#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
Date 2006-07-10 Time 20:55:31 PDT -0700


##-------------------------------------------##
## WARNING:                                  ##
## Number of residues unspecified            ##
##-------------------------------------------##


Effective parameters: 
scaling.input {
  parameters {
    asu_contents {
      n_residues = None
      n_bases = None
      n_copies_per_asu = None
    }
    misc_twin_parameters {
      missing_symmetry {
        tanh_location = 0.08
        tanh_slope = 50
      }
      twinning_with_ncs {
        perform_analyses = True
        n_bins = 7
      }
      twin_test_cuts {
        low_resolution = 10
        high_resolution = None
        isigi_cut = 3
        completeness_cut = 0.85
      }
    }
    reporting {
      verbose = 1
      log = "logfile.log"
      ccp4_style_graphs = True
    }
  }
  xray_data {
    file_name = "1upp_refine_001.mtz"
    obs_labels = OBS
    calc_labels = MODEL
    unit_cell = 155.8800049 156.25 199.75 90 90 90
    space_group = "C 2 2 21"
    high_resolution = None
    low_resolution = None
  }
}


Symmetry, cell and reflection file content summary

Miller array info: 1upp_refine_001.mtz:FOBS,SIGFOBS
Observation type: xray.amplitude
Type of data: double, size=108166
Type of sigmas: double, size=108166
Number of Miller indices: 108166
Anomalous flag: False
Unit cell: (155.88, 156.25, 199.75, 90, 90, 90)
Space group: C 2 2 21 (No. 20)
Systematic absences: 0
Centric reflections: 4807
Resolution range: 74.0507 2.09391
Completeness in resolution range: 0.758469
Completeness with d_max=infinity: 0.758442

##----------------------------------------------------##
##                    Basic statistics                ##
##----------------------------------------------------##


Matthews coefficient and Solvent content statistics

Number of residues unknown, assuming 50% solvent content

----------------------------------------------------------------
|              Best guess : 2225  residues in the asu          |
----------------------------------------------------------------


Completeness and data strength analyses 

  The following table lists the completeness in various resolution
  ranges, after applying a I/sigI cut. Miller indices for which
  individual I/sigI values are larger than the value specified in
  the top row of the table, are retained, while other intensities
  are discarded. The resulting completeness profiles are an indication
  of the strength of the data.

----------------------------------------------------------------------------------------
| Res. Range   | I/sigI>1  | I/sigI>2  | I/sigI>3  | I/sigI>5  | I/sigI>10 | I/sigI>15 |
----------------------------------------------------------------------------------------
| 74.10 - 5.16 | 98.4%     | 97.4%     | 96.9%     | 95.4%     | 89.6%     | 80.9%     |
|  5.16 - 4.10 | 95.6%     | 94.9%     | 94.5%     | 93.3%     | 88.2%     | 77.4%     |
|  4.10 - 3.58 | 79.7%     | 79.0%     | 78.4%     | 76.8%     | 71.0%     | 58.5%     |
|  3.58 - 3.25 | 72.9%     | 71.9%     | 71.2%     | 68.7%     | 59.0%     | 40.8%     |
|  3.25 - 3.02 | 71.4%     | 68.6%     | 67.1%     | 62.3%     | 47.2%     | 28.3%     |
|  3.02 - 2.84 | 70.6%     | 66.6%     | 64.6%     | 58.7%     | 40.2%     | 21.2%     |
|  2.84 - 2.70 | 69.7%     | 63.9%     | 60.5%     | 52.4%     | 30.8%     | 14.3%     |
|  2.70 - 2.58 | 68.7%     | 60.3%     | 56.2%     | 46.6%     | 25.2%     | 10.5%     |
|  2.58 - 2.48 | 68.2%     | 58.4%     | 53.7%     | 41.4%     | 19.0%     | 6.3%      |
|  2.48 - 2.40 | 68.0%     | 56.1%     | 50.2%     | 37.3%     | 13.7%     | 3.8%      |
|  2.40 - 2.32 | 67.2%     | 53.5%     | 46.9%     | 32.6%     | 11.5%     | 3.1%      |
|  2.32 - 2.26 | 66.2%     | 48.7%     | 41.2%     | 26.6%     | 8.2%      | 1.8%      |
|  2.26 - 2.20 | 65.7%     | 46.1%     | 37.9%     | 22.8%     | 5.5%      | 0.9%      |
|  2.20 - 2.14 | 65.4%     | 43.2%     | 34.5%     | 19.4%     | 3.7%      | 0.5%      |
----------------------------------------------------------------------------------------



Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of 1upp_refine_001.mtz:FOBS,SIGFOBS:
17.86 A**(-2)
Estimated -log of scale factor of 1upp_refine_001.mtz:FOBS,SIGFOBS:
 0.97


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of 1upp_refine_001.mtz:FOBS,SIGFOBS:
19.15,  0.00,  0.00
       19.25,  0.00
              16.40
Equivalent representation as U_cif: 
 0.24, -0.00, -0.00
        0.24,  0.00
               0.21

ML estimate of  -log of scale factor of 1upp_refine_001.mtz:FOBS,SIGFOBS:
 0.97
Correcting for anisotropy in the data

Some basic intensity statistics follow.



Low resolution completeness analyses 

 The following table shows the completeness
 of the data to 5 Angstrom.
unused:         - 74.0588 [   0/5   ] 0.000
bin  1: 74.0588 - 10.7622 [1152/1174] 0.981
bin  2: 10.7622 -  8.5464 [1075/1085] 0.991
bin  3:  8.5464 -  7.4672 [1089/1093] 0.996
bin  4:  7.4672 -  6.7850 [1086/1089] 0.997
bin  5:  6.7850 -  6.2990 [1081/1086] 0.995
bin  6:  6.2990 -  5.9277 [1064/1072] 0.993
bin  7:  5.9277 -  5.6310 [1051/1060] 0.992
bin  8:  5.6310 -  5.3859 [1060/1068] 0.993
bin  9:  5.3859 -  5.1787 [1066/1076] 0.991
bin 10:  5.1787 -  5.0000 [1049/1059] 0.991
unused:  5.0000 -         [   0/0   ]



Mean intensity analyses 
 Analyses of the mean intensity. 
 Inspired by: Morris et al. (2004). J. Synch. Rad.11, 56-59.
 The following resolution shells are worrisome: 
------------------------------------------------
| d_spacing | z_score | compl. | <Iobs>/<Iexp> |
------------------------------------------------
|    3.131  |   5.87  |   0.72 |     0.847     |
------------------------------------------------

 Possible reasons for the presence of the reported
 unexpected low or elevated mean intensity in
 a given resolution bin are : 
 - missing overloaded or weak reflections
 - suboptimal data processing
 - satelite (ice) crystals
 - NCS
 - translational pseudo symmetry (detected elsewhere)
 - outliers (detected elsewhere)
 - ice rings (detected elsewhere)
 - other problems
 Note that the presence of abnormalities 
 in a certain region of reciprocal space might
 confuse the data validation algorithm throughout
 a large region of reciprocal space, even though
 the data is acceptable in those areas. 


Possible outliers 
  Inspired by: Read, Acta Cryst. (1999). D55, 1759-1764

 Acentric reflections:

-----------------------------------------------------------------
| d_space |      H     K     L |  |E|  | p(wilson) | p(extreme) |
-----------------------------------------------------------------
|   2.265 |      8,    8,   87 |  4.12 |  4.29e-08 |   4.39e-03 |
|   4.229 |     26,   26,    4 |  4.17 |  2.78e-08 |   2.85e-03 |
|   2.343 |     45,   49,    4 |  3.83 |  4.19e-07 |   4.21e-02 |
|   2.256 |     48,   48,   17 |  3.78 |  6.24e-07 |   6.20e-02 |
-----------------------------------------------------------------

 p(wilson)  : 1-(1-exp[-|E|^2]) 
 p(extreme) : 1-(1-exp[-|E|^2])^(n_acentrics)
 p(wilson) is the probability that an E-value of the specified
 value would be observed when it would selected at random from
 the given data set.
 p(extreme) is the probability that the largest |E| value is 
 larger or equal then the observed largest |E| value.

 Both measures can be used for outlier detection. p(extreme)
 takes into account the size of the dataset.


 Centric reflections:

            None 


Ice ring related problems

 The following statistics were obtained from ice-ring 
 insensitive resolution ranges 
  mean bin z_score      : 1.59
      ( rms deviation   : 1.23 )
  mean bin completeness : 0.78
     ( rms deviation   : 0.17 )

 The following table shows the z-scores 
 and completeness in ice-ring sensitive areas.
 Large z-scores and high completeness in these 
 resolution ranges might be a reason to re-assess
 your data processsing if ice rings were present.

------------------------------------------------
| d_spacing | z_score | compl. | Rel. Ice int. |
------------------------------------------------
|    3.897  |   1.62  |   0.81 |     1.000     |
|    3.669  |   1.47  |   0.76 |     0.750     |
|    3.441  |   3.58  |   0.72 |     0.530     |
|    2.671  |   1.48  |   0.72 |     0.170     |
|    2.249  |   0.89  |   0.73 |     0.390     |
------------------------------------------------

 Abnormalities in mean intensity or completeness at
 resolution ranges with a relative ice ring intensity
 lower then 0.10 will be ignored.

 No ice ring related problems detected.
 If ice rings were present, the data does not look
 worse at ice ring related d_spacings as compared
 to the rest of the data set 




Basic analyses completed

##----------------------------------------------------##
##                   Twinning Analyses                ##
##----------------------------------------------------##



Using data between 10.00 to 4.10 Angstrom.

Determining possible twin laws.

The following twin laws have been found:

-------------------------------------------------------------------------------
| Type | Axis   | R metric (%) | delta (le Page) | delta (Lebedev) | Twin law |
-------------------------------------------------------------------------------
|  PM  | 2-fold | 0.090        | 0.136           | 0.002           | -k,-h,-l |
-------------------------------------------------------------------------------
M:  Merohedral twin law
PM: Pseudomerohedral twin law

  0 merohedral twin operators found
  1 pseudo-merohedral twin operators found
In total,   1 twin operator were found


Number of centrics  : 1540
Number of acentrics : 16075

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.500    0.000    0.500
 Distance to origin  : 126.687
 Height (origin=100) :  44.250
 p_value(height)     :   1.568e-04

   The reported p_value has the following meaning: 
     The probability that a peak of the specified height 
     or larger is found in a Patterson function of a 
     macro molecule that does not have any translational
     pseudo symmetry is equal to  1.568e-04 
     p_values smaller then 0.05 might indicate 
     weak translation pseudo symmetry, or the self vector of 
     a large anomalous scatterer such as Hg, whereas values 
     smaller then 1e-3 are a very strong indication for 
     the presence of translational pseudo symmetry.


The full list of patterson peaks is: 

  x      y      z            height   p-value(height)
( 0.500, 0.000, 0.500 ) :   44.250   (1.568e-04)
(-0.000, 0.000, 0.215 ) :    2.898   (1.000e-00)


Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :2.092   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.800   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.728   (untwinned: 0.736; perfect twin 0.541)


Centric reflections 
   <I^2>/<I>^2    :2.896   (untwinned: 3.000; perfect twin 2.000)
   <F>^2/<F^2>    :0.693   (untwinned: 0.637; perfect twin 0.785)
   <|E^2 - 1|>    :0.859   (untwinned: 0.968; perfect twin 0.736)



NZ test (0<=z<1) to detect twinning and possible translational NCS


-----------------------------------------------
|  Z  | Nac_obs | Nac_theo | Nc_obs | Nc_theo |
-----------------------------------------------
| 0.0 |   0.000 |    0.000 |  0.000 |   0.000 |
| 0.1 |   0.051 |    0.095 |  0.164 |   0.248 |
| 0.2 |   0.138 |    0.181 |  0.278 |   0.345 |
| 0.3 |   0.226 |    0.259 |  0.371 |   0.419 |
| 0.4 |   0.308 |    0.330 |  0.440 |   0.474 |
| 0.5 |   0.384 |    0.394 |  0.505 |   0.520 |
| 0.6 |   0.455 |    0.451 |  0.564 |   0.561 |
| 0.7 |   0.519 |    0.503 |  0.608 |   0.597 |
| 0.8 |   0.571 |    0.551 |  0.645 |   0.629 |
| 0.9 |   0.616 |    0.593 |  0.676 |   0.657 |
| 1.0 |   0.656 |    0.632 |  0.706 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.044    |
| Maximum deviation centric       :  0.084    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : -0.006    |
| <NZ(obs)-NZ(twinned)>_centric   : -0.016    |
-----------------------------------------------


 L test for acentric data

 using difference vectors (dh,dk,dl) of the form: 
(2hp,2kp,2lp)
  where hp, kp, and lp are random signed integers such that 
  2 <= |dh| + |dk| + |dl| <= 8 

  Mean |L|   :0.429  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.256  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.11. Note that this estimate is not as reliable as obtained
  via a Britton plot or H-test if twin laws are available. 



---------------------------------------------
 Analysing possible twin law :  -k,-h,-l
---------------------------------------------


Results of the H-test on a-centric data: 

 (Only 50.0% of the strongest twin pairs were used)

mean |H| : 0.038   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.002   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.462
Estimation of twin fraction via cum. dist. of H: 0.467



Britton analyses

  Extrapolation performed on  0.47 < alpha < 0.495 
  Estimated twin fraction: 0.452
  Correlation: 0.9939

R vs R statistic:
  R_abs_twin = <|I1-I2|>/<|I1+I2|>
  Lebedev, Vagin, Murshudov. Acta Cryst. (2006). D62, 83-95

   R_abs_twin observed data   : 0.040
   R_abs_twin calculated data : 0.303

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.002
   R_sq_twin calculated data  : 0.105



Maximum Likelihood twin fraction determination
    Zwart, Read, Grosse-Kunstleve & Adams, to be published.


   The estimated twin fraction is equal to 0.467


Estimation of twin fraction, while taking into account the
effects of possible NCS parallel to the twin axis.
    Zwart, Read, Grosse-Kunstleve & Adams, to be published.

  A parameters D_ncs will be estimated as a function of resolution,
  together with a global twin fraction.
  D_ncs is an estimate of the correlation coefficient between
  untwinned, error-free, twin related, normalized intensities.
  Large values (0.95) could indicate an incorrect point group.
  Value of D_ncs larger than say, 0.5, could indicate the presence
  of NCS. The twin fraction should be smaller or similar to other
  estimates given elsewhere.

  The refinement can take some time. 
  For numerical stability issues, D_ncs is limited between 0 and 0.95.
  The twin fraction is allowed to vary between 0 and 0.45.
  Refinement cycle numbers are printed out to keep you entertained.

. . . .   5  . . . .  10  . . . .  15  . . . .  20  . . . .  25  . . . .  30 
. . . .  35  . . . .  40  . . . .  45  . . . .  50  . . . .  55  . . . .  60 
. . . .  65  . . . .  70  . . . .  75  . . . .  80  . . . .  85  . . . .  90 
.

  Cycle :  91
  -----------
  Log[likelihood]:       81690.143
  twin fraction: 0.405
  D_ncs in resolution ranges: 
     9.9974 -- 6.9861 :: 0.948
     6.9861 -- 5.9017 :: 0.933
     5.9017 -- 5.2791 :: 0.916
     5.2791 -- 4.8567 :: 0.890
     4.8567 -- 4.5436 :: 0.884
     4.5436 -- 4.2982 :: 0.851
     4.2982 -- 4.0985 :: 0.826

 The correlation of the calculated F^2 should be similar to 
 the estimated values. 

 Observed correlation between twin related, untwinned calculated F^2
 in resolutiuon ranges, as well as ewstimates D_ncs^2 values:
 Bin    d_max     d_min     CC_obs   D_ncs^2 
  1)    9.9974 -- 6.9861 ::  0.924    0.898
  2)    6.9861 -- 5.9017 ::  0.799    0.871
  3)    5.9017 -- 5.2791 ::  0.719    0.840
  4)    5.2791 -- 4.8567 ::  0.683    0.791
  5)    4.8567 -- 4.5436 ::  0.572    0.781
  6)    4.5436 -- 4.2982 ::  0.606    0.725
  7)    4.2982 -- 4.0985 ::  0.419    0.682


Exploring higher metric symmetry

The point group of data as dictated by the space group is C 2 2 2
  the point group in the niggli setting is Hall:  C 2 2 (x-y,x+y,z)
The point group of the lattice is P 4 2 2
A summary of R values for various possible point groups follow.

-----------------------------------------------------------------------------------------------
| Point group              | mean R_used | max R_used | mean R_unused | min R_unused | choice |
-----------------------------------------------------------------------------------------------
| Hall:  C 2 2 (x-y,x+y,z) | None        | None       | 0.040         | 0.040        |        |
| P 4 2 2                  | 0.040       | 0.040      | None          | None         | <---   |
-----------------------------------------------------------------------------------------------

R_used: mean and maximum R value for symmetry operators *used* in this point group
R_unused: mean and minimum R value for symmetry operators *not used* in this point group
 The likely point group of the data is:  P 4 2 2

Possible space groups in this point groups are:
   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 41 2 2 (No. 91)

   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 41 21 2 (No. 92)

   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 42 2 2 (No. 93)

   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 42 21 2 (No. 94)

   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 43 2 2 (No. 95)

   Unit cell: (110.355, 110.355, 199.75, 90, 90, 90)
   Space group: P 43 21 2 (No. 96)

Note that this analyses does not take into account the effects of twinning.
If the data is (allmost) perfectly twinned, the symmetry will appear to be
higher than it actually is.





-------------------------------------------------------------------------------
Twinning and intensity statistics summary (acentric data):

Statistics independent of twin laws
  - <I^2>/<I>^2 : 2.092
  - <F>^2/<F^2> : 0.800
  - <|E^2-1|>   : 0.728
  - 
, <L^2>: 0.429, 0.256
       Multivariate Z score L-test: 5.314 
       The multivariate Z score is a quality measure of the given
       spread in intensities. Good to reasonable data is expected
       to have a Z score lower than 3.5. 
       Large values can indicate twinning, but small values do not
       neccesarily exclude it. 


Statistics depending on twin laws
-----------------------------------------------------------------------------------
| Operator | type | R_abs obs. | R_abs calc. | Britton alpha | H alpha | ML alpha |
-----------------------------------------------------------------------------------
| -k,-h,-l |  PM  | 0.040      | 0.303       | 0.452         | 0.467   | 0.467    |
-----------------------------------------------------------------------------------

Patterson analyses
  - Largest peak height   : 44.250
   (correpsonding p value : 1.568e-04)


The analyses of the Patterson function reveals a significant off-origin
peak that is 44.25 % of the origin peak, indicating pseudo translational symmetry.
The chance of finding a peak of this or larger height by random in a 
structure without pseudo translational symmetry is equal to the 1.5682e-04.
The detected tranlational NCS is most likely also responsible for the elevated intensity ratio.
See the relevant section of the logfile for more details.
The results of the L-test indicate that the intensity statistics
are significantly different then is expected from good to reasonable,
untwinned data.
As there are twin laws possible given the crystal symmetry, twinning could
be the reason for the departure of the intensity statistics from normality.
It might be worthwhile carrying refinement with a twin specific target function.

Note that the symmetry of the intensities suggest that the assumed space group
is too low. As twinning is however suspected, it is not immediuatly clear if this
is the case. Carefull reprocessing and (twin)refinement for all cases might resolve
this question.

-------------------------------------------------------------------------------


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010004   2173074.723905   2060211.719024   1828295.734726
0.014004   1399630.496549   1484642.177178   1440245.060930
0.018004   1088874.706218   1104834.153961   1057611.608785
0.022004   978702.216816   971724.549878   906111.705758
0.026004   902454.085592   922787.735133   905629.729106
0.030004   948820.428083   1013034.199624   996607.969131
0.034004   1172880.967887   1153407.579061   1210614.996362
0.038004   1511567.622054   1424617.385898   1551270.800150
0.042004   1851306.051963   1979848.610195   1937096.144924
0.046004   2109008.265514   2181905.551719   2253933.367114
0.050004   2262378.230676   2284745.812483   2431445.185704
0.054004   2333790.295884   2269538.691848   2472803.442374
0.058004   2357752.362695   2231908.127410   2431343.115979
0.062004   2356897.907356   2380132.736379   2366920.755141
0.066004   2335560.698101   2435070.645952   2314435.551783
0.070004   2286907.934425   2270431.965729   2277014.009775
0.074004   2204327.953430   2130933.077289   2237938.242123
0.078004   2089242.452907   2080693.521689   2178054.672900
0.082004   1952187.567166   1824475.602368   2087977.605458
0.086004   1808477.011861   1773458.303822   1971177.913164
0.090004   1672080.534194   1730728.551689   1839890.301795
0.094004   1551221.036457   1692275.698601   1708333.923612
0.098004   1447452.245674   1417738.577958   1587233.216321
0.102004   1357873.545524   1255141.640573   1481547.194182
0.106004   1278703.962536   1239178.783391   1391213.940007
0.110004   1208149.771544   1265588.875051   1313504.243060
0.114004   1147238.803006   1196283.244299   1245418.982994
0.118004   1098531.072471   1092728.810095   1185121.212814
0.122004   1063709.894362   1082823.983400   1132167.430544
0.126004   1041534.567935   1008092.077682   1086896.892408
0.130004   1027349.201724   975040.382582   1049575.349503
0.134004   1014492.631175   1050941.719928   1019798.046330
0.138004   996970.673712   1024115.724480   996383.518359
0.142004   972096.811251   939336.486323   977703.009222
0.146004   941781.324641   903774.326827   962208.879021
0.150004   911765.865800   895883.952367   948890.387395
0.154004   889080.372395   933200.318764   937469.956418
0.158004   878882.740874   878478.115145   928293.406098
0.162004   882188.174449   849196.843313   921996.506832
0.166004   895590.949519   887692.729526   919102.002224
0.170004   913071.241442   882850.466698   919702.326731
0.174004   928849.833501   970830.606810   923328.149735
0.178004   939640.171881   949807.234741   929022.406697
0.182004   945013.619641   923306.044148   935566.355596
0.186004   945896.817461   940360.799197   941761.775966
0.190004   942746.525194   919418.423211   946670.137729
0.194004   935508.570886   914677.786235   949739.405501
0.198004   926060.669390   972011.772921   950796.590314
0.202004   920674.214990   941193.253971   949930.970393
0.206004   927464.913437   900007.200398   947324.308986
0.210004   946203.844901   954616.087809   943092.999302
0.214004   958789.591659   976496.264764   937193.746228
0.218004   943129.438862   922040.369474   929416.600439
0.222004   922113.102208   930264.243722   919457.575460
0.226004   943850.927607   922574.989946   907037.928027
0.228079   873950.321992   662454.323210   899576.200631
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010004   1.458461   0.992771
0.014004   0.479509   0.992754
0.018004   0.815574   0.996364
0.022004   1.679258   0.995847
0.026004   0.451511   0.993884
0.030004   0.380958   0.990518
0.034004   1.207488   0.993956
0.038004   2.198576   0.989744
0.042004   0.558086   0.989571
0.046004   0.811837   0.982394
0.050004   1.586057   0.959551
0.054004   2.333759   0.935150
0.058004   2.547504   0.903987
0.062004   0.176660   0.862588
0.066004   1.623678   0.811330
0.070004   0.092624   0.787542
0.074004   1.562265   0.762767
0.078004   1.470595   0.762184
0.082004   4.423700   0.737265
0.086004   3.583463   0.723413
0.090004   2.121661   0.726964
0.094004   0.329716   0.724066
0.098004   4.004865   0.724857
0.102004   5.869765   0.717255
0.106004   4.036245   0.733307
0.110004   1.300936   0.725844
0.114004   1.443981   0.717678
0.118004   3.036329   0.716524
0.122004   1.717771   0.721551
0.126004   2.985197   0.716720
0.130004   2.886969   0.713109
0.134004   1.144759   0.716707
0.138004   1.023706   0.717958
0.142004   1.483415   0.720875
0.146004   2.329322   0.716293
0.150004   2.159375   0.710271
0.154004   0.176746   0.713231
0.158004   2.202014   0.713454
0.162004   3.378552   0.711945
0.166004   1.415921   0.719962
0.170004   1.656263   0.717472
0.174004   1.966091   0.721016
0.178004   0.851807   0.723502
0.182004   0.504549   0.715311
0.186004   0.056646   0.716342
0.190004   1.136893   0.724693
0.194004   1.489033   0.718458
0.198004   0.891778   0.727168
0.202004   0.382985   0.726476
0.206004   2.143563   0.722380
0.210004   0.505419   0.734896
0.214004   1.694847   0.728693
0.218004   0.324839   0.730737
0.222004   0.471598   0.734739
0.226004   0.641236   0.599893
0.228079   0.357861   0.011364
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.002182   18.498156
0.006182   22.474136
0.010182   25.225659
0.014182   25.469021
0.018182   23.569727
0.022182   23.145043
0.026182   22.790803
0.030182   22.677404
0.034182   22.921399
0.038182   23.361095
0.042182   25.013628
0.046182   24.247863
0.050182   23.789327
0.054182   23.450011
0.058182   22.685490
0.062182   22.702944
0.066182   21.579633
0.070182   20.315908
0.074182   19.635026
0.078182   18.701542
0.082182   16.649385
0.086182   15.616384
0.090182   15.580184
0.094182   15.212842
0.098182   13.656887
0.102182   12.736887
0.106182   12.514643
0.110182   12.651475
0.114182   11.743886
0.118182   11.110135
0.122182   10.605569
0.126182   9.900375
0.130182   9.562480
0.134182   9.438445
0.138182   9.300241
0.142182   8.382315
0.146182   7.976140
0.150182   7.719539
0.154182   7.447292
0.158182   6.859494
0.162182   6.410749
0.166182   6.310133
0.170182   5.973081
0.174182   6.203007
0.178182   5.710627
0.182182   5.311198
0.186182   5.215345
0.190182   4.727733
0.194182   4.615692
0.198182   4.451859
0.202182   4.284228
0.206182   3.801230
0.210182   3.880421
0.214182   3.699339
0.218182   3.366741
0.222182   3.255779
0.226182   3.069118
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.050949   0.095200   0.163636   0.248100
0.200000   0.137667   0.181300   0.277922   0.345300
0.300000   0.225879   0.259200   0.371429   0.418700
0.400000   0.307683   0.329700   0.439610   0.473800
0.500000   0.383764   0.393500   0.505195   0.520500
0.600000   0.455303   0.451200   0.563636   0.561400
0.700000   0.518818   0.503400   0.608442   0.597200
0.800000   0.571322   0.550700   0.644805   0.628900
0.900000   0.615739   0.593400   0.675974   0.657200
1.000000   0.656299   0.632100   0.706494   0.683300
$$


$TABLE: L test,acentric data:
$GRAPHS
:L test, acentric data 
:A:1,2,3,4:
$$
|l|   Observed   Acentric_theory   Acentric_theory,_perfect_twin   $$ 
$$
0.000000   0.006132   0.000000   0.000000
0.020000   0.030517   0.020000   0.029996
0.040000   0.056970   0.040000   0.059968
0.060000   0.079358   0.060000   0.089892
0.080000   0.105740   0.080000   0.119744
0.100000   0.129269   0.100000   0.149500
0.120000   0.154082   0.120000   0.179136
0.140000   0.177683   0.140000   0.208628
0.160000   0.201783   0.160000   0.237952
0.180000   0.224599   0.180000   0.267084
0.200000   0.249412   0.200000   0.296000
0.220000   0.272799   0.220000   0.324676
0.240000   0.297184   0.240000   0.353088
0.260000   0.319857   0.260000   0.381212
0.280000   0.345455   0.280000   0.409024
0.300000   0.369840   0.300000   0.436500
0.320000   0.391872   0.320000   0.463616
0.340000   0.417611   0.340000   0.490348
0.360000   0.439786   0.360000   0.516672
0.380000   0.461676   0.380000   0.542564
0.400000   0.485205   0.400000   0.568000
0.420000   0.508520   0.420000   0.592956
0.440000   0.531551   0.440000   0.617408
0.460000   0.555579   0.460000   0.641332
0.480000   0.577112   0.480000   0.664704
0.500000   0.600143   0.500000   0.687500
0.520000   0.621319   0.520000   0.709696
0.540000   0.642781   0.540000   0.731268
0.560000   0.663957   0.560000   0.752192
0.580000   0.684920   0.580000   0.772444
0.600000   0.703244   0.600000   0.792000
0.620000   0.723066   0.620000   0.810836
0.640000   0.744456   0.640000   0.828928
0.660000   0.765276   0.660000   0.846252
0.680000   0.785597   0.680000   0.862784
0.700000   0.804492   0.700000   0.878500
0.720000   0.823529   0.720000   0.893376
0.740000   0.841783   0.740000   0.907388
0.760000   0.859323   0.760000   0.920512
0.780000   0.876078   0.780000   0.932724
0.800000   0.890909   0.800000   0.944000
0.820000   0.905241   0.820000   0.954316
0.840000   0.920428   0.840000   0.963648
0.860000   0.933547   0.860000   0.971972
0.880000   0.947380   0.880000   0.979264
0.900000   0.958645   0.900000   0.985500
0.920000   0.970125   0.920000   0.990656
0.940000   0.981747   0.940000   0.994708
0.960000   0.990873   0.960000   0.997632
0.980000   0.997077   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -k,-h,-l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.000000   0.000000
0.019802   0.000000   0.000000
0.029703   0.000000   0.000000
0.039604   0.000000   0.000000
0.049505   0.000000   0.000000
0.059406   0.000000   0.000000
0.069307   0.000000   0.000000
0.079208   0.000000   0.000000
0.089109   0.000000   0.000000
0.099010   0.000000   0.000000
0.108911   0.000000   0.000000
0.118812   0.000000   0.000000
0.128713   0.000000   0.000000
0.138614   0.000000   0.000000
0.148515   0.000000   0.000000
0.158416   0.000000   0.000000
0.168317   0.000127   0.000000
0.178218   0.000127   0.000000
0.188119   0.000190   0.000000
0.198020   0.000190   0.000000
0.207921   0.000190   0.000000
0.217822   0.000190   0.000000
0.227723   0.000190   0.000000
0.237624   0.000253   0.000000
0.247525   0.000316   0.000000
0.257426   0.000443   0.000000
0.267327   0.000759   0.000000
0.277228   0.000949   0.000000
0.287129   0.001266   0.000000
0.297030   0.001392   0.000000
0.306931   0.001772   0.000000
0.316832   0.002088   0.000000
0.326733   0.002151   0.000000
0.336634   0.002721   0.000000
0.346535   0.003037   0.000000
0.356436   0.003670   0.000000
0.366337   0.004556   0.000000
0.376238   0.006138   0.000000
0.386139   0.007593   0.000000
0.396040   0.009428   0.000000
0.405941   0.011643   0.000000
0.415842   0.016325   0.000000
0.425743   0.021387   0.000000
0.435644   0.030246   0.000000
0.445545   0.045178   0.000000
0.455446   0.069856   0.027758
0.465347   0.113009   0.109804
0.475248   0.182928   0.191850
0.485149   0.279613   0.273896
$$


$TABLE: H test for possible twin law -k,-h,-l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.046824   0.000000
0.020000   0.364971   0.298806
0.040000   0.614528   0.597612
0.060000   0.794482   0.896418
0.080000   0.896988   1.000000
0.100000   0.952923   1.000000
0.120000   0.978740   1.000000
0.140000   0.989876   1.000000
0.160000   0.994432   1.000000
0.180000   0.997216   1.000000
0.200000   0.998734   1.000000
0.220000   0.998988   1.000000
0.240000   0.999241   1.000000
0.260000   0.999241   1.000000
0.280000   0.999747   1.000000
0.300000   0.999747   1.000000
0.320000   0.999747   1.000000
0.340000   0.999747   1.000000
0.360000   0.999747   1.000000
0.380000   1.000000   1.000000
0.400000   1.000000   1.000000
0.420000   1.000000   1.000000
0.440000   1.000000   1.000000
0.460000   1.000000   1.000000
0.480000   1.000000   1.000000
0.500000   1.000000   1.000000
0.520000   1.000000   1.000000
0.540000   1.000000   1.000000
0.560000   1.000000   1.000000
0.580000   1.000000   1.000000
0.600000   1.000000   1.000000
0.620000   1.000000   1.000000
0.640000   1.000000   1.000000
0.660000   1.000000   1.000000
0.680000   1.000000   1.000000
0.700000   1.000000   1.000000
0.720000   1.000000   1.000000
0.740000   1.000000   1.000000
0.760000   1.000000   1.000000
0.780000   1.000000   1.000000
0.800000   1.000000   1.000000
0.820000   1.000000   1.000000
0.840000   1.000000   1.000000
0.860000   1.000000   1.000000
0.880000   1.000000   1.000000
0.900000   1.000000   1.000000
0.920000   1.000000   1.000000
0.940000   1.000000   1.000000
0.960000   1.000000   1.000000
0.980000   1.000000   1.000000
$$


$TABLE: Likelihood based twin fraction estimation for possible twin law -k,-h,-l:
$GRAPHS
:Likelihood based twin fraction estimate 
:A:1,2:
$$
alpha   NLL_(acentric_data)   $$ 
$$
0.021739   31189.669008
0.043478   30456.339281
0.065217   29687.672462
0.086957   28880.421118
0.108696   28030.942232
0.130435   27133.207137
0.152174   26181.930659
0.173913   25170.414098
0.195652   24090.391007
0.217391   22932.185409
0.239130   21682.465973
0.260870   20325.680146
0.282609   18843.588052
0.304348   17212.932106
0.326087   15403.018067
0.347826   13380.429566
0.369565   11097.596993
0.391304   8502.482092
0.413043   5564.882663
0.434783   2445.976791
0.456522   124.576172
0.478261   2352.846555
$$