#############################################################
##                        mmtbx.xtriage                    ##
##                                                         ##
##      P.H. Zwart, R.W. Grosse-Kunstleve & P.D. Adams     ##
##                                                         ##
#############################################################
#phil __OFF__
  This cryptic code, together with the tags __ON__ and __OFF__
  allows one to use the log file as an input file for xtriage.
  Try : mmtbx.xtriage  <logfile> to give it a try!

Date 2006-08-28 Time 16:15:10 PDT -0700


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


Effective parameters: 
#phil __ON__
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 = False
        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 = "zza_pmt_srt-unique.mtz"
    obs_labels = "IMEAN,SIGIMEAN"
    calc_labels = None
    unit_cell = 53.02999878 71.96299744 27.9260006 98.63200378 104.3919983 \
                74.5719986
    space_group = "P 1"
    high_resolution = None
    low_resolution = None
    reference {
      data {
        file_name = None
        labels = None
        unit_cell = None
        space_group = None
      }
    }
  }
}
#phil __END__


Symmetry, cell and reflection file content summary

Miller array info: zza_pmt_srt-unique.mtz:IMEAN,SIGIMEAN
Observation type: xray.amplitude
Type of data: double, size=12907
Type of sigmas: double, size=12907
Number of Miller indices: 12907
Anomalous flag: False
Unit cell: (53.03, 71.963, 27.926, 98.632, 104.392, 74.572)
Space group: P 1 (No. 1)
Systematic absences: 0
Centric reflections: 0
Resolution range: 25.6734 2.40006
Completeness in resolution range: 0.859206
Completeness with d_max=infinity: 0.858635

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


Matthews coefficient and Solvent content statistics

Number of residues unknown, assuming 50% solvent content

----------------------------------------------------------------
|              Best guess :  363  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 |
----------------------------------------------------------------------------------------
| 25.67 - 5.90 | 87.3%     | 87.3%     | 87.2%     | 87.0%     | 84.9%     | 81.8%     |
|  5.90 - 4.69 | 92.1%     | 91.5%     | 91.4%     | 89.7%     | 87.3%     | 81.9%     |
|  4.69 - 4.10 | 94.2%     | 94.1%     | 93.9%     | 93.2%     | 90.7%     | 84.4%     |
|  4.10 - 3.73 | 94.1%     | 94.0%     | 93.7%     | 92.0%     | 86.7%     | 78.1%     |
|  3.73 - 3.46 | 94.3%     | 93.3%     | 92.7%     | 90.9%     | 82.7%     | 68.2%     |
|  3.46 - 3.26 | 93.2%     | 91.7%     | 90.5%     | 86.8%     | 75.5%     | 54.1%     |
|  3.26 - 3.09 | 92.6%     | 90.9%     | 88.9%     | 84.9%     | 71.3%     | 49.4%     |
|  3.09 - 2.96 | 90.6%     | 87.9%     | 85.4%     | 78.8%     | 58.2%     | 28.8%     |
|  2.96 - 2.85 | 88.4%     | 86.0%     | 80.5%     | 72.0%     | 42.4%     | 7.8%      |
|  2.85 - 2.75 | 86.4%     | 81.6%     | 74.9%     | 62.0%     | 29.4%     | 3.4%      |
|  2.75 - 2.66 | 83.3%     | 76.1%     | 68.2%     | 53.5%     | 20.2%     | 2.4%      |
|  2.66 - 2.59 | 81.1%     | 72.1%     | 63.2%     | 44.9%     | 11.9%     | 0.4%      |
|  2.59 - 2.52 | 78.0%     | 68.3%     | 55.5%     | 38.4%     | 9.7%      | 0.8%      |
|  2.52 - 2.46 | 72.3%     | 61.7%     | 48.7%     | 30.4%     | 4.6%      | 0.0%      |
----------------------------------------------------------------------------------------

  The completeness of data for which I/sig(I)>3.00, exceeds  85% for
  for resolution ranges lower than 2.96A.
  The data is cut at this resolution for the potential twin tests 
  and intensity statistics.


Maximum likelihood isotropic Wilson scaling 
ML estimate of overall B value of zza_pmt_srt-unique.mtz:IMEAN,SIGIMEAN:
40.91 A**(-2)
Estimated -log of scale factor of zza_pmt_srt-unique.mtz:IMEAN,SIGIMEAN:
-1.62


Maximum likelihood anisotropic Wilson scaling 
ML estimate of overall B_cart value of zza_pmt_srt-unique.mtz:IMEAN,SIGIMEAN:
41.77,  2.11, -6.92
       29.78, -0.38
              51.22
Equivalent representation as U_cif: 
 0.48, -0.07,  0.06
        0.38,  0.05
               0.65

ML estimate of  -log of scale factor of zza_pmt_srt-unique.mtz:IMEAN,SIGIMEAN:
-1.64
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:         - 25.6737 [  0/10 ] 0.000
bin  1: 25.6737 - 10.5435 [121/167] 0.725
bin  2: 10.5435 -  8.4673 [147/167] 0.880
bin  3:  8.4673 -  7.4266 [138/159] 0.868
bin  4:  7.4266 -  6.7612 [147/164] 0.896
bin  5:  6.7612 -  6.2842 [164/178] 0.921
bin  6:  6.2842 -  5.9185 [145/151] 0.960
bin  7:  5.9185 -  5.6253 [149/162] 0.920
bin  8:  5.6253 -  5.3828 [148/163] 0.908
bin  9:  5.3828 -  5.1773 [167/185] 0.903
bin 10:  5.1773 -  5.0000 [154/168] 0.917
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> |
------------------------------------------------
|    4.660  |   6.22  |   0.95 |     0.673     |
|    4.470  |   4.53  |   0.93 |     0.751     |
|    4.301  |   4.66  |   0.95 |     0.753     |
|    3.194  |   6.04  |   0.93 |     1.491     |
|    3.130  |   5.72  |   0.93 |     1.450     |
|    3.071  |   4.78  |   0.92 |     1.331     |
------------------------------------------------

 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) |
-----------------------------------------------------------------
|   2.666 |    -14,   12,    4 |  5.21 |  1.55e-12 |   1.98e-08 |
|   3.858 |      6,  -14,    0 |  3.44 |  7.47e-06 |   9.13e-02 |
|   2.654 |     16,   -4,    3 |  3.76 |  7.08e-07 |   9.03e-03 |
-----------------------------------------------------------------

 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      : 2.77
      ( rms deviation   : 1.69 )
  mean bin completeness : 0.86
     ( rms deviation   : 0.12 )

 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  |   0.70  |   0.95 |     1.000     |
|    3.669  |   1.62  |   0.95 |     0.750     |
|    3.441  |   0.41  |   0.95 |     0.530     |
|    2.671  |   0.76  |   0.85 |     0.170     |
------------------------------------------------

 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 2.96 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 | 5.268        | 2.559           | 0.037           | -h-l,-k-l,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  : 0
Number of acentrics : 7250

 Largest patterson peak with length larger then 15 Angstrom 

 Frac. coord.        :   0.462    0.070   -0.243
 Distance to origin  :  28.836
 Height (origin=100) :   7.219
 p_value(height)     :   4.594e-01

   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  4.594e-01 
     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.



Wilson ratio and moments 

Acentric reflections 
   <I^2>/<I>^2    :2.127   (untwinned: 2.000; perfect twin 1.500)
   <F>^2/<F^2>    :0.784   (untwinned: 0.785; perfect twin 0.885)
   <|E^2 - 1|>    :0.741   (untwinned: 0.736; perfect twin 0.541)



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 |   0.085 |    0.095 |  0.000 |   0.248 |
| 0.2 |   0.178 |    0.181 |  0.000 |   0.345 |
| 0.3 |   0.261 |    0.259 |  0.000 |   0.419 |
| 0.4 |   0.336 |    0.330 |  0.000 |   0.474 |
| 0.5 |   0.403 |    0.394 |  0.000 |   0.520 |
| 0.6 |   0.461 |    0.451 |  0.000 |   0.561 |
| 0.7 |   0.514 |    0.503 |  0.000 |   0.597 |
| 0.8 |   0.560 |    0.551 |  0.000 |   0.629 |
| 0.9 |   0.604 |    0.593 |  0.000 |   0.657 |
| 1.0 |   0.644 |    0.632 |  0.000 |   0.683 |
-----------------------------------------------
| Maximum deviation acentric      :  0.012    |
| Maximum deviation centric       :  0.683    |
|                                             |
| <NZ(obs)-NZ(twinned)>_acentric  : +0.005    |
| <NZ(obs)-NZ(twinned)>_centric   : -0.467    |
-----------------------------------------------


 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|   :0.480  (untwinned: 0.500; perfect twin: 0.375)
  Mean  L^2  :0.310  (untwinned: 0.333; perfect twin: 0.200)

  The distribution of |L| values indicates a twin fraction of
  0.02. 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 :  -h-l,-k-l,l
---------------------------------------------


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

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

mean |H| : 0.449   (0.50: untwinned; 0.0: 50% twinned)
mean H^2 : 0.288   (0.33: untwinned; 0.0: 50% twinned)
Estimation of twin fraction via mean |H|: 0.051
Estimation of twin fraction via cum. dist. of H: 0.045



Britton analyses

  Extrapolation performed on  0.00 < alpha < 0.495 
  Estimated twin fraction: 0.021
  Correlation: 0.9994

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   : 0.472

  R_sq_twin = <(I1-I2)^2>/<(I1+I2)^2>
   R_sq_twin observed data    : 0.290
  No calculated data available.
  R_twin for calculated data not determined.


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


   The estimated twin fraction is equal to 0.022



Exploring higher metric symmetry

The point group of data as dictated by the space group is P 1
  the point group in the niggli setting is P 1
The point group of the lattice is C 1 2 1 (-x+y,z,2*x-z)
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 |
---------------------------------------------------------------------------------------------
| C 1 2 1 (-x+y,z,2*x-z) | 0.472       | 0.472      | None          | None         |        |
| P 1                    | None        | None       | 0.472         | 0.472        | <---   |
---------------------------------------------------------------------------------------------

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 1

Possible space groups in this point groups are:
   Unit cell: (27.926, 53.03, 71.963, 74.572, 81.368, 75.608)
   Space group: P 1 (No. 1)

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 : 2.127
  - <F>^2/<F^2> : 0.784
  - <|E^2-1|>   : 0.741
  - 
, <L^2>: 0.480, 0.310
       Multivariate Z score L-test: 0.509 
       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 obs. | Britton alpha | H alpha | ML alpha |
--------------------------------------------------------------------
| -h-l,-k-l,l |  PM  | 0.472  | 0.021         | 0.045   | 0.022    |
--------------------------------------------------------------------

Patterson analyses
  - Largest peak height   : 7.219
   (correpsonding p value : 4.594e-01)


The largest off-origin peak in the Patterson function is 7.22% of the 
height of the origin peak. No significant pseudotranslation is detected.

The results of the L-test indicate that the intensity statistics
behave as expected. No twinning is suspected.
Even though no twinning is suspected, it might be worthwhile carrying out 
a refinement using a dedicated twin target anyway, as twinned structures with
low twin fractions are difficult to distinguish from non-twinned structures.


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


$TABLE: Intensity plots:
$GRAPHS
:Intensity plots 
:A:1,2,3,4:
$$
1/resol^2   <I>_smooth_approximation   <I>_via_binning   <I>_expected   $$ 
$$
0.010048   8.589184   29352.161386   37237.910847
0.014048   8.424577   20311.989686   29268.608526
0.018048   8.378625   22571.989358   21508.806259
0.022048   8.276274   19483.419955   18466.268883
0.026048   8.372087   20488.300544   18478.754184
0.030048   8.532229   25631.631975   20356.648534
0.034048   8.600429   28571.185138   24751.868385
0.038048   8.613027   25781.824690   31720.737123
0.042048   8.661499   29898.940449   39585.778451
0.046048   8.761420   30974.745312   46021.178295
0.050048   8.868378   37235.941043   49607.942580
0.054048   8.949148   37989.015392   50425.988263
0.058048   9.007445   42803.146101   49569.283349
0.062048   9.057894   39032.234410   48255.552253
0.066048   9.097744   45296.905107   47189.268919
0.070048   9.109995   48930.900817   46427.998479
0.074048   9.088269   41816.250213   45628.388366
0.078048   9.052301   40397.982758   44400.985815
0.082048   9.036413   43636.199462   42557.245153
0.086048   9.061289   41113.236496   40170.541074
0.090048   9.114655   49383.560586   37491.581267
0.094048   9.157714   43310.566649   34810.064136
0.098048   9.151765   48221.391454   32343.532814
0.102048   9.083030   43768.702158   30191.826393
0.106048   8.966615   37735.363009   28352.800216
0.110048   8.829129   35017.936289   26770.495392
0.114048   8.687774   26594.871415   25383.897028
0.118048   8.545682   24912.627747   24155.869868
0.122048   8.406561   22802.307795   23077.631670
0.126048   8.290640   19852.581803   22156.177004
0.130048   8.229019   17330.364626   21396.825506
0.134048   8.233831   18782.471885   20791.142466
0.138048   8.272263   19761.373433   20314.885439
0.142048   8.281402   20761.364427   19934.796576
0.146048   8.226177   17151.780894   19619.391005
0.150048   8.145055   17262.177067   19348.209776
0.154048   8.113732   16654.916890   19115.753794
0.158048   8.142690   17201.400490   18929.182503
0.162048   8.153219   17460.805499   18801.479995
0.166048   8.127399   16278.248758   18743.240185
0.170048   8.151415   17616.041336   18756.229536
0.173602   8.143970   16381.201443   18819.945458
$$


$TABLE: Z scores and completeness:
$GRAPHS
:Data sanity and completeness check 
:A:1,2,3:
$$
1/resol^2   Z_score   Completeness   $$ 
$$
0.010048   1.901162   0.857143
0.014048   3.747626   0.830189
0.018048   0.518469   0.939394
0.022048   0.628376   0.877005
0.026048   1.266917   0.960000
0.030048   2.658814   0.921951
0.034048   1.844263   0.904959
0.038048   3.106532   0.914729
0.042048   4.116134   0.935622
0.046048   6.216211   0.951493
0.050048   4.530035   0.930556
0.054048   4.657880   0.951724
0.058048   2.313432   0.930403
0.062048   3.817772   0.957055
0.066048   0.697865   0.951368
0.070048   0.865510   0.921283
0.074048   1.497679   0.927711
0.078048   1.617546   0.950000
0.082048   0.442187   0.949602
0.086048   0.410348   0.946381
0.090048   4.359501   0.920000
0.094048   3.620017   0.932642
0.098048   6.037176   0.930851
0.102048   5.716100   0.927083
0.106048   4.776968   0.922717
0.110048   4.414368   0.905569
0.114048   0.856112   0.910377
0.118048   0.572607   0.888631
0.122048   0.223879   0.867612
0.126048   2.146812   0.886747
0.130048   4.454694   0.843220
0.134048   2.052978   0.863539
0.138048   0.519390   0.820961
0.142048   0.758568   0.854077
0.146048   2.674046   0.808642
0.150048   2.195257   0.815965
0.154048   2.731971   0.806383
0.158048   1.943062   0.767355
0.162048   1.454049   0.761341
0.166048   2.619543   0.643287
0.170048   1.052161   0.537428
0.173602   1.402384   0.423256
$$


$TABLE: <I/sigma_I>:
$GRAPHS
:Signal to noise 
:N:1,2:
$$
1/resol^2   <I/sigma_I>;_Signal_to_noise   $$ 
$$
0.003517   22.510961
0.007517   24.689290
0.011517   24.111021
0.015517   24.490168
0.019517   24.344330
0.023517   23.918365
0.027517   24.466378
0.031517   23.683284
0.035517   22.928196
0.039517   23.562665
0.043517   23.533916
0.047517   23.574894
0.051517   23.140869
0.055517   22.955285
0.059517   22.971036
0.063517   22.044784
0.067517   20.975396
0.071517   21.000889
0.075517   19.810832
0.079517   17.331339
0.083517   15.456616
0.087517   14.879946
0.091517   15.185623
0.095517   14.427043
0.099517   14.741062
0.103517   13.021334
0.107517   12.024707
0.111517   11.393169
0.115517   10.007593
0.119517   9.464005
0.123517   8.641250
0.127517   8.160513
0.131517   7.719907
0.135517   7.137649
0.139517   6.445382
0.143517   6.141164
0.147517   5.902341
0.151517   5.761205
0.155517   5.248673
0.159517   4.942808
0.163517   4.622733
0.167517   4.500523
0.171517   4.391574
0.175517   3.746674
$$


$TABLE: NZ test:
$GRAPHS
:NZ test, acentric and centric data 
:A:1,2,3,4,5:
$$
z   Acentric_observed   Acentric_untwinned   Centric_observed   Centric_untwinned   $$ 
$$
0.000000   0.000000   0.000000   0.000000   0.000000
0.100000   0.084966   0.095200   0.000000   0.248100
0.200000   0.178207   0.181300   0.000000   0.345300
0.300000   0.260966   0.259200   0.000000   0.418700
0.400000   0.336276   0.329700   0.000000   0.473800
0.500000   0.402759   0.393500   0.000000   0.520500
0.600000   0.461103   0.451200   0.000000   0.561400
0.700000   0.514207   0.503400   0.000000   0.597200
0.800000   0.560276   0.550700   0.000000   0.628900
0.900000   0.604414   0.593400   0.000000   0.657200
1.000000   0.644276   0.632100   0.000000   0.683300
$$


$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   0.000000   0.000000   0.000000
0.020000   0.024446   0.020000   0.029996
0.040000   0.044882   0.040000   0.059968
0.060000   0.064935   0.060000   0.089892
0.080000   0.084798   0.080000   0.119744
0.100000   0.108289   0.100000   0.149500
0.120000   0.131016   0.120000   0.179136
0.140000   0.151070   0.140000   0.208628
0.160000   0.175516   0.160000   0.237952
0.180000   0.197288   0.180000   0.267084
0.200000   0.217723   0.200000   0.296000
0.220000   0.235676   0.220000   0.324676
0.240000   0.255348   0.240000   0.353088
0.260000   0.275401   0.260000   0.381212
0.280000   0.296409   0.280000   0.409024
0.300000   0.319710   0.300000   0.436500
0.320000   0.339763   0.320000   0.463616
0.340000   0.358671   0.340000   0.490348
0.360000   0.377387   0.360000   0.516672
0.380000   0.396486   0.380000   0.542564
0.400000   0.416157   0.400000   0.568000
0.420000   0.440222   0.420000   0.592956
0.440000   0.462185   0.440000   0.617408
0.460000   0.484339   0.460000   0.641332
0.480000   0.502865   0.480000   0.664704
0.500000   0.519672   0.500000   0.687500
0.520000   0.543163   0.520000   0.709696
0.540000   0.562261   0.540000   0.731268
0.560000   0.581933   0.560000   0.752192
0.580000   0.605997   0.580000   0.772444
0.600000   0.623568   0.600000   0.792000
0.620000   0.645913   0.620000   0.810836
0.640000   0.668258   0.640000   0.828928
0.660000   0.685065   0.660000   0.846252
0.680000   0.706646   0.680000   0.862784
0.700000   0.728801   0.700000   0.878500
0.720000   0.749236   0.720000   0.893376
0.740000   0.770244   0.740000   0.907388
0.760000   0.789534   0.760000   0.920512
0.780000   0.811115   0.780000   0.932724
0.800000   0.831360   0.800000   0.944000
0.820000   0.849694   0.820000   0.954316
0.840000   0.867838   0.840000   0.963648
0.860000   0.888464   0.860000   0.971972
0.880000   0.905653   0.880000   0.979264
0.900000   0.926280   0.900000   0.985500
0.920000   0.943277   0.920000   0.990656
0.940000   0.963331   0.940000   0.994708
0.960000   0.979565   0.960000   0.997632
0.980000   0.991979   0.980000   0.999404
$$


$TABLE: Britton plot for twin law -h-l,-k-l,l:
$GRAPHS
:percentage negatives 
:A:1,2,3:
$$
alpha   percentage_negatives   fit   $$ 
$$
0.000000   0.000000   0.000000
0.009901   0.002839   0.000000
0.019802   0.006275   0.000000
0.029703   0.012401   0.008129
0.039604   0.020021   0.017605
0.049505   0.027940   0.027081
0.059406   0.037352   0.036558
0.069307   0.044823   0.046034
0.079208   0.052592   0.055510
0.089109   0.061557   0.064986
0.099010   0.071567   0.074463
0.108911   0.079635   0.083939
0.118812   0.088899   0.093415
0.128713   0.096967   0.102892
0.138614   0.107127   0.112368
0.148515   0.116988   0.121844
0.158416   0.127148   0.131321
0.168317   0.136859   0.140797
0.178218   0.144928   0.150273
0.188119   0.156880   0.159749
0.198020   0.163753   0.169226
0.207921   0.173764   0.178702
0.217822   0.183475   0.188178
0.227723   0.194532   0.197655
0.237624   0.204841   0.207131
0.247525   0.215748   0.216607
0.257426   0.227103   0.226084
0.267327   0.235171   0.235560
0.277228   0.244285   0.245036
0.287129   0.253399   0.254512
0.297030   0.263260   0.263989
0.306931   0.273868   0.273465
0.316832   0.282833   0.282941
0.326733   0.291648   0.292418
0.336634   0.299567   0.301894
0.346535   0.311071   0.311370
0.356436   0.321082   0.320847
0.366337   0.329150   0.330323
0.376238   0.339459   0.339799
0.386139   0.350067   0.349275
0.396040   0.359331   0.358752
0.405941   0.370686   0.368228
0.415842   0.380696   0.377704
0.425743   0.389960   0.387181
0.435644   0.398327   0.396657
0.445545   0.410279   0.406133
0.455446   0.419842   0.415610
0.465347   0.428956   0.425086
0.475248   0.437323   0.434562
0.485149   0.447184   0.444039
$$


$TABLE: H test for possible twin law -h-l,-k-l,l:
$GRAPHS
:H test for Acentric data 
:A:1,2,3:
$$
H   Observed_S(H)   Fitted_S(H)   $$ 
$$
0.000000   0.053796   0.000000
0.020000   0.080693   0.021976
0.040000   0.100418   0.043952
0.060000   0.119546   0.065928
0.080000   0.139271   0.087903
0.100000   0.159594   0.109879
0.120000   0.187089   0.131855
0.140000   0.204423   0.153831
0.160000   0.221757   0.175807
0.180000   0.241482   0.197783
0.200000   0.265989   0.219759
0.220000   0.280335   0.241734
0.240000   0.303048   0.263710
0.260000   0.325762   0.285686
0.280000   0.338314   0.307662
0.300000   0.357442   0.329638
0.320000   0.376569   0.351614
0.340000   0.399880   0.373589
0.360000   0.420801   0.395565
0.380000   0.435744   0.417541
0.400000   0.452481   0.439517
0.420000   0.478183   0.461493
0.440000   0.496115   0.483469
0.460000   0.512851   0.505445
0.480000   0.528990   0.527420
0.500000   0.549313   0.549396
0.520000   0.573819   0.571372
0.540000   0.598326   0.593348
0.560000   0.618649   0.615324
0.580000   0.634788   0.637300
0.600000   0.656904   0.659276
0.620000   0.671249   0.681251
0.640000   0.693365   0.703227
0.660000   0.710699   0.725203
0.680000   0.729229   0.747179
0.700000   0.749552   0.769155
0.720000   0.771070   0.791131
0.740000   0.793784   0.813106
0.760000   0.808727   0.835082
0.780000   0.829647   0.857058
0.800000   0.843395   0.879034
0.820000   0.866109   0.901010
0.840000   0.880454   0.922986
0.860000   0.897788   0.944962
0.880000   0.911536   0.966937
0.900000   0.930663   0.988913
0.920000   0.948595   1.000000
0.940000   0.964136   1.000000
0.960000   0.982068   1.000000
0.980000   0.992230   1.000000
$$


$TABLE: Likelihood based twin fraction estimation for possible twin law -h-l,-k-l,l:
$GRAPHS
:Likelihood based twin fraction estimate 
:A:1,2:
$$
alpha   NLL_(acentric_data)   $$ 
$$
0.021739   15100.505586
0.043478   19600.019903
0.065217   28128.478012
0.086957   38846.375163
0.108696   50724.931813
0.130435   63365.757934
0.152174   78537.925131
0.173913   94668.751049
0.195652   110133.620056
0.217391   126292.589040
0.239130   143225.940225
0.260870   160761.827601
0.282609   178988.550992
0.304348   197484.598106
0.326087   215613.708466
0.347826   235122.267603
0.369565   255438.463212
0.391304   273493.290919
0.413043   292451.670736
0.434783   312840.214813
0.456522   334524.670919
0.478261   356152.873754
$$