7.1.499. timing_tool.py

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(-stim_times format: where each row is a separate run)

This program is meant to work with ascii files containing rows of floats (‘*’ characters are ignored). This is the format used by 3dDeconvolve with the -stim_times option. Some timing files do not need evaluation, such as those where the timing is very consistent. However, it may be important to examine those files from a random timing design.

Recall that an ISI (inter-stimulus interval) is the interval of time between the end of one stimulus and start of the next.

The basic program operations include:

o reporting ISI statistics, such as min/mean/max values per run o reporting overall ISI statistics for a set of timing files o converting stim_times format to stim_file format o adding a constant offset to time o combining multiple timing files into 1 (like ‘1dcat’ + sort) o appending additional timing runs (like ‘cat’) o sort times per row (though 3dDeconvolve does not require this) o converting between local and global stim times

A sample stimulus timing file having 3 runs with 4 stimuli per run might look something like the following. Note that the file does not imply the durations of the stimuli, except that stimuli are generally not allowed to overlap.

17.3 24.0 66.0 71.6 11.0 30.6 49.2 68.5 19.4 28.7 53.8 69.4

The program works on either a single timing element (which can be modified), or a list of them (which cannot be modified). The only real use of a list of timing elements is to show statistics (via -multi_show_isi_stats).

Example 0. Basic commands:

timing_tool.py -help timing_tool.py -hist timing_tool.py -show_valid_opts timing_tool.py -ver
Example 1. Combine the timing of 2 files (extend one timing by another and
sort). Write to a new timing file.
timing_tool.py -timing stimesB_01_houses.1D
-extend stimesB_02_faces.1D
-sort
-write_timing stimesB_extended.1D
Example 2. Subtract 12 seconds from each stimulus time (to offset TRs

dropped prior to the magnetization steady state).

timing_tool.py -timing stimesB_01_houses.1D
-add_offset -12.0 -write_timing stimesB1_offset12.1D
Example 2b. Similar to 2, but scale times (multiply) by 0.975, perhaps to

account for a different TR or stimulus duration.

timing_tool.py -timing stimesB_01_houses.1D
-scale_data 0.975 -write_timing stimesB1_scaled.1D
Example 2c. Similar to 2, but shift run times so that the first time occurs

at the beginning of the run.

timing_tool.py -timing stimesB_01_houses.1D
-shift_to_run_offset 0 -write_timing stimesB1_offset0.1D
Example 3. Show timing statistics for the 3 timing files generated by
example 3 from “make_random_timing -help”. To be accurate, specify the run and stimulus durations.
timing_tool.py -multi_timing stimesC_*.1D
-run_len 200 -multi_stim_dur 3.5 -multi_show_isi_stats
Example 4. Show timing statistics for the timing files generated by example

6 from “make_random_timing -help”. Since both the run and stimulus durations vary, 4 run lengths and 3 stimulus durations are given.

timing_tool.py -multi_timing stimesF_*.1D
-run_len 200 190 185 225 -multi_stim_dur 3.5 4.5 3 -multi_show_isi_stats
Example 5. Partition the stimulus timing file ‘response_times.1D’ into

multiple timing files based on the labels in a partition file, partitions.1D. If partitions.txt contains (0, correct, incorrect), there will be 2 output timing files, new_times_correct.1D and new_times_incorrect.1D. Times where the partition label is ‘0’ will be skipped.

timing_tool.py -timing response_times.1D
-partition partitions.txt new_times
Example 6a. Convert a stim_times timing file to 0/1 stim_file format.
Suppose the timing is random where each event lasts 2.5 seconds and runs are of lengths 360, 360 and 400 seconds. Convert timing.txt to sfile.1D on a TR grid of 0.5 seconds (oversampling), where a TR gets an event if at least 30% of the TR is is occupied by stimulus.
timing_tool.py -timing timing.txt -timing_to_1D sfile.1D
-tr 0.5 -stim_dur 2.5 -min_frac 0.3 -run_len 360 360 400
Example 6b. Evaluate the results. Use waver to convolve sfile.1D with GAM

and use 3dDeconvolve to convolve the timing file with BLOCK(2.5).

waver -GAM -TR 0.5 -peak 1 -input sfile.1D > waver.1D

3dDeconvolve -nodata 2240 0.5 -concat ‘1D: 0 720 1440’
-polort -1 -num_stimts 1 -stim_times 1 timing.txt ‘BLOCK(2.5)’ -x1D X.xmat.1D -x1D_stop

1dplot -sepscl sfile.1D waver.1D X.xmat.1D

Example 6c. Do this per run, but leave each run in a separate file.

timing_tool.py -timing timing.txt -timing_to_1D sfile.1D
-tr 0.5 -stim_dur 2.5 -min_frac 0.3 -run_len 360 360 400 -per_run_file

Example 7a. Truncate stimulus times to the beginning of respective TRs.

Given a TR of 2.5 seconds and random stimulus times, truncate those times to multiples of the TR (2.5).
timing_tool.py -timing timing.txt -tr 2.5 -truncate_times
-write_timing trunc_times.txt

Here, 11.83 would get truncated down to 10, the largest multiple of 2.5 less than or equal to the original time.

Example 7b. Instead of just truncating the times, round them to the nearest
TR, based on some TR fraction. In this example, round up to the next TR when a stimulus occurs at least 70% into a TR, otherwise round down to the beginning.
timing_tool.py -timing timing.txt -tr 2.5 -round_times 0.7
-write_timing round_times.txt

With no rounding, a time of 11.83 would be truncated to 10.0. But 11.83 is 1.83 seconds into the TR, or is 73.2 percent into the TR. Since it is at least 70% into the TR, it is rounded up to the next one.

Here, 11.83 would get rounded up to 12.5.

Example 8a. Create an event list from stimulus timing files. The TR is

1.25s, events are ~1 TR long, and require them to occupy at least half of the given TR. Specify that rows should be per run and the run durations are all 370.

timing_tool.py -multi_timing stimes.*.txt
-multi_timing_to_events all.events.txt -tr 1.25 -multi_stim_dur 1 -min_frac 0.5
-per_run -run_len 370
Example 8b. Break the event list into 2, one for a sequence of changing

event types, one for a sequence of ISIs (TRs from one event to the next, including the TR of the event). So if the event file from #8 shows:

0 0 3 0 0 0 0 1 0 2 2 0 0 0 ...
The resulting event/ISI files would read:

event: 0 3 1 2 2 ... ISI: 2 5 2 1 4 ...

timing_tool.py -multi_timing stimes.*.txt
-multi_timing_to_event_pair events.txt isi.txt -tr 1.25 -multi_stim_dur 1 -min_frac 0.5 -per_run -run_len 370
Example 9a. Convert from global stim times to local.

This requires knowing the run lengths, say 4 runs of 200 seconds here. The result will have 4 rows, each starting at time 0.

timing_tool.py -timing stim.1D
-global_to_local local.1D -run_len 200 200 200

Note that if stim.1D looks like this ( ** but as a single column ** ):

12.3 115 555 654 777 890

then local.1D will look like this:

12.3 115 ^ 155 254 377 490

It will complain about the 3 times after the last run ends (no run should have times above 200 sec).

Example 9b. Convert from local timing back to global.

timing_tool.py -timing local.1D
-local_to_global global.1D -run_len 200 200 200
Example 10. Display within-TR statistics of stimulus timing files, to show

when stimuli occur within TRs. The -tr option must be specified.

  1. one file: show offset statistics (using -show_tr_stats)

    timing_tool.py -timing stim01_houses.txt -tr 2.0 -show_tr_stats

  2. (one or) many files (use -multi_timing)

    timing_tool.py -multi_timing stim*.txt -tr 2.0 -show_tr_stats

  3. only warn about potential problems (use -warn_tr_stats)

    timing_tool.py -multi_timing stim*.txt -tr 2.0 -warn_tr_stats

Example 11. Test a timing file for timing issues, which currently means

having times that are intended to be local but might be read as global.

timing_tool.py -multi_timing stim*.txt -test_local_timing

Examples 12 and 13 : akin to Example 8...

Example 12. Create a timing style event list.

Create a simple horizontal event list (one row per run), where the event class is the (1-based) index of the given input file. This is very similar to the first file output in example 8b, but no TR information is required here. Events are simply ordered.

timing_tool.py -multi_timing stimes.*.txt
-multi_timing_to_event_list index elist12.txt

Example 13a. Create a vertical GE (global events) list, showing ALL fields.

timing_tool.py -multi_timing stim.* -multi_timing_to_event_list GE:ALL -

Example 13b. Like 13a, but restrict the output to:

event index (i), duration (d), offset from previous (o), start time (t), and stim file (f)

Also, write the output to elist13b.txt, rather than the screen.

timing_tool.py -multi_timing stimes.*.txt
-multi_timing_to_event_list GE:idotf elist13b.txt

Example 14. Partition one stimulus class based on others.

Class ‘1’ (from the first input) is partitioned based on the class that precedes it. If none precede an early class 1 event, event INIT is used

as the default (else consider ‘-part_init 2’, for example).

timing_tool.py -multi_timing stimes.*.txt
-multi_timing_to_event_list part part1.pred.txt

The result could be applied to actually partition the first timing file, akin to Example 5:

timing_tool.py -timing stimes.1.txt
-partition part1.pred.txt stimes.1.part
  1. Action options are performed in the order of the options.
Note: -chrono has been removed.
  1. Either -timing or -multi_timing is required for processing.
  2. Option -run_len applies to single or multiple stimulus classes. A single parameter would be used for all runs. Otherwise one duration per run should be supplied.
-help : show this help
-help_basis : describe various basis functions
-hist : show the module history
-show_valid_opts : show all valid options
-ver : show the version number

-timing TIMING_FILE : specify a stimulus timing file to load

e.g. -timing stimesB_01_houses.1D

Use this option to specify a single stimulus timing file. The user can modify this timing via some of the action options listed below.

-show_isi_stats : display timing and ISI statistics

With this option, the program will display timing statistics for the single (possibly modified) timing element.

If -tr is included, TR offset statistics are also shown.

-show_timing_ele : display info on the main timing element

With this option, the program will display information regarding the single (possibly modified) timing element.

-stim_dur DURATION : specify the stimulus duration, in seconds

e.g. -stim_dur 3.5

This option allows the user to specify the duration of the stimulus, as applies to the single timing element. The only use of this is in conjunction with -show_isi_stats.

Consider ‘-show_isi_stats’ and ‘-run_len’.

-multi_timing FILE1 FILE2 ... : specify multiple timing files to load

e.g. -timing stimesB_*.1D

Use this option to specify a list of stimulus timing files. The user cannot modify this data, but can display the overall ISI statistics from it.

Options that pertain to this timing list include:

-multi_show_isi_stats -multi_show_timing_ele -multi_stim_dur -run_len -write_all_rest_times

-multi_show_isi_stats : display timing and ISI statistics

With this option, the program will display timing statistics for the multiple timing files.

If -tr is included, TR offset statistics are also shown.

If -write_all_rest_times is included, write a file of rest durations.

-multi_show_timing_ele : display info on the multiple timing elements

With this option, the program will display information regarding the multiple timing element list.

-multi_stim_dur DUR1 ... : specify the stimulus duration(s), in seconds

e.g. -multi_stim_dur 3.5 e.g. -multi_stim_dur 3.5 4.5 3

This option allows the user to specify the durations of the stimulus classes, as applies to the multiple timing elements. The only use of this is in conjunction with -multi_show_isi_stats.

If only one duration is specified, it is applied to all elements. Otherwise, there should be as many stimulus durations as files specified with -multi_timing.

Consider ‘-multi_show_isi_stats’ and ‘-run_len’.

** Note that these options are processed in the order they are read.

-add_offset OFFSET : add OFFSET to every time in main element

e.g. -add_offset -12.0

Use this option to add a single offset to all of the times in the main timing element. For example, if the user deletes 3 4-second TRs from the EPI data, they may wish to subtract 12 seconds from every stimulus time, so that the times match the modified EPI data.

Consider ‘-write_timing’.

-add_rows NEW_FILE : append these timing rows to main element

e.g. -add_rows more_times.1D

Use this option to append rows from NEW_FILE to those of the main timing element. If the user then wrote out the result, it would be identical to using cat: “cat times1.txt times2.txt > both_times.txt”.

Consider ‘-write_timing’.

-extend NEW_FILE : extend the timing rows with those in NEW_FILE

e.g. -extend more_times.1D

Use this option to extend each row (run) with the times in NEW_FILE. This has an effect similar to that of ‘1dcat’. Sorting the times is optional, done via ‘-sort’. Note that 3dDeconvolve does not need the times to be sorted, though it is more understandable to the user.

Consider ‘-sort’ and ‘-write_timing’.

-global_to_local LOCAL_NAME.1D : convert from global timing to local

e.g. -global_to_local local_times.1D

Use this option to convert from global stimulus timing (in a single column format) to local stimulus timing. Run durations must be given of course, to determine which run each stimulus occurs in. Each stimulus time will be adjusted to be an offset into the current run, e.g. if each run is 120 s, a stimulus at time 143.6 would occur in run #2 (1-based) at time 23.6 s.

Consider example 9a and options ‘-run_len’ and ‘-local_to_global’.

-local_to_global GLOBAL_NAME.1D : convert from local timing to global

e.g. -local_to_global global_times.1D

Use this option to convert from local stimulus timing (one row of times per run) to global stimulus timing (a single column of times across the runs, where time is considered continuous across the runs).

Run durations must be given of course, to determine which run each stimulus occurs in. Each stimulus time will be adjusted to be an offset from the beginning of the first run, as if there were no breaks between the runs. e.g. if each run is 120 s, a stimulus in run #2 (1-based) at time 23.6 s would be converted to a stimulus at global time 143.6 s.

Consider example 9b and options ‘-run_len’ and ‘-global_to_local’.

-partition PART_FILE PREFIX : partition the stimulus timing file

e.g. -partition partitions.txt new_times

Use this option to partition the input timing file into multiple timing files based on the labels in a partition file, PART_FILE. The partition file would have the same number of rows and entries on each row as the timing file, but would contain labels to use in partitioning the times into multiple output files.

A label of 0 will cause that timing entry to be dropped. Otherwise, each distinct label will have those times put into its timing file.

e.g.

timing file:
23.5 46.0 79.3 84.9 116.2 11.4 38.2 69.7 93.5 121.8
partition file:
correct 0 0 incorrect incorrect 0 correct 0 correct correct

==> results in new_times_good.1D and new_times_bad.1D

new_times_correct.1D:
23.5 0 0 0 0 0 38.2 0 93.5 121.8
new_times_incorrect.1D:
0 0 0 84.9 116.2 ^
-round_times FRAC : round times to multiples of the TR
0.0 <= FRAC <= 1.0

e.g. -round_times 0.7

All stimulus times will be rounded to a multiple TR, rounding down if the fraction of the TR that has passed is less than FRAC, rounding up otherwise.

Using the example of FRAC=0.7, if the TR is 2.5 seconds, then times are rounded down if they occur earlier than 1.75 seconds into the TR. So 11.83 would get rounded up to 12.5, while 11.64 would be rounded down to 10.

FRAC = 1.0 is essentially floor() (as in -truncate_times), while FRAC = 0.0 is essentially ceil().

This option requires -tr.

Consider example 7b. See also -truncate_times.

-scale_data SCALAR : multiply every stim time by SCALAR

e.g. -scale_data 0.975

Use this option to scale (multiply) all times by a single value. This might be useful in effectively changing the TR, or changing the stimulus frequency, if it is regular.

Consider ‘-write_timing’.

-show_timing : display the current single timing data

This prints the current (possibly modified) single timing data to the terminal. If the user is making multiple modifications to the timing data, they may wish to display the updated timing after each step.

-show_tr_stats : display within-TR statistics of stimuli

This displays the mean, max and stdev of stimulus times modulo the TR, both in seconds and as fractions of the TR.

See ‘-warn_tr_stats’ for more details.

-warn_tr_stats : display within-TR stats only for warnings

This is akin to -show_tr_stats, but output is only displayed if there might be a warning based on the timing.

Warnings occur when the minimum fraction is positive and the maximum fraction is small (less than -min_frac, 0.3). If such warnings are encountered, particularly in the case of TENT basis functions used in the linear regression, they can affect the X-matrix, essentially scaling beta #0 by the reciprocal of the fraction (noise dependent).

In such a case the stimuli are almost TR-locked, and the user might be better off making them exactly TR-locked (by creating new timing files using “timing_tool.py -round_times”).

See also ‘-show_tr_stats’, ‘-min_frac’ and ‘-round_times’.
-sort

: sort the times, per row (run)

This will cause each row (run) of the main timing element to be sorted (from smallest to largest). Such a step may be highly desired after using ‘-extend’, or after some external manipulation that causes the times to be unsorted.

Note that 3dDeconvolve does not require sorted timing.

Consider ‘-write_timing’.

-test_local_timing : test for certain problems with local timing

The main purpose of this is to test for timing files that are intended to be interpreted by 3dDeconvolve as being LOCAL TIMES, but might actually be interpreted as being GLOBAL TIMES.

Note that as of 18 Feb, 2014, any ‘*’ in a timing file will cause it to be interpreted by 3dDeconvolve as LOCAL TIMES, even if the file is only a single column.

-timing_to_1D output.1D : convert stim_times format to stim_file

e.g. -timing_to_1D stim_file.1D

This action is used to convert stimulus times to set (i.e. 1) values in a 1D stim_file.

Besides an input -timing file, -tr is needed to specify the timing grid of the output 1D file, -stim_dur is needed to specify the duration of each stimulus (which might cross many output TRs), and -run_len is needed to specify the duration of each (or all) of the runs.

The -min_frac option may be applied to give a minimum cutoff for the fraction of a TR occupied by a stimulus required to label that TR as a 1. If not, the default cutoff is 0.3.

For example, assume options: ‘-tr 2’, ‘-stim_dur 4.2’, ‘-min_frac 0.2’. A stimulus at time 9.7 would last until 13.9. TRs 0..4 would certainly be 0, TR 5 would also be 0 as the stimulus covers only .15 of the TR (.3 seconds out of 2 seconds). TR 6 would be 1 since it is completely covered, and TR 7 would be 1 since .95 (1.9/2) would be covered.

So the resulting 1D file would start with:

0 0 0 0 0 1 1

The main use of this operation is for PPI analysis, to partition the time series (maybe on a fine grid) with 1D files that are 1 when the given stimulus is on and 0 otherwise.

Consider -tr, -stim_dur, -min_frac, -run_len, -per_run_file.

Consider example 6a or 6c.

-transpose : transpose the data (only if rectangular)

This works exactly like 1dtranspose, and requires each row to have the same number of entries (rectangular data). The first row would be swapped with the first column, etc.

Consider ‘-write_timing’.
-truncate_times
 

: truncate times to multiples of the TR

All stimulus times will be truncated to the largest multiple of the TR that is less than or equal to each respective time. That is to say, shift each stimulus time to the beginning of its TR.

This is particularly important when stimulus times are at a constant offset into each TR and at the same time using TENT basis functions for regression (in 3dDeconvolve, say). The shorter the (non-zero) offset, the more correlated the first two tent regressors will be, possibly leading to unpredictable results.

This option requires -tr.

Consider example 7.

-write_timing NEW_FILE : write the current timing to a new file

e.g. -write_timing new_times.1D

After modifying the timing data, the user will probably want to write out the result. Alternatively, the user could use -show_timing and cut-and-paste to write such a file.

-multi_timing_to_events FILE : create event list from stimulus timing

e.g. -multi_timing_to_events all.events.txt

Decide which TR each stimulus event belongs to and make an event file (of TRs) containing a sequence of values between 0 (no event) and N (the index of the event class, for the N timing files).

This option requires -tr, -multi_stim_dur, -min_frac and -run_len.

Consider example 8.

-multi_timing_to_event_pair Efile Ifile : break event file into 2 pieces

e.g. -multi_timing_to_event_pair events.txt isi.txt

Similar to -multi_timing_to_events, but break the output event file into 2 pieces, an event list and an ISI list. Each event E followed by K zeros in the previous events file would be broken into a single E (in the new event file) and K+1 (in the ISI file). Note that K+1 is appropriate from the assumption that events are 0-duration. The ISI entries should sum to the total number of TRs per run.

Suppose the event file shows 2 TRs of rest, event type 3 followed by 4 TRs of rest, event type 1 followed by 1 TR of rest, type 2 and no rest, type 2 and 3 TRs of rest. So it would read:

all events: 0 0 3 0 0 0 0 1 0 2 2 0 0 0 ...

Then the event_pair files would read:

events: 0 3 1 2 2 ... ISIs: 2 5 2 1 4 ...

Note that the only 0 events occur at the beginnings of runs. Note that the ISI is always at least 1, for the TR of the event.

This option requires -tr, -multi_stim_dur, -min_frac and -run_len.

Consider example 8b.

-multi_timing_to_event_list STYLE FILE : make an event list file

e.g. -multi_timing_to_event_list index events.txt e.g. -multi_timing_to_event_list GE:itodf event.list.txt

Similar to -multi_timing_to_events, but make a more simple event list that does not require knowing the TR or run lengths.

The output is written to FILE, where ‘stdout’ or ‘-‘ mean to write to the terminal window.

The information and format is specified by the STYLE field:

index : write event index classes, in order, one row per run

part : partition the first class of events according to the
predecessor classes - the output is a list of class indices for events the precede those of the first class (this STYLE is esoteric, written for W Tseng)

GE:TYPE : write a vertical list of events, according to TYPE

TYPE is a list comprised of the following specifiers, where column output is in order specified (e.g. if i comes first, then the first column of output will be the class index).

i : event class index p : previous event class index t : event onset time d : event duration o : offset from previous event (including previous duration) f : event class file name
-chrono

: process options chronologically

This option has been removed.

-min_frac FRAC : specify minimum TR fraction

e.g. -min_frac 0.1

This option applies to either -timing_to_1D action or -warn_tr_stats.

For -warn_tr_stats (or -show), if the maximum tr fraction is below this limit, TRs are considered to be approximately TR-locked.

For -timing_to_1D, when a random timing stimulus is converted to part of a 0/1 1D file, if the stimulus occupies at least FRAC of a TR, then that TR gets a 1 (meaning it is “on”), else it gets a 0 (“off”).

FRAC is required to be within [0,1], though clearly 0 is not very useful. Also, 1 is not recommended unless that TR can be stored precisely as a floating point number. For example, 0.1 cannot be stored exactly, so 0.999 might be safer to basically mean 1.0.

Consider -timing_to_1D.

-part_init NAME : specify a default partition NAME

e.g. -part_init 2 e.g. -part_init frogs default: -part_init INIT

This option applies to ‘-multi_timing_to_event_list part’. In the case of generating a partition based on the previous events, this option allow the user to specify the partition class to be used when the class in question comes first (i.e. there is no previous event).

The default class is the label INIT (the other classes will be small integers, from 1 to #inputs).

-nplaces NPLACES : specify # decimal places used in printing

e.g. -nplaces 1

This option allows the user to specify the number of places to the right of the decimal that are used when printing a stimulus time (to the screen via -show_timing or to a file via -write_timing). The default is -1, which uses the minimum needed for accuracy.

Consider ‘-show_timing’ and ‘-write_timing’.
-per_run

: perform relevant operations per run

e.g. -per_run

This option applies to -timing_to_1D, so that each 0/1 array is one row per run, as opposed to a single column across runs.

-per_run_file : per run, but output multiple files

e.g. -per_run_file

This option applies to -timing_to_1D, so that the 0/1 array goes in a separate file per run. With -per_run, each run is just a separate row.

-run_len RUN_TIME ... : specify the run duration(s), in seconds

e.g. -run_len 300 e.g. -run_len 300 320 280 300

This option allows the user to specify the duration of each run. If only one duration is provided, it is assumed that all runs are of that length of time. Otherwise, the user must specify the same number of runs that are found in the timing files (one run per row).

This option applies to both -timing and -multi_timing files.

The run durations only matter for displaying ISI statistics.

Consider ‘-show_isi_stats’ and ‘-multi_show_isi_stats’.
-tr TR : specify the time resolution in 1D output
(in seconds)

e.g. -tr 2.0 e.g. -tr 0.1

For any action that write out 1D formatted data (currently just the -timing_to_1D action), this option is used to set the temporal resolution of the data. For example, given -run_len 200 and -tr 0.5, one run would be 400 time points.

Consider -timing_to_1D and -run_len.

-verb LEVEL : set the verbosity level

e.g. -verb 3

This option allows the user to specify how verbose the program is. The default level is 1, 0 is quiet, and the maximum is (currently) 4.

-write_all_rest_times
 

: write all rest durations to ‘timing’ file

e.g. -write_all_rest_times all_rest.txt

In the case of a show_isi_stats option, the user can opt to save all rest (pre-stim, isi, post-stim) durations to a timing-style file. Each row (run) would have one more entry than the number of stimuli (for pre- and post- rest). Note that pre- and post- might be 0.

R Reynolds December 2008

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