Difference between revisions of "SOCR EduMaterials AnalysesCommandLineFDR Correction"

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=== Introduction===
 
=== Introduction===
−
In addition to the graphical user interfaces, via a web-browser, all [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] allow command-line shell execution on local systems. In a nutshell, FDR is a statistical method used in multiple hypothesis testing to correct the probability values for the effect of multiple comparisons. FDR controls the expected proportion of incorrectly rejected null hypotheses (i.e., FDR controls the type I error, <math>\alpha</math>). For example, if 1000 observations were experimentally predicted to be different, and a maximum FDR for these observations was ''q=0.10'', then 100 of these observations would be expected to be false positives. The ''q''-value is the FDR analogue of the p-value. The q-value of an individual hypothesis test is the minimum FDR at which the test may be called significant. One can directly estimate q-values or alternatively, fix a level at which to control the FDR. See the [[SOCR_EduMaterials_AnalysesCommandLineFDR_Correction#Supplementary_information | references below]] for more information on FDR.
+
In addition to the graphical user interfaces, via a web-browser, all [http://socr.ucla.edu/htmls/SOCR_Analyses.html SOCR Analyses] allow command-line shell execution on local systems.  
 +
 
 +
In a nutshell, FDR is a statistical method used in multiple hypothesis testing to correct the probability values for the effect of multiple comparisons. FDR controls the expected proportion of incorrectly rejected null hypotheses (i.e., FDR controls the type I error, <math>\alpha</math>). For example, if 1000 observations were experimentally predicted to be different, and a maximum FDR for these observations was ''q=0.10'', then 100 of these observations would be expected to be false positives. The ''q''-value is the FDR analogue of the p-value. The q-value of an individual hypothesis test is the minimum FDR at which the test may be called significant. One can directly estimate q-values or alternatively, fix a level at which to control the FDR. See the [[SOCR_EduMaterials_AnalysesCommandLineFDR_Correction#Supplementary_information | references below]] for more information on FDR.
 +
 
 +
Suppose we perform m simultaneous hypothesis tests with a common procedure (test). For any given procedure, we classify the results as shown below. Only these values are observed m, D, and N. The other ones are unknown. Let T=true, F=False, D=Discovery, and N=Nondiscovery. FDR provides a protocol that balances the
 +
competing demands of [[AP_Statistics_Curriculum_2007_Hypothesis_Basics |sensitivity and specificity of the test]].
 +
 
 +
<center>
 +
{| class="wikitable"
 +
|-
 +
!  ||Ho Retained || Ho Rejected || Total
 +
|-
 +
| Ho True || TN || FD || To
 +
|-
 +
| Ho False || FN || TD || T1
 +
|-
 +
| Total || N || D || m
 +
|}
 +
</center>
 +
 
 +
Then, FDR guarantees that the [[AP_Statistics_Curriculum_2007_Distrib_MeanVar |expectation]] of the relative-false-discovery (falsely-rejecting Ho, when it's true) is <math>E \left ( {FD \over D}\right ) \leq \alpha</math>.
 +
 
 +
The [[SOCR]] analysis implementation of FDR is based on [http://bioinformatics.oxfordjournals.org/cgi/content/full/21/12/2921 this article].
  
 
===FDR Usage===
 
===FDR Usage===

Revision as of 21:09, 19 May 2009

Analyses Command-Line - False Discovery Rate (FDR) Corection

This page includes the information on how to use the SOCR Analyses library for the purpose of computing the False Discovery Rate (FDR) correction for multiple testing in volumetric and shape-based analyses. Access is provided via shell-based command-line interface on local machines. More information about other SOCR Analyses command-line interfaces is available here.

Introduction

In addition to the graphical user interfaces, via a web-browser, all SOCR Analyses allow command-line shell execution on local systems.

In a nutshell, FDR is a statistical method used in multiple hypothesis testing to correct the probability values for the effect of multiple comparisons. FDR controls the expected proportion of incorrectly rejected null hypotheses (i.e., FDR controls the type I error, \(\alpha\)). For example, if 1000 observations were experimentally predicted to be different, and a maximum FDR for these observations was q=0.10, then 100 of these observations would be expected to be false positives. The q-value is the FDR analogue of the p-value. The q-value of an individual hypothesis test is the minimum FDR at which the test may be called significant. One can directly estimate q-values or alternatively, fix a level at which to control the FDR. See the references below for more information on FDR.

Suppose we perform m simultaneous hypothesis tests with a common procedure (test). For any given procedure, we classify the results as shown below. Only these values are observed m, D, and N. The other ones are unknown. Let T=true, F=False, D=Discovery, and N=Nondiscovery. FDR provides a protocol that balances the competing demands of sensitivity and specificity of the test.

Ho Retained Ho Rejected Total
Ho True TN FD To
Ho False FN TD T1
Total N D m

Then, FDR guarantees that the expectation of the relative-false-discovery (falsely-rejecting Ho, when it's true) is \(E \left ( {FD \over D}\right ) \leq \alpha\).

The SOCR analysis implementation of FDR is based on this article.

FDR Usage

java -ms500m -mx1000m -cp /ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_core.jar:/ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_plugin.jar edu.ucla.stat.SOCR.analyses.command.volume.Test_FDR -input Input_PValues_File -output Output_PValuesCorrected_File [-type type] [-fdr_rate q] -number integer -byteorder string

  • Options:
    • -help: prints usage
    • -v: verbose mode (will print all input/output data in standard output stream.
    • -input [InputFileName]: specify a file-name for an ASCII or binary file containing the raw p-values.
    • -output [OutputFileName]: specify a file-name for the corresponfing output file that will contain the FDR-corrected p-values.
    • -type [0,1]: Type=0 is for ASCII text input file type, Type=1 is for binary 4Byte=Float Input file;
    • -fdr_rate [double]: the False Discovery Rate level (e.g., 0.05)
    • -number [int]: enter the number of P-values stored in the input file (output file will have the same number of floats).
    • -byteorder string: string is one of {big, little, other}.
      • big = BIG_ENDIAN processor
      • little = LITTLE_ENDIAN processor
      • other = default processor (java.nio.ByteOrder.nativeOrder())

Shape-based p-Value FDR correction example

Edit a new file (FDR_Correction.csh) using any editor and paste this inside (make sure the file has executable permissions). Some operating systems/platforms may require variants of this (C-shell) script.

Results of FDR thresholding (right) the raw p-values (left) of comparing the local shape measures for hippocampal models for 2 groups

#!/bin/csh

date

java -ms500m -mx1000m -cp /ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_core.jar:/ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_plugin.jar edu.ucla.stat.SOCR.analyses.command.volume.Test_FDR -input /ifs/ccb/CCB_SW_Tools/Statistics/SOCR_Statistics/SOCR_CSV_test_Scripts_Data/FDR_Test_Input_PValues.txt -output /ifs/ccb/CCB_SW_Tools/Statistics/SOCR_Statistics/SOCR_CSV_test_Scripts_Data/FDR_Test_PValuesCorrected_Output.txt -type 0 -fdr_rate 0.05 -number 1000 -byteorder little

date

exit

Volume-based p-Value FDR correction example

Edit a new file (FDR_Correction.csh) using any editor and paste this inside (make sure the file has executable permissions). Some operating systems/platforms may require variants of this (C-shell) script.

Results of volumetric FDR thresholding (right) the raw p-values (left) obtained by comparing the Jacobians of the displacement fields of registering 2 groups of 3D MRI scans in a common anatomical atlas-space.

#!/bin/csh

date

java -ms500m -mx1000m -cp /ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_core.jar:/ifs/ccb/CCB_SW_Tools/others/Statistics/SOCR_Statistics/bin/SOCR_plugin.jar edu.ucla.stat.SOCR.analyses.command.volume.Test_FDR -input P_Value_mask_New_Reg_GROUP.img -output P_Value_mask_New_Reg_GROUP_FDRcorrected.img -type 1 -fdr_rate 0.05 -number 10648000 -byteorder little

date

exit

Example

The table below shows the results of applying FDR-correction to the P_values obtained by non-parametric statistical test comparing the hippocampi surfaces (consisting of 1,00 vertices) of 2 groups of subject(AD and MCI). The FDR-corrected p-values were obtained by the command line included above.

Index Raw P-Values FDR-Corrected P-values
1.00000000 0.00041800 0.00041800
2.00000000 0.00060500 0.00060500
3.00000000 0.06424300 0.00000000
4.00000000 0.14547100 0.00000000
5.00000000 0.78607900 0.00000000
6.00000000 0.08867100 0.00000000
7.00000000 0.38782900 0.00000000
8.00000000 0.04057200 0.00000000
9.00000000 0.07980900 0.00000000
10.00000000 0.00072400 0.00072400
11.00000000 0.53734700 0.00000000
12.00000000 0.38782900 0.00000000
13.00000000 0.00060500 0.00060500
14.00000000 0.00715900 0.00000000
15.00000000 0.33592200 0.00000000
16.00000000 0.78607900 0.00000000
17.00000000 0.20827100 0.00000000
18.00000000 0.33592200 0.00000000
19.00000000 0.00530200 0.00000000
20.00000000 0.00829000 0.00000000
21.00000000 0.01104300 0.00000000
22.00000000 0.01458000 0.00000000
23.00000000 0.01270300 0.00000000
24.00000000 0.94099500 0.00000000
25.00000000 0.07980900 0.00000000
26.00000000 0.00013100 0.00013100
27.00000000 0.94099500 0.00000000
28.00000000 0.05127400 0.00000000
29.00000000 0.00122800 0.00000000
30.00000000 0.19098200 0.00000000
31.00000000 0.28871400 0.00000000
32.00000000 0.00060500 0.00060500
33.00000000 0.07980900 0.00000000
34.00000000 0.00389200 0.00000000
35.00000000 0.00086600 0.00086600
36.00000000 0.36129100 0.00000000
37.00000000 0.00023700 0.00023700
38.00000000 0.03182800 0.00000000
39.00000000 0.28871400 0.00000000
40.00000000 0.36129100 0.00000000
41.00000000 0.12008600 0.00000000
42.00000000 0.03597400 0.00000000
43.00000000 0.14547100 0.00000000
44.00000000 0.00019500 0.00019500
45.00000000 0.00007100 0.00007100
46.00000000 0.14547100 0.00000000
47.00000000 0.00389200 0.00000000
48.00000000 0.00715900 0.00000000
49.00000000 0.44435000 0.00000000
50.00000000 0.00389200 0.00000000
51.00000000 0.22666800 0.00000000
52.00000000 0.00530200 0.00000000
53.00000000 0.00829000 0.00000000
54.00000000 0.00240700 0.00000000
55.00000000 0.78607900 0.00000000
56.00000000 0.00530200 0.00000000
57.00000000 0.19098200 0.00000000
58.00000000 0.86287800 0.00000000
59.00000000 0.07980900 0.00000000
60.00000000 0.05127400 0.00000000
61.00000000 0.03597400 0.00000000
62.00000000 0.63921900 0.00000000
63.00000000 0.26687300 0.00000000
64.00000000 0.78607900 0.00000000
65.00000000 0.67489200 0.00000000
66.00000000 0.36129100 0.00000000
67.00000000 0.74839900 0.00000000
68.00000000 0.09831000 0.00000000
69.00000000 0.00023700 0.00023700
70.00000000 0.00172700 0.00000000
71.00000000 0.31172900 0.00000000
72.00000000 0.02809800 0.00000000
73.00000000 0.01104300 0.00000000
74.00000000 0.00122800 0.00000000
75.00000000 0.17477300 0.00000000
76.00000000 0.17477300 0.00000000
77.00000000 0.00283200 0.00000000
78.00000000 0.00530200 0.00000000
79.00000000 0.00204100 0.00000000
80.00000000 0.36129100 0.00000000
81.00000000 0.01669800 0.00000000
82.00000000 0.94099500 0.00000000
83.00000000 0.53734700 0.00000000
84.00000000 0.17477300 0.00000000
85.00000000 0.00013100 0.00013100
86.00000000 0.00028700 0.00028700
87.00000000 0.00454800 0.00000000
88.00000000 0.00957900 0.00000000
89.00000000 0.13230700 0.00000000
90.00000000 0.02809800 0.00000000
91.00000000 0.00204100 0.00000000
92.00000000 0.20827100 0.00000000
93.00000000 0.05127400 0.00000000
94.00000000 0.74839900 0.00000000
95.00000000 0.41552200 0.00000000
96.00000000 0.03597400 0.00000000
97.00000000 0.07980900 0.00000000
98.00000000 0.00023700 0.00023700
99.00000000 0.00829000 0.00000000
100.00000000 0.36129100 0.00000000
101.00000000 0.41552200 0.00000000
102.00000000 0.98031600 0.00000000
103.00000000 0.12008600 0.00000000
104.00000000 0.14547100 0.00000000
105.00000000 0.08867100 0.00000000
106.00000000 0.20827100 0.00000000
107.00000000 0.00389200 0.00000000
108.00000000 0.00023700 0.00023700
109.00000000 0.00034700 0.00034700
110.00000000 0.98031600 0.00000000
111.00000000 0.00086600 0.00086600
112.00000000 0.01908100 0.00000000
113.00000000 0.14547100 0.00000000
114.00000000 0.00332400 0.00000000
115.00000000 0.00034700 0.00034700
116.00000000 0.00103200 0.00000000
117.00000000 0.19098200 0.00000000
118.00000000 0.10876800 0.00000000
119.00000000 0.05127400 0.00000000
120.00000000 0.00060500 0.00060500
121.00000000 0.00204100 0.00000000
122.00000000 0.60436300 0.00000000
123.00000000 0.07168000 0.00000000
124.00000000 0.00389200 0.00000000
125.00000000 0.07980900 0.00000000
126.00000000 0.01908100 0.00000000
127.00000000 0.24619500 0.00000000
128.00000000 0.00389200 0.00000000
129.00000000 0.00616800 0.00000000
130.00000000 0.00103200 0.00000000
131.00000000 0.00122800 0.00000000
132.00000000 0.08867100 0.00000000
133.00000000 0.24619500 0.00000000
134.00000000 0.15961400 0.00000000
135.00000000 0.00060500 0.00060500
136.00000000 0.28871400 0.00000000
137.00000000 0.02175600 0.00000000
138.00000000 0.02175600 0.00000000
139.00000000 0.05745500 0.00000000
140.00000000 0.31172900 0.00000000
141.00000000 0.00103200 0.00000000
142.00000000 0.10876800 0.00000000
143.00000000 0.14547100 0.00000000
144.00000000 0.71131000 0.00000000
145.00000000 0.02809800 0.00000000
146.00000000 0.00240700 0.00000000
147.00000000 0.03597400 0.00000000
148.00000000 0.44435000 0.00000000
149.00000000 0.00122800 0.00000000
150.00000000 0.19098200 0.00000000
151.00000000 0.00060500 0.00060500
152.00000000 0.00007100 0.00007100
153.00000000 0.63921900 0.00000000
154.00000000 0.47428600 0.00000000
155.00000000 0.78607900 0.00000000
156.00000000 0.50529900 0.00000000
157.00000000 0.00616800 0.00000000
158.00000000 0.13230700 0.00000000
159.00000000 0.00829000 0.00000000
160.00000000 0.08867100 0.00000000
161.00000000 0.94099500 0.00000000
162.00000000 0.98031600 0.00000000
163.00000000 0.36129100 0.00000000
164.00000000 0.00016000 0.00016000
165.00000000 0.00145800 0.00000000
166.00000000 0.00023700 0.00023700
167.00000000 0.38782900 0.00000000
168.00000000 0.98031600 0.00000000
169.00000000 0.20827100 0.00000000
170.00000000 0.28871400 0.00000000
171.00000000 0.01669800 0.00000000
172.00000000 0.02475100 0.00000000
173.00000000 0.10876800 0.00000000
174.00000000 0.00072400 0.00072400
175.00000000 0.33592200 0.00000000
176.00000000 0.74839900 0.00000000
177.00000000 0.38782900 0.00000000
178.00000000 0.36129100 0.00000000
179.00000000 0.01908100 0.00000000
180.00000000 0.74839900 0.00000000
181.00000000 0.02475100 0.00000000
182.00000000 0.01270300 0.00000000
183.00000000 0.00028700 0.00028700
184.00000000 0.63921900 0.00000000
185.00000000 0.00240700 0.00000000
186.00000000 0.00715900 0.00000000
187.00000000 0.24619500 0.00000000
188.00000000 0.00715900 0.00000000
189.00000000 0.00240700 0.00000000
190.00000000 0.00616800 0.00000000
191.00000000 0.00957900 0.00000000
192.00000000 0.57038600 0.00000000
193.00000000 0.00829000 0.00000000
194.00000000 0.14547100 0.00000000
195.00000000 0.00122800 0.00000000
196.00000000 0.41552200 0.00000000
197.00000000 0.00332400 0.00000000
198.00000000 0.00010700 0.00010700
199.00000000 0.12008600 0.00000000
200.00000000 0.07168000 0.00000000
201.00000000 0.19098200 0.00000000
202.00000000 0.04565900 0.00000000
203.00000000 0.94099500 0.00000000
204.00000000 0.12008600 0.00000000
205.00000000 0.02809800 0.00000000
206.00000000 0.00103200 0.00000000
207.00000000 0.20827100 0.00000000
208.00000000 0.31172900 0.00000000
209.00000000 0.74839900 0.00000000
210.00000000 0.20827100 0.00000000
211.00000000 0.36129100 0.00000000
212.00000000 0.57038600 0.00000000
213.00000000 0.17477300 0.00000000
214.00000000 0.82426800 0.00000000
215.00000000 0.14547100 0.00000000
216.00000000 0.00060500 0.00060500
217.00000000 0.02809800 0.00000000
218.00000000 0.00005800 0.00005800
219.00000000 0.05127400 0.00000000
220.00000000 0.82426800 0.00000000
221.00000000 0.01908100 0.00000000
222.00000000 0.00389200 0.00000000
223.00000000 0.01669800 0.00000000
224.00000000 0.00616800 0.00000000
225.00000000 0.63921900 0.00000000
226.00000000 0.01458000 0.00000000
227.00000000 0.07168000 0.00000000
228.00000000 0.94099500 0.00000000
229.00000000 0.74839900 0.00000000
230.00000000 0.17477300 0.00000000
231.00000000 0.00103200 0.00000000
232.00000000 0.00957900 0.00000000
233.00000000 0.24619500 0.00000000
234.00000000 0.44435000 0.00000000
235.00000000 0.00050300 0.00050300
236.00000000 0.50529900 0.00000000
237.00000000 0.00957900 0.00000000
238.00000000 0.60436300 0.00000000
239.00000000 0.14547100 0.00000000
240.00000000 0.00145800 0.00000000
241.00000000 0.02809800 0.00000000
242.00000000 0.36129100 0.00000000
243.00000000 0.63921900 0.00000000
244.00000000 0.19098200 0.00000000
245.00000000 0.04057200 0.00000000
246.00000000 0.00103200 0.00000000
247.00000000 0.00204100 0.00000000
248.00000000 0.00041800 0.00041800
249.00000000 0.00060500 0.00060500
250.00000000 0.71131000 0.00000000
251.00000000 0.00204100 0.00000000
252.00000000 0.05745500 0.00000000
253.00000000 0.00028700 0.00028700
254.00000000 0.01908100 0.00000000
255.00000000 0.86287800 0.00000000
256.00000000 0.04565900 0.00000000
257.00000000 0.00050300 0.00050300
258.00000000 0.63921900 0.00000000
259.00000000 0.00389200 0.00000000
260.00000000 0.50529900 0.00000000
261.00000000 0.07980900 0.00000000
262.00000000 0.90181700 0.00000000
263.00000000 0.01270300 0.00000000
264.00000000 0.01458000 0.00000000
265.00000000 0.98031600 0.00000000
266.00000000 0.02809800 0.00000000
267.00000000 0.20827100 0.00000000
268.00000000 0.00389200 0.00000000
269.00000000 0.38782900 0.00000000
270.00000000 0.08867100 0.00000000
271.00000000 0.15961400 0.00000000
272.00000000 0.00013100 0.00013100
273.00000000 0.01270300 0.00000000
274.00000000 0.00332400 0.00000000
275.00000000 0.00957900 0.00000000
276.00000000 0.05745500 0.00000000
277.00000000 0.60436300 0.00000000
278.00000000 0.98031600 0.00000000
279.00000000 0.63921900 0.00000000
280.00000000 0.71131000 0.00000000
281.00000000 0.01908100 0.00000000
282.00000000 0.01908100 0.00000000
283.00000000 0.08867100 0.00000000
284.00000000 0.00086600 0.00086600
285.00000000 0.06424300 0.00000000
286.00000000 0.00086600 0.00086600
287.00000000 0.00240700 0.00000000
288.00000000 0.02175600 0.00000000
289.00000000 0.00530200 0.00000000
290.00000000 0.28871400 0.00000000
291.00000000 0.07168000 0.00000000
292.00000000 0.03597400 0.00000000
293.00000000 0.00016000 0.00016000
294.00000000 0.04565900 0.00000000
295.00000000 0.38782900 0.00000000
296.00000000 0.00008700 0.00008700
297.00000000 0.20827100 0.00000000
298.00000000 0.00204100 0.00000000
299.00000000 0.00145800 0.00000000
300.00000000 0.00172700 0.00000000
301.00000000 0.26687300 0.00000000
302.00000000 0.02175600 0.00000000
303.00000000 0.00240700 0.00000000
304.00000000 0.00530200 0.00000000
305.00000000 0.01270300 0.00000000
306.00000000 0.01458000 0.00000000
307.00000000 0.44435000 0.00000000
308.00000000 0.08867100 0.00000000
309.00000000 0.33592200 0.00000000
310.00000000 0.00829000 0.00000000
311.00000000 0.00041800 0.00041800
312.00000000 0.03597400 0.00000000
313.00000000 0.04565900 0.00000000
314.00000000 0.00283200 0.00000000
315.00000000 0.06424300 0.00000000
316.00000000 0.01104300 0.00000000
317.00000000 0.28871400 0.00000000
318.00000000 0.15961400 0.00000000
319.00000000 0.00028700 0.00028700
320.00000000 0.00829000 0.00000000
321.00000000 0.28871400 0.00000000
322.00000000 0.20827100 0.00000000
323.00000000 0.57038600 0.00000000
324.00000000 1.00000000 0.00000000
325.00000000 0.86287800 0.00000000
326.00000000 0.19098200 0.00000000
327.00000000 0.10876800 0.00000000
328.00000000 0.00283200 0.00000000
329.00000000 0.02475100 0.00000000
330.00000000 0.03182800 0.00000000
331.00000000 0.05127400 0.00000000
332.00000000 0.22666800 0.00000000
333.00000000 0.10876800 0.00000000
334.00000000 0.02175600 0.00000000
335.00000000 0.15961400 0.00000000
336.00000000 0.01270300 0.00000000
337.00000000 0.01908100 0.00000000
338.00000000 0.00008700 0.00008700
339.00000000 0.00072400 0.00072400
340.00000000 0.38782900 0.00000000
341.00000000 0.02809800 0.00000000
342.00000000 0.82426800 0.00000000
343.00000000 0.00103200 0.00000000
344.00000000 0.00034700 0.00034700
345.00000000 0.00010700 0.00010700
346.00000000 0.00616800 0.00000000
347.00000000 0.08867100 0.00000000
348.00000000 0.01104300 0.00000000
349.00000000 0.17477300 0.00000000
350.00000000 0.98031600 0.00000000
351.00000000 0.20827100 0.00000000
352.00000000 0.53734700 0.00000000
353.00000000 0.53734700 0.00000000
354.00000000 0.00103200 0.00000000
355.00000000 0.00028700 0.00028700
356.00000000 0.10876800 0.00000000
357.00000000 0.00050300 0.00050300
358.00000000 0.24619500 0.00000000
359.00000000 0.00041800 0.00041800
360.00000000 0.60436300 0.00000000
361.00000000 0.00086600 0.00086600
362.00000000 0.26687300 0.00000000
363.00000000 0.00086600 0.00086600
364.00000000 0.33592200 0.00000000
365.00000000 0.15961400 0.00000000
366.00000000 0.00829000 0.00000000
367.00000000 0.00145800 0.00000000
368.00000000 0.04057200 0.00000000
369.00000000 0.00086600 0.00086600
370.00000000 0.22666800 0.00000000
371.00000000 0.00829000 0.00000000
372.00000000 0.00122800 0.00000000
373.00000000 0.01270300 0.00000000
374.00000000 0.00122800 0.00000000
375.00000000 0.01669800 0.00000000
376.00000000 0.53734700 0.00000000
377.00000000 0.02809800 0.00000000
378.00000000 0.90181700 0.00000000
379.00000000 0.98031600 0.00000000
380.00000000 0.00283200 0.00000000
381.00000000 0.33592200 0.00000000
382.00000000 0.33592200 0.00000000
383.00000000 0.00034700 0.00034700
384.00000000 0.00389200 0.00000000
385.00000000 0.50529900 0.00000000
386.00000000 0.00829000 0.00000000
387.00000000 0.00172700 0.00000000
388.00000000 0.00034700 0.00034700
389.00000000 0.13230700 0.00000000
390.00000000 0.50529900 0.00000000
391.00000000 0.04565900 0.00000000
392.00000000 0.00034700 0.00034700
393.00000000 0.00072400 0.00072400
394.00000000 0.00283200 0.00000000
395.00000000 0.01104300 0.00000000
396.00000000 0.00072400 0.00072400
397.00000000 0.07980900 0.00000000
398.00000000 0.15961400 0.00000000
399.00000000 0.10876800 0.00000000
400.00000000 0.00332400 0.00000000
401.00000000 0.07980900 0.00000000
402.00000000 0.00283200 0.00000000
403.00000000 0.00616800 0.00000000
404.00000000 0.05745500 0.00000000
405.00000000 0.05745500 0.00000000
406.00000000 0.38782900 0.00000000
407.00000000 0.38782900 0.00000000
408.00000000 0.90181700 0.00000000
409.00000000 0.24619500 0.00000000
410.00000000 0.00028700 0.00028700
411.00000000 0.00957900 0.00000000
412.00000000 0.47428600 0.00000000
413.00000000 0.44435000 0.00000000
414.00000000 0.24619500 0.00000000
415.00000000 0.00172700 0.00000000
416.00000000 0.00240700 0.00000000
417.00000000 0.00204100 0.00000000
418.00000000 0.00034700 0.00034700
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