10.1107/S0567739476001873). The placements are judged by
their log-likelihood gain, from the Rice and Woolfson distributions of the observed normalised amplitudes
given the model's, with sigma_A from the model's expected coordinate error: R. J. Read, "Pushing the
boundaries of molecular replacement with maximum likelihood" (2001), Acta Cryst. D57, 1373-1382
[doi:10.1107/S0907444901012471](https://doi.org/10.1107/S0907444901012471); and the gain is read as a
Z-score over the same orientation at other positions, as the likelihood-enhanced translation function's
is: A. J. McCoy, R. W. Grosse-Kunstleve, L. C. Storoni and R. J. Read, "Likelihood-enhanced fast
translation functions" (2005), Acta Cryst. D61, 458-464
[doi:10.1107/S0907444905001617](https://doi.org/10.1107/S0907444905001617). A model whose expected
log-likelihood gain - the sum of sigma_A^4 / 2 over the reflections - is too small for a placement to stand
out is not searched for: A. J. McCoy, R. D. Oeffner, A. G. Wrobel, J. R. M. Ojala, K. Tryggvason,
B. Lohkamp and R. J. Read, "Ab initio solution of macromolecular crystal structures without direct
methods" (2017), Proc. Natl. Acad. Sci. USA 114, 3637-3641
[doi:10.1073/pnas.1701640114](https://doi.org/10.1073/pnas.1701640114). Translational NCS is looked
for in the native Patterson before the search, an off-origin peak read as Read, Adams and McCoy read
it (see
[Translational pseudo-symmetry](#space-group-twinning-and-pseudo-symmetry) above). The logarithm of the Bessel
function I0 in it is evaluated with the polynomial approximations of M. Abramowitz and I. A. Stegun,
"Handbook of Mathematical Functions" (1964), National Bureau of Standards, 9.8.1-9.8.2. A predicted
model is cut into rigid domains by its predicted aligned error, as Oeffner et al. (above) do before
molecular replacement; the error itself is AlphaFold's: J. Jumper, R. Evans, A. Pritzel et al., "Highly
accurate protein structure prediction with AlphaFold" (2021), Nature 596, 583-589
[doi:10.1038/s41586-021-03819-2](https://doi.org/10.1038/s41586-021-03819-2).

**Structure refinement** (of a placed model) — the placed model is refined against the maximum-likelihood
amplitude target, the Rice distribution of an observed amplitude given the model's (its centric
counterpart for a centric reflection): N. S. Pannu and R. J. Read, "Improved structure refinement
through maximum likelihood" (1996), Acta Cryst. A52, 659-668
[doi:10.1107/S0108767396004370](https://doi.org/10.1107/S0108767396004370); G. N. Murshudov,
A. A. Vagin and E. J. Dodson, "Refinement of macromolecular structures by the maximum-likelihood method"
(1997), Acta Cryst. D53, 240-255 [doi:10.1107/S0907444996012255](https://doi.org/10.1107/S0907444996012255).
Its two parameters are fitted by maximum likelihood in resolution bins - the variance on the free
reflections, D on the working reflections with the measurement error added to that variance, which is how
REFMAC5 divides them (Murshudov et al. 2011, above); the refined model's maps are weighted by the same D
and figure of merit. Estimating the likelihood's parameters on free reflections follows V. Y. Lunin and T. P. Skovoroda, "R-free likelihood-based estimates of errors for phases
calculated from atomic models" (1995), Acta Cryst. A51, 880-887
[doi:10.1107/S010876739500688X](https://doi.org/10.1107/S010876739500688X); V. Y. Lunin, P. V. Afonine and
A. G. Urzhumtsev, "Likelihood-based refinement. I. Irremovable model errors" (2002), Acta Cryst. A58,
270-282 [doi:10.1107/S0108767302001046](https://doi.org/10.1107/S0108767302001046). The gradient with
respect to every atom is taken by the FFT method - the derivatives of the target with respect to the
structure factors transformed into a map and summed against each atom's density derivatives:
R. C. Agarwal, "A new least-squares refinement technique based on the fast Fourier transform algorithm"
(1978), Acta Cryst. A34, 791-809 [doi:10.1107/S0567739478001618](https://doi.org/10.1107/S0567739478001618).
The positions and B factors are minimised by L-BFGS (rugnux's own, its memory kept from one macro-cycle to
the next, the B factors' steps scaled by their estimated curvature): D. C. Liu and J. Nocedal, "On the limited
memory BFGS method for large scale optimization" (1989), Math. Program. 45, 503-528
[doi:10.1007/BF01589116](https://doi.org/10.1007/BF01589116), whose two-loop recursion is J. Nocedal's, "Updating
quasi-Newton matrices with limited storage" (1980), Math. Comp. 35, 773-782
[doi:10.1090/S0025-5718-1980-0572855-7](https://doi.org/10.1090/S0025-5718-1980-0572855-7). The geometry restraints are those of the CCP4
Monomer Library, a subset of which rugnux carries (see THIRD_PARTY_NOTICES.md): A. A. Vagin,
R. A. Steiner, A. A. Lebedev, L. Potterton, S. McNicholas, F. Long and G. N. Murshudov, "REFMAC5
dictionary: organization of prior chemical knowledge and guidelines for its use" (2004), Acta Cryst. D60,
2184-2195 [doi:10.1107/S0907444904023510](https://doi.org/10.1107/S0907444904023510); applied to the model
through GEMMI's topology (links, modifications, planes, chiral volumes, torsions): M. Wojdyr, "GEMMI: A
library for structural biology" (2022), J. Open Source Softw. 7, 4200
[doi:10.21105/joss.04200](https://doi.org/10.21105/joss.04200). The torsion derivatives follow
A. Blondel and M. Karplus, "New formulation for derivatives of torsion angles and improper torsion angles
in molecular mechanics: elimination of singularities" (1996), J. Comput. Chem. 17, 1132-1141
[doi:10.1002/(SICI)1096-987X(19960715)17:9<1132::AID-JCC5>3.0.CO;2-T](https://doi.org/10.1002/(SICI)1096-987X(19960715)17:9%3C1132::AID-JCC5%3E3.0.CO;2-T).
The B factors of bonded atoms, and of atoms in contact, are restrained to each other in the
Kullback-Leibler form REFMAC5 uses, whose tolerance grows with B (Murshudov et al. 2011, above; the divergence itself
is S. Kullback and R. A. Leibler's, "On information and sufficiency" (1951), Ann. Math. Statist. 22, 79-86
[doi:10.1214/aoms/1177729694](https://doi.org/10.1214/aoms/1177729694)), and the
overall isotropic B of the scale is moved into the atoms as phenix.refine moves it (Afonine et al. 2012,
below). The weights of the X-ray term against the geometry and against the B restraints start from the
ratios of the gradients, as X-PLOR's crystallographic weight was first set: A. T. Brünger, M. Karplus and
G. A. Petsko, "Crystallographic refinement by simulated annealing: application to crambin" (1989), Acta Cryst.
A45, 50-61 [doi:10.1107/S0108767388009195](https://doi.org/10.1107/S0108767388009195); and they are chosen
among short refinements by R-free with the geometry held within bounds, as phenix.refine chooses them: P. V. Afonine, R. W. Grosse-Kunstleve, N. Echols, J. J. Headd,
N. W. Moriarty, M. Mustyakimov, T. C. Terwilliger, A. Urzhumtsev, P. H. Zwart and P. D. Adams,
"Towards automated crystallographic structure refinement with phenix.refine" (2012), Acta Cryst. D68,
352-367 [doi:10.1107/S0907444912001308](https://doi.org/10.1107/S0907444912001308). R-free itself:
A. T. Brünger, "Free R value: a novel statistical quantity for assessing the accuracy of crystal
structures" (1992), Nature 355, 472-475 [doi:10.1038/355472a0](https://doi.org/10.1038/355472a0).
The model the refinement scores is scaled to the data with the overall scale and anisotropic B fitted by
robust least squares - iteratively reweighted, with the pseudo-Huber weight of each reflection's residual -
so that a few reflections the model cannot explain do not set the scale of the rest: P. J. Huber, "Robust
estimation of a location parameter" (1964), Ann. Math. Statist. 35, 73-101
[doi:10.1214/aoms/1177703732](https://doi.org/10.1214/aoms/1177703732), in the smooth (pseudo-Huber) form of
P. Charbonnier, L. Blanc-Féraud, G. Aubert and M. Barlaud, "Deterministic edge-preserving regularization in
computed imaging" (1997), IEEE Trans. Image Process. 6, 298-311
[doi:10.1109/83.551699](https://doi.org/10.1109/83.551699).
The bonds of metal ions to their donor atoms that the model's LINK records name are restrained at the
distances of the Monomer Library's own statistics of metal sites (its `metals.json`, embedded as
`monomers/metals.cif`; per metal, donor element and coordination number), in line with the surveys of
M. M. Harding, "Geometry of metal-ligand interactions in proteins" (2001), Acta Cryst. D57, 401-411
[doi:10.1107/S0907444900019168](https://doi.org/10.1107/S0907444900019168) and "Small revisions to
predicted distances around metal sites in proteins" (2006), Acta Cryst. D62, 678-682
[doi:10.1107/S0907444906014594](https://doi.org/10.1107/S0907444906014594), and, for Mg²⁺, Na⁺ and K⁺ at
nucleic acids, F. Leonarski, L. D'Ascenzo and P. Auffinger, "Mg2+ ions: do they bind to nucleobase
nitrogens?" (2017), Nucleic Acids Res. 45, 987-1004 [doi:10.1093/nar/gkw1175](https://doi.org/10.1093/nar/gkw1175).
The anisotropic displacements: a TLS group's U is that of a rigid body's translation, libration and their
correlation, U = T + A L A^T + A S + S^T A^T, of V. Schomaker and K. N. Trueblood, "On the rigid-body motion of
molecules in crystals" (1968), Acta Cryst. B24, 63-76
[doi:10.1107/S0567740868001718](https://doi.org/10.1107/S0567740868001718), refined against the likelihood with a
residual B per atom, and a model's B column read as the total or as the residual to its TLS groups, as in
M. D. Winn, M. N. Isupov and G. N. Murshudov, "Use of TLS parameters to model anisotropic displacements in
macromolecular refinement" (2001), Acta Cryst. D57, 122-133
[doi:10.1107/S0907444900014736](https://doi.org/10.1107/S0907444900014736). The chains are cut into TLS groups as
TLSMD cuts them - contiguous segments, by dynamic programming over the fit of an isotropic TLS model to the
refined B factors: J. Painter and E. A. Merritt, "Optimal description of a protein structure in terms of multiple
groups undergoing TLS motion" (2006), Acta Cryst. D62, 439-450
[doi:10.1107/S0907444906005270](https://doi.org/10.1107/S0907444906005270). Atoms refined with a U of their own are
restrained by the rigid-bond postulate of F. L. Hirshfeld, "Can X-ray data distinguish bonding effects from
vibrational smearing?" (1976), Acta Cryst. A32, 239-244
[doi:10.1107/S0567739476000533](https://doi.org/10.1107/S0567739476000533), in the form of SHELXL's RIGU - the
components of U along the bond and across it in the bond's plane: A. Thorn, B. Dittrich and G. M. Sheldrick,
"Enhanced rigid-bond restraints" (2012), Acta Cryst. A68, 448-451
[doi:10.1107/S0108767312014535](https://doi.org/10.1107/S0108767312014535) - with SHELXL's similarity (SIMU) and
approximate-isotropy (ISOR) restraints as G. M. Sheldrick, "Crystal structure refinement with SHELXL" (2015), Acta
Cryst. C71, 3-8 [doi:10.1107/S2053229614024218](https://doi.org/10.1107/S2053229614024218) documents them. Which
displacement model a refinement keeps - isotropic, TLS, or a U per atom - is decided on the free set, as a test of
what the data support rather than a rule by resolution: E. A. Merritt, "To B or not to B: a question of
resolution?" (2012), Acta Cryst. D68, 468-477 [doi:10.1107/S0907444911028320](https://doi.org/10.1107/S0907444911028320).

**NCS restraints** — copies of a molecule in the model are found by sequence alignment with REFMAC5's criterion
(more than 15 residues aligned, 80% identity - here of the longer chain - and 2.5 Å rms after superposition;
Murshudov et al. 2011, above) and restrained locally, on pairs of
corresponding interatomic distances under the Geman-McClure robust loss, as REFMAC5's local NCS restraints are, with
the distance range of R. A. Nicholls, F. Long and G. N. Murshudov, "Low-resolution refinement tools in REFMAC5"
(2012), Acta Cryst. D68, 404-417 [doi:10.1107/S090744491105606X](https://doi.org/10.1107/S090744491105606X), and
the bonds and angles left out as they leave them out. The case for local restraints over a superposition, and for
deciding them by R-free, is G. J. Kleywegt's, "Use of non-crystallographic symmetry in protein structure refinement"
(1996), Acta Cryst. D52, 842-857 [doi:10.1107/S0907444995016477](https://doi.org/10.1107/S0907444995016477); I. Usón,
E. Pohl, T. R. Schneider, Z. Dauter, A. Schmidt, H.-J. Fritz and G. M. Sheldrick, "1.7 Å structure of the stabilized
REIv mutant T39K. Application of local NCS restraints" (1999), Acta Cryst. D55, 1158-1167
[doi:10.1107/S0907444999003972](https://doi.org/10.1107/S0907444999003972); and J. J. Headd, N. Echols,
P. V. Afonine, N. W. Moriarty, R. J. Gildea and P. D. Adams, "Flexible torsion-angle noncrystallographic symmetry
restraints for improved macromolecular structure refinement" (2014), Acta Cryst. D70, 1346-1356
[doi:10.1107/S1399004714003277](https://doi.org/10.1107/S1399004714003277), whose comparison of global, torsion and
no NCS is why the copies' B factors are refined independently here.

**Unmodelled density** — the blobs the refinement lists are the connected regions of the difference map above
a cutoff, found by flood fill as Coot's "unmodelled blobs" finds them, in GEMMI's implementation
(`find_blobs_by_flood_fill`): P. Emsley, B. Lohkamp, W. G. Scott and K. Cowtan, "Features and development
of Coot" (2010), Acta Cryst. D66, 486-501 [doi:10.1107/S0907444910007493](https://doi.org/10.1107/S0907444910007493).

**Special positions** — an atom on a crystallographic special position is placed on it and its shifts are
confined to the subspace its site symmetry leaves unchanged, as R. W. Grosse-Kunstleve and P. D. Adams treat
special positions, "Algorithms for deriving crystallographic space-group information. II. Treatment of special
positions" (2002), Acta Cryst. A58, 60-65 [doi:10.1107/S0108767301016658](https://doi.org/10.1107/S0108767301016658).

**Water build** — the waters the refinement adds and removes follow the documented ordered-solvent defaults of
phenix.refine: difference-map peaks from 3 σ, hydrogen-bond partners to 3.2 Å and picking only to 2.8 Å, with
the waters added, filtered and refined between macro-cycles:
Afonine et al. (2012, above);
the distances to the model that Coot's Find Waters keeps (2.4-3.2 Å), from the Coot manual and Emsley et al.
(2010, above); and the removal of a water in negative difference density at -3 σ, the cut Echols et al. (2014,
below) use to exclude a site.

**Solvent audit** — the waters and ions of the refined model are scored by their surroundings with the
stereochemical criteria of the surveys of ions at nucleic acids by P. Auffinger's group: the coordination bands
1.9-2.3 / 2.3-2.6 / 2.6-3.2 Å, the Mg²⁺ exclusion zone and the clash shells of N. Naleem, A. Henning-Knechtel,
S. Kirmizialtin and P. Auffinger, "Cat_Wiz: a stereochemistry-guided toolkit for locating, diagnosing, and
annotating Mg2+ ions in RNA structures" (2026), Nucleic Acids Res. 54, gkag120
[doi:10.1093/nar/gkag120](https://doi.org/10.1093/nar/gkag120); the Mg-O and Mg-N distances and the
2.3-3.4 Å exclusion zone of F. Leonarski, A. Henning-Knechtel, S. Kirmizialtin, E. Ennifar and P. Auffinger,
"Principles of ion binding to RNA inferred from the analysis of a 1.55 Å resolution bacterial ribosome
structure – Part I: Mg2+" (2025), Nucleic Acids Res. 53, gkae1148
[doi:10.1093/nar/gkae1148](https://doi.org/10.1093/nar/gkae1148); the Na⁺, K⁺ and water distances and
coordination numbers of F. Leonarski, L. D'Ascenzo and P. Auffinger, "Nucleobase carbonyl groups are poor
Mg2+ inner-sphere binders but excellent monovalent ion binders—a critical PDB survey" (2019), RNA 25, 173-192
[doi:10.1261/rna.068437.118](https://doi.org/10.1261/rna.068437.118), and the distance bands of their
2017 survey (above). The ligand sphere of the bond-valence sums and the reading of halides by the donors
around them follow N. Echols, N. Morshed, P. V. Afonine, A. J. McCoy, M. D. Miller, R. J. Read,
J. S. Richardson, T. C. Terwilliger and P. D. Adams, "Automated identification of elemental ions in
macromolecular crystal structures" (2014), Acta Cryst. D70, 1104-1114
[doi:10.1107/S1399004714001308](https://doi.org/10.1107/S1399004714001308), and the halide's positive and
negative neighbours N. Morshed, N. Echols and P. D. Adams, "Using support vector machines to improve elemental
ion identification in macromolecular crystal structures" (2015), Acta Cryst. D71, 1147-1158
[doi:10.1107/S1399004715004241](https://doi.org/10.1107/S1399004715004241); the chloride's shell of donors
at up to 3.4 Å is O. Carugo's, "Buried chloride stereochemistry in the Protein Data Bank" (2014), BMC
Struct. Biol. 14, 19 [doi:10.1186/s12900-014-0019-8](https://doi.org/10.1186/s12900-014-0019-8). The
bond-valence sums are I. D. Brown and D. Altermatt's, "Bond-valence parameters obtained from a systematic
analysis of the Inorganic Crystal Structure Database" (1985), Acta Cryst. B41, 244-247
[doi:10.1107/S0108768185002063](https://doi.org/10.1107/S0108768185002063), with the R₀ of N. E. Brese and
M. O'Keeffe, "Bond-valence parameters for solids" (1991), Acta Cryst. B47, 192-197
[doi:10.1107/S0108768190011041](https://doi.org/10.1107/S0108768190011041), as tabulated by H. Zheng,
K. M. Langner, G. P. Shields, J. Hou, M. Kowiel, F. H. Allen, G. Murshudov and W. Minor, "Data mining of
iron(II) and iron(III) bond-valence parameters, and their relevance for macromolecular crystallography"
(2017), Acta Cryst. D73, 316-325 [doi:10.1107/S2059798317000584](https://doi.org/10.1107/S2059798317000584),
weighted by occupancy as P. Müller, S. Köpke and G. M. Sheldrick weight them, "Is the bond-valence method
able to identify metal atoms in protein structures?" (2003), Acta Cryst. D59, 32-37
[doi:10.1107/S0907444902018000](https://doi.org/10.1107/S0907444902018000); their normalised vector sum and
its outlier bound are CheckMyMetal's: H. Zheng, D. R. Cooper, P. J. Porebski, I. G. Shabalin, K. B. Handing
and W. Minor, "CheckMyMetal: a macromolecular metal-binding validation tool" (2017), Acta Cryst. D73, 223-233
[doi:10.1107/S2059798317001061](https://doi.org/10.1107/S2059798317001061). The score that combines them is
our own. The divalent ion's place on a purine N7 - in the base's plane, 3.5-3.9 Å from its O6 or N6 - is the test of
Leonarski et al. (2017, above). A light ion is told from a water by a density above the waters', as Echols et al.
(2014, above) flag one; a halide's few or no donors are allowed as Z. Dauter and M. Dauter describe halides binding
also at hydrophobic surfaces, "Entering a new phase: using solvent halide ions in protein structure determination"
(2001), Structure 9, R21-R26 [doi:10.1016/S0969-2126(01)00565-2](https://doi.org/10.1016/S0969-2126(01)00565-2).
The anomalous scattering expected of each species is f″ at the data's wavelength by D. T. Cromer and D. A.
Liberman, "Anomalous dispersion calculations near to and on the long-wavelength side of an absorption edge"
(1981), Acta Cryst. A37, 267-268 [doi:10.1107/S0567739481000600](https://doi.org/10.1107/S0567739481000600),
with the corrections of L. Kissel and R. H. Pratt, "Corrections to tabulated anomalous-scattering factors"
(1990), Acta Cryst. A46, 170-175 [doi:10.1107/S0108767389010718](https://doi.org/10.1107/S0108767389010718), as
GEMMI computes them (its port of the Larch routines).

## Software and computing methods

Decoding bitshuffle+LZ4 images on the GPU, rather than decompressing them on the host and uploading
the result, follows Jon Wright (ESRF): "Experiences with GPU decompression for bitshuffle + LZ4
data", HDF5 User Group meeting (2021), and [bslz4decoders](https://github.com/jonwright/bslz4decoders).
The CUDA kernels in Jungfraujoch are its own, but the approach is his.

Removing the small islands of solvent from the bulk-solvent mask on the GPU labels the connected
components with a parallel union-find, following D. P. Playne and K. Hawick, "A New Algorithm for
Parallel Connected-Component Labelling on GPUs" (2018), IEEE Trans. Parallel Distrib. Syst. 29,
1217-1230 [doi:10.1109/TPDS.2018.2799216](https://doi.org/10.1109/TPDS.2018.2799216).

The FFT indexer's GPU peak search divides by a fixed window width with a reciprocal multiplication
corrected once by the exact remainder, which returns the correctly rounded quotient, following
P. W. Markstein, "Computation of elementary functions on the IBM RISC System/6000 processor"
(1990), IBM J. Res. Dev. 34, 111-119.

The per-frame scaling loops of the rotation merge are accelerated by Anderson acceleration in the
type-II form analysed by Walker and Ni: H. F. Walker and P. Ni, "Anderson acceleration for fixed-point
iterations" (2011), SIAM J. Numer. Anal. 49, 1715-1735
[doi:10.1137/10078356X](https://doi.org/10.1137/10078356X), after D. G. Anderson, "Iterative
procedures for nonlinear integral equations" (1965), J. ACM 12, 547-560
[doi:10.1145/321296.321305](https://doi.org/10.1145/321296.321305).

The interval the report gives for ISa comes from a bootstrap over the unique reflections:
B. Efron, "Bootstrap methods: another look at the jackknife" (1979), Ann. Statist. 7, 1-26
[doi:10.1214/aos/1176344552](https://doi.org/10.1214/aos/1176344552). Its draws are Poisson weights
hashed from the replicate and the reflection with the SplitMix64 finaliser of G. L. Steele Jr.,
D. Lea and C. H. Flood, "Fast splittable pseudorandom number generators" (2014), Proc. OOPSLA 2014,
453-472 [doi:10.1145/2660193.2660195](https://doi.org/10.1145/2660193.2660195).

The single-precision exp the Bragg integration's profile fit shares between the CPU and an Apple GPU
(`BraggExp.h`) is built from textbook error-free floating-point arithmetic: the argument reduction of
W. J. Cody and W. Waite, "Software Manual for the Elementary Functions" (1980), Prentice-Hall; the
exact product (with Veltkamp's split) and Fast2Sum of T. J. Dekker, "A floating-point technique for
extending the available precision" (1971), Numer. Math. 18, 224-242; and the 2Sum of D. E. Knuth,
"The Art of Computer Programming, Vol. 2: Seminumerical Algorithms", section 4.2.2.

This software uses the Viridis, Magma and Inferno colormaps from Matplotlib under its
BSD-compatible license. J. D. Hunter, "Matplotlib: A 2D graphics environment" (2007), Comput. Sci.
Eng. 9, 90-95 [doi:10.1109/MCSE.2007.55](https://doi.org/10.1109/MCSE.2007.55).

The Mol* structure viewer of the web frontend follows the setup Guillaume Gotthard (PSI) tuned for
[AareDB](https://gitea.psi.ch/mx/aaredb), the sample-management and data-pipeline system of the PSI MX
beamlines: its Coot-style mouse controls and trackball, the model representations and colours, and the
display of the density maps (carved wireframe meshes at absolute levels from the whole cell's
statistics, contour-level defaults and colours).

## File formats read from a published specification

**CBF / imgCIF** - the native miniCBF reader implements the `x-CBF_BYTE_OFFSET` compression scheme
and reads the imgCIF `_axis` table (the laboratory directions of the image's fast and slow pixel
directions, of the goniometer axes and of a 2theta arm) from the specification alone; no CBFlib or
other CBF code is used, so there is no licence obligation, only this credit.
H. J. Bernstein and A. P. Hammersley, "Specification of the Crystallographic Binary File
(CBF/imgCIF)" (2006), International Tables for Crystallography Vol. G, 37-43
[doi:10.1107/97809553602060000729](https://doi.org/10.1107/97809553602060000729);
A. P. Hammersley, H. J. Bernstein and J. D. Westbrook, "Image dictionary (imgCIF)" (2006),
International Tables for Crystallography Vol. G, 444-458
[doi:10.1107/97809553602060000746](https://doi.org/10.1107/97809553602060000746).

**d\*TREK SMV** - the SMV reader reads the d\*TREK header vocabulary written by Rigaku's
CrystalClear (Saturn and R-AXIS detectors: detector and spatial-distortion vectors, detector
circles, 2theta arm, encoded overflows) from the headers themselves, interpreting the detector
vectors as dxtbx does for these detectors; no d\*TREK or dxtbx code is used.
J. W. Pflugrath, "The finer things in X-ray diffraction data collection" (1999), Acta Cryst. D55,
1718-1725 [doi:10.1107/S090744499900935X](https://doi.org/10.1107/S090744499900935X);
[dxtbx](https://github.com/cctbx/dxtbx): J. M. Parkhurst, A. S. Brewster, L. Fuentes-Montero,
D. G. Waterman et al., "dxtbx: the diffraction experiment toolbox" (2014), J. Appl. Cryst. 47,
1459-1465 [doi:10.1107/S1600576714011996](https://doi.org/10.1107/S1600576714011996).

## Public diffraction data used for testing

In addition to in-house datasets collected at SLS 2.0, Jungfraujoch is tested against public
diffraction data collected on other people's beamlines, on detectors and in file formats we do not
produce ourselves - most of it at other facilities, a few sets at the Swiss Light Source but not by
this system. That data was collected and published by other people. Every dataset used, the DOI to
cite for it, and the deposition it belongs to are listed in
[EXTERNAL_TEST_DATA](EXTERNAL_TEST_DATA.md); we thank the depositors, and the repositories that make
the data findable and citable.

**[IRRMC](https://proteindiffraction.org/)**, the Integrated Resource for Reproducibility in
Macromolecular Crystallography (Minor lab, University of Virginia), is the source of most of them.
IRRMC releases its data under CC0 and asks that the DOI of the dataset be
cited. M. Grabowski, K. M. Langner, M. Cymborowski, P. J. Porebski, P. Sroka, H. Zheng,
D. R. Cooper, M. D. Zimmerman, M.-A. Elsliger, S. K. Burley and W. Minor, "A public database of
macromolecular diffraction experiments" (2016), Acta Cryst. D72, 1181-1193
[doi:10.1107/S2059798316014716](https://doi.org/10.1107/S2059798316014716); M. Grabowski,
M. Cymborowski, P. J. Porebski, T. Osinski, I. G. Shabalin, D. R. Cooper and W. Minor, "The
Integrated Resource for Reproducibility in Macromolecular Crystallography: Experiences of the first
four years" (2019), Struct. Dyn. 6, 064301
[doi:10.1063/1.5128672](https://doi.org/10.1063/1.5128672).

**[SBGrid Data Bank](https://data.sbgrid.org/)**, the structural biology community's data
publication service (SBGrid Consortium, Harvard Medical School). P. A. Meyer,
S. Socias, J. Key, E. Ransey, E. C. Tjon, A. Buschiazzo et al., "Data publication with the
structural biology data grid supports live analysis" (2016), Nat. Commun. 7, 10882
[doi:10.1038/ncomms10882](https://doi.org/10.1038/ncomms10882).

**[Zenodo](https://zenodo.org/)**, CERN's open repository, hosts datasets deposited there directly
by the groups that collected them. European Organization for Nuclear Research and OpenAIRE,
"Zenodo" (2013), CERN [doi:10.25495/7GXK-RD71](https://doi.org/10.25495/7GXK-RD71). Some of those
deposits are described in IUCrData Raw Data Letters; the letters are cited on the
[EXTERNAL_TEST_DATA](EXTERNAL_TEST_DATA.md) page, beside the datasets they describe.

**[CXIDB](https://cxidb.org/)**, the Coherent X-ray Imaging Data Bank, is the source of the serial
(XFEL stills) datasets of the still battery, listed with their DOIs on
[EXTERNAL_TEST_DATA_STILLS](EXTERNAL_TEST_DATA_STILLS.md). F. R. N. C. Maia, "The Coherent X-ray
Imaging Data Bank" (2012), Nat. Methods 9, 854-855
[doi:10.1038/nmeth.2110](https://doi.org/10.1038/nmeth.2110).

**[MXRDR](https://mxrdr.icm.edu.pl/)**, the Macromolecular Xtallography Raw Data Repository
(ICM, University of Warsaw), releases its data under CC0 and asks that the DOI of the dataset be
cited.

**[XRDa](https://xrda.pdbj.org/)**, the Xtal Raw Data Archive (Protein Data Bank Japan), which
publishes raw diffraction images - X-ray, electron and neutron - and mints a DOI for each; it asks
that the DOI of the dataset be cited. It has no canonical citation paper.

**The [ESRF data portal](https://data.esrf.fr/)**, through which the European Synchrotron
publishes raw data under its data policy (CC BY 4.0, with the dataset DOI to be cited).
R. Dimper, A. Götz, A. De Maria, V. A. Solé, M. Chaillet and B. Lebayle, "ESRF Data Policy,
Storage, and Services" (2019), Synchrotron Rad. News 32, 7-12
[doi:10.1080/08940886.2019.1608119](https://doi.org/10.1080/08940886.2019.1608119).

**The [Keele University research data repository](https://researchdata.keele.ac.uk/)** and
**[UQ eSpace](https://espace.library.uq.edu.au/)** (The University of Queensland), which host the
raw images of datasets deposited there by the groups that collected them; the dataset DOIs are
cited on the [EXTERNAL_TEST_DATA](EXTERNAL_TEST_DATA.md) page.

The beamline, resolution, space group and unit cell quoted for each dataset are the values
deposited with the corresponding PDB entry, read from the RCSB PDB data API. H. M. Berman,
J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov and P. E. Bourne,
"The Protein Data Bank" (2000), Nucleic Acids Res. 28, 235-242
[doi:10.1093/nar/28.1.235](https://doi.org/10.1093/nar/28.1.235).

**The [AlphaFold Protein Structure Database](https://alphafold.ebi.ac.uk/)** (EMBL-EBI and Google
DeepMind) supplies the start models of the battery's timing benchmark: the predictions of horse
myoglobin (AF-P68082-F1) and bovine cytochrome c (AF-P62894-F1), model version 6, with their predicted
aligned error, kept unmodified in `tools/battery/models/` under CC BY 4.0. J. Jumper, R. Evans,
A. Pritzel et al., "Highly accurate protein structure prediction with AlphaFold" (2021), Nature 596,
583-589 [doi:10.1038/s41586-021-03819-2](https://doi.org/10.1038/s41586-021-03819-2); M. Varadi,
S. Anyango, M. Deshpande et al., "AlphaFold Protein Structure Database: massively expanding the
structural coverage of protein-sequence space with high-accuracy models" (2022), Nucleic Acids Res. 50,
D439-D444 [doi:10.1093/nar/gkab1061](https://doi.org/10.1093/nar/gkab1061); M. Varadi, D. Bertoni,
P. Magana et al., "AlphaFold Protein Structure Database in 2024: providing structure coverage for over
214 million protein sequences" (2024), Nucleic Acids Res. 52, D368-D375
[doi:10.1093/nar/gkad1011](https://doi.org/10.1093/nar/gkad1011). Its third start model is the
deposited model of PDB entry 4NWV, moved away from its place.

## Generative AI usage declaration

Large language models were used extensively in developing this code. Jungfraujoch development was
supported with JetBrains AI (mostly GPT models) to refactor and verify particular code fragments.
Rugnux was developed with the assistance of Claude Code (mostly the Opus model). This documentation
was written with the assistance of Claude Opus and Fable models.