mtk(1)                                                                  mtk(1)



NAME
       mtk - to analyze spatial relationship between objects in 3D

SYNOPSIS
       mtk

DESCRIPTION
       MTK analyzes the distribution of distances of closest approach between
       objects in IMOD models.  It considers objects of 3 kinds: open contour
       objects, which are referred to as "line" objects; scattered point
       objects; and meshed closed contour objects, referred to as "meshed"
       objects.  Each kind of object is generally composed of multiple items
       that are considered separately in the analysis.  For an open contour
       object, each contour forms a separate line.  It is possible to measure
       the closest approach of other items to the whole line, or to break the
       line into multiple segments and measure the closest approaches to each
       of the segments.  For a scattered point object, each point is a sepa-
       rate item, a sphere with a defined radius that may be different for
       each  point.  Distances can be measured either from the center of the
       sphere or from its surface.  For a meshed object, each connected set of
       mesh triangles is considered as a separate entity, referred to as a
       surface.  These surfaces are not the same as the surfaces that can be
       defined within the model in 3dmod.  The model need not contain formally
       defined surfaces; Mtk will analyze the meshes and divide an object into
       surfaces based upon which portions of the mesh are connected to each
       other.

       In general, Mtk measures a quasi-density (number per cubic micron) of
       one kind of object as a function of distance from another kind of
       object.  It does this by considering each item in the second kind of
       object (referred to as reference objects) and measuring the closest
       approach to each of the items in the first kind of object (referred to
       as neighbor objects).  From this, it gets a count of the number of
       closest approaches at each distance from the reference objects.  It
       also estimates the amount of volume at each distance from the reference
       objects, and divides the count by the volume to obtain a density at
       each distance.  Each kind of entity (point, line, line segment, or mesh
       surface) can serve as the reference object; while points, whole lines,
       and mesh surfaces can serve as the neighboring object.

       Ideally, a density analysis will give a graph that is flat or constant
       with distance when items are randomly arranged relative to each other.
       This is rarely the case for the densities produced by Mtk, for several
       reasons.  For anything besides measurements of distance between the
       center of spheres, the density is skewed by using a closest approach
       measure and by the difficulty of estimating the volume of space at a
       given distance from reference items.  Also, there is no provision to
       deal with edge effects as there is in Nda, so density graphs will
       always fall off at large distances.

       The standard way to determine whether a distribution of items is non-
       random is to shift some of the items randomly in space and compare the
       density graph with shifted items to the actual density graph.  In order
       for this approach to be valid, it is essential that the locations of
       the randomly placed items be constrained to about the same degree as
       they are in their original positions.  One main constraint is that
       shifted items should be placed only in the region where they were orig-
       inally modeled.  Mtk allows one to specify an object with contours
       bounding the valid region for shifting.  A second kind of constraint is
       that items should be not occupy the same space as, or come too close
       to, other items of various kinds.  Imposing this constraint can make
       the shifting process very time-consuming.

       Mtk was first written to analyze closest approaches between the trajec-
       tories of microtubules in 3 dimensions (i.e. MicroTubule Kissing).  It
       was adapted from Nda, and many of the entries and commands are identi-
       cal. Some of the terminology used here is a holdover from these ori-
       gins; for example, a "region" refers to the portion of a model being
       analyzed, which is generally the whole model here, and an IMOD model
       object is sometimes referred to as a "type".

       Because these analyses can be very time consuming, you will probably
       want to run mtk through a command file.  The $IMOD_DIR/com directory
       has 4 sample command files that you can examine and adapt for your use:
       mtksimple.com for complete analysis of a simple model; mtkgraph.com
       showing how to plot a saved graph to a postscript file; and mtkcom-
       plex1.com and mtcomplex2.com, based on part of the analysis of Brad
       Marsh's HIT cell model.

       Mtk starts with a number of entries required to define a model file and
       the first analysis and get to the point where numerous options can be
       selected.  These entries are:

       Name of a file to take entries from, or Return to take entries from the
       keyboard.  You can place a laborious series of initial entries into
       such a command file, with one line for each line that you would other-
       wise type in to the program.  However, you would need to have, at
       least, all of the entries that are required to get to the point in the
       program where options may be selected.  Finish the command file with a
       24 to return to input from the keyboard, or with a 25 to exit the pro-
       gram.

       Name of a file to store density values in, or Return for none.  You can
       later use option 12 to store density values for selected graphs in this
       file.  This capability is not as flexible as the ones provided by the
       options for saving and reading graphs from a file (28 and 32).

       0 to get graphs displayed in a graphics window, or 1 to suppress
       graphs.

       0 for analysis of densities and closest approaches in 3D, or 1 for
       analysis of the frequency of MT ends as a function of distance from a
       bundle.  The latter analysis is not documented here.

       The name of the model file, or Return to skip to the point in the pro-
       gram where options may be entered.

       After entering a model file, there are 1 or 4 entries to describe the
       scaling of the coordinates in 3-D:

       Name of file with tilt information, or Return if none If the sections
       were significantly tilted during microscopy, the program can adjust for
       these tilts given the proper information.  Prepare a file in which the
       first line shows the Z value and the tilt of the first tilted section
       (or of the first section, if that one was tilted), and each successive
       line shows the Z value and tilt for each section on which tilt was
       changed.  Z values should occur in ascending order.

       IF the model file has no information about scaling in its header, the
       next three entries are required:

          Magnification of negatives (without any commas)

          Scale, in microns per pixel, at which negatives were digitized

          Section thickness in nanometers

       Next enter a list of Z values (numbered from zero) specifying gaps in
       the data across which meshed objects should be connected to form one
       surface if they overlap in X and Y.  This entry is used when you have a
       gap in modeling between two serial tomograms, and meshed objects that
       span the gap.  If you do not specify the gap, then two pieces of a
       meshed object that are located on opposite sides of the gap will be
       considered separate surfaces even if they overlap in X and Y.  With
       this entry, the program will seek to connect pieces of an object that
       are just adjacent to, or protrude into, the gap, with corresponding
       pieces on the oter side of the gap.  Enter the widest gap that will be
       encounted between entities that you want connected.

       Next enter the lower and upper section numbers within which open con-
       tour (line) objects will be analyzed, or enter 0,0 to have no limits in
       Z for these objects, or 0,-1 to go back and read from a new model.

       Next enter the bin width in microns, and the number of bins to include
       in the density graphs.

       Next are 4 entries that govern density measurements involving lines or
       points:

       0 to find the single closest approach over the entire length of a line,
       or the interval in microns at which lines should be sampled.  With an
       interval, each line is divided into samples, or segments, of this
       length, and distances are measured to/from each segment independently.

       The power to apply in scaling the counts of items at various distances
       from lines into relative density values, and the number of points to
       fit over to determine the 3-D trajectory of a line.  The power is rele-
       vant only when finding the closest approaches to whole lines rather
       than distances to line segments.  Counts are divided by distance to the
       given power.  In choosing a power, the goal is to have a scaled graph
       that is relatively flat over medium distances; a power near 0.4 may
       accomplish this for inter-microtubule distances.  The number of points
       to fit over is relevant to trajectories modeled predominantly through
       the Z dimension (e.g., MTs tracked through serial sections).  For more
       randomly oriented data (e.g., from tomograms), enter 0 for this number.
       If the number of points to fit is 2, then the actual coordinates of
       digitized points, and the line segments connecting them, will be used
       to describe the position of the MT.  With a number great than 2, each
       segment of the MT will be represented by a line least-squares fit to
       that number of points.

       0 to find distances from the start of each line segment, or 1 to find
       the distance of closest approach to each segment.  This entry is rele-
       vant only if lines are being divided into segments.

       0 to measure distances from the center of scattered points or 1 to mea-
       sure from the surface, relying on the radius or size of each point.

       Next enter the number of density graphs to compute.  After this, enter
       two lines for each graph:

          A list of IMOD object numbers of "reference" objects to measure
             distances FROM
          A list of the "neighboring" objects to measure the distances TO,
             from those reference objects.

       You can compute multiple graphs at once, as long as all of the refer-
       ence objects are the same kind (lines, points, or meshes) and all of
       the neighboring objects are the same kind.  If objects to do satisfy
       this constraint, you will be asked to enter the graphs again.

       At this point, the program will compute the distributions then go to
       the central option point.  Here is the option summary:

       1/2: Type/Average selected bins of the graph in a specified window 3:
       Compute integrated number of (excess/missing) items in selected bins
       4/5: Display one graph in a window/Enter list of graphs to display 6/7:
       Rescale X or Y axis of one window/Y axis of all windows 8/9: Plot one
       window/all windows to PostScript graphics file 10/11: Output PostScript
       file to screen/printer 12: Output single or average graph to file 13:
       Loop back to specify new range of Z to analyze (or new model) 14:
       Change radial weighting of a graph 15: Analyze new region and average
       with previous region(s) 16: Redo current region(s) with new bin size, #
       of bins, or types for graphs 17: Set min & max distances at which to
       compute angles and add lines to model 18: Save bins of a graph to spec-
       ify rejection probabilities for random points 19/26/20: Do current
       region(s) with shuffled/converted types or random shifts 21: Save cur-
       rent set of objects and their types as a new model 22/27/23: Do many
       sets & integrals with shuffled/converted types/random
             shifts 24: Take command input from file        25: Exit 28/29/30
       Save a graph/Average/Combine 2 graphs into an extra graph location
       31/32: Save graph in file/Read from file into an extra graph location
       33: Replace some sets of bins by their averages 37/38/39 Add list of
       graphs/Read list of graphs from file/Read&Add from file 40: Unshift an
       object 41: Toggle between including and excluding items that failed to
       shift 42: Export graph values or points for drawing to file 43: List
       distances of close approach between min/max limits 44: Toggle between
       recording distances to all and nearest neighbors

       Here is a specific description of each option:

       1/2: To type or average some of the bins of a graph that is currently
       displayed in a window; enter the window number (1 to 4) and the start-
       ing and ending bin numbers to type or average, or / for all bins.  If
       you enter the negative of the graph number for option 1, you will get
       the raw values of the number of items counted in each bin, rather than
       the density averaged over the reference items.

       3: Use this option to integrate the number of neighboring items that
       are represented by a particular set of bins in a density graph dis-
       played in a window.  Enter the window number, the starting and ending
       bins to integrate, and the baseline or control level.  If you enter a
       control level of 0, you will get the total number of items in that
       range of radial or angular distances.  Otherwise, you will get the num-
       ber of items that are excess or deficient relative to the control
       level.  The default value for the control level (selected by terminat-
       ing the entry with ",," or "/" instead of a value) is the last average
       obtained with option 2.

       4: To display one graph in a window; enter the graph number and the
       window number.

       5: To display a set of graphs in up to 4 windows; enter a list (ranges
       allowed, e.g. 5-8) of up to 4 graph numbers, which will then be dis-
       played in windows 1 to 4.

       6: Rescale X or Y axis of one window; enter the window number and 0 to
       rescale X or 1 to rescale Y.  The program tells you the maximum value
       of the data in that dimension and the current full-scale value on that
       axis.  Then enter the desired full scale X or Y value.

       7: Use this option to rescale the Y axis of all windows to the same
       value, the largest full-scale value needed by any one window.  Note
       that you need to set up the scaling of the graphs to your liking with
       options 6 and 7 before using a plot command.

       8: Plot one window to a PostScript graphics file; enter the window num-
       ber and either 1, 2, 3, or 4 to put the graph in one of the 4 standard
       positions on a page, or 0 to specify the graph location and dimensions.
       Next, enter 1 to start the graph on a new page from a previous graph
       (if there was any previous graph).  IF you elected to specify the graph
       location and position, you now have many entries to make; see the sec-
       tion at the Nda man page for details.

       9: Plot all windows (up to 4) to a PostScript graphics file.  The
       graphs will go in the four standard positions.  Enter 1 to start the
       graph on a new page from a previous graph.  Note that you need to set
       up the scaling of the graphs to your liking with options 6 and 7 before
       using a plot command.

       10: Graph the PostScript file on the screen.  When you return from this
       option, the program will start a new graphics file if you make any more
       graphs with options 8 or 9, and you will lose the file for the graphs
       that you have just seen.  So, if you want those graphs, you need to
       print them immediately with option 11 or rename the file from gmeta.ps.

       11: Print the graphs in the Postscript graphics file.

       12: Print the density values and other pertinent information about a
       graph in the output file defined when you started the program; enter
       the graph number.

       13: Loop back to specify a new range of sections to analyze (for line
       objects), or a new model file entirely.  The new results will replace
       any previously obtained results.

       14: Rescale an existing graph by applying a different power to distance
       in scaling the counts of numbers of items at each different distance.
       This can be useful in making a graph appear flatter after an initial
       peak.

       15: Average a new range of sections (for line objects), or a completely
       different model, with the results already obtained.

       16: Re-analyze the currently defined region(s) with different bin
       sizes, number of bins, line and point parameter settings, or different
       specifications of the types to be used to build graphs from.  After
       entering a new bin size or number of bins, enter 1 if you want to
       change any of the parameters governing line and point distance measure-
       ments, or 0 to use existing parameters.  After changing those parame-
       ters or not, as the case may be, enter 1 if you want to specify new
       types of graphs, or 0 to use the existing specifications.  If several
       regions have been averaged together, then the program will automati-
       cally analyze and average all of those regions.

       17: Set minimum and maximum distances for determining the mean angle of
       closest approach between lines and obtaining markers of points of clos-
       est approach when outputting a model file.  After setting these limits,
       the program will re-analyze the current data, first allowing you to
       enter bin and other parameters and define graphs as if you had selected
       option 16. For any closest approach between these two limits, the pro-
       gram will save the information about the closest approach in case you
       write out a new model file.  For an approach between two lines, it will
       also compute the angle between the two lines.

       43: List all of the distances that fell between the minimum and maximum
       set with option 17, corresponding to the lengths of the connector lines
       that would appear after saving a model file.

       18: Save the initial bins of a graph to use later as a list of proba-
       bilities for rejecting a randomly shifted item that is too close to
       another item.  Enter the graph number and a baseline density level that
       corresponds to a probability of 1.0.  The densities in the bins that
       are less than this baseline level will be converted to probabilities
       between 0 and 1 and stored for later use with options 20 and 23.  This
       option is convenient but does not produce a very good match to the
       rising phase of a density graph; to do that, you have to adjust proba-
       bilities by hand.

       19: Do the currently defined analysis on the currently defined
       region(s), but with line and point contours randomly shuffled among
       objects.  Do not use this option if the model has both line and point
       objects.  It will work for line objects because each line is in one
       contour.  It will work properly for point objects only if each point is
       in a separate contour.

       26: Do the currently defined analysis on the currently defined
       region(s), but with some of the contours in line and point objects ran-
       domly converted to other objects.  This option gives more control than
       option 19 and is suitable if there are both line and point objects,
       because you can prevent conversion between them.  It will always work
       for line objects, but will not work well for point objects unless each
       point is in a separate contour. This option requires the following
       entries:

        Number of objects to convert into other objects

        For each of the objects to be converted, then enter:
           The object to convert, the object to change it into, and the frac-
       tion of
              contours in that object to convert

       20: Do the current region(s) after applying random shifts to the posi-
       tions of selected objects.  Shifting typically requires many attempts
       (trials) to find a position that fits all of the constraints.  This can
       be done in a series of cycles, where the allowed distance to shift is
       increased from one cycle to the next.  There are many entries to make:

          Minimum and maximum distance to shift in the X/Y plane.  The program
          will attempt to shift objects by a distance between these limits for
       a
          certain number of trials on the first cycle, then increase the lim-
       its
          for each following cycle of trials.  If none of these attempts
          succeed, the entity will remain unshifted.

          Maximum amount to shift in Z relative to the maximum shift in the
       X/Y
          plane.  Enter 1.0 for shifts in Z as large as shifts in X and Y, or
       0
          for no shifting in Z, or a number in between to constrain Z shifts
       to
          be smaller than shifts in X and Y.

          List of object numbers of objects to shift, or Return for all
          objects.  The objects must all be of the same kind.

          List of other objects to check distances from, or Return for all
       other
          objects.  When the program attempts to shift an entity, it checks
       its
          distance of closest approach to all entities in the objects speci-
       fied
          in this entry.  This is in addition to checking its distance from
          entities in the objects that are being shifted.

          The number of probability curves to use for determining whether a
          shifted entity is too close to other items.  The first curve will be
          used for checking the spacing between entities in the objects being
          shifted.  Any one of the curves can be used for checking the spacing
          from other objects.

          IF you have previously saved probability values with option 18,
          enter 1 to use these values for the first curve, or 0 not to.

          Make the following entries for each of the probability curves:

             The number of bins of probability values to use for rejecting
             a shifted entity as being too close to other entities, and the
       bin
             size (a radial distance).  This bin size need not match the bin
       size
             the density analysis.

             The probability values for each bin (between 0 and 1)

          IF you have entered more than one curve, next enter the number of
       the
          probability curve to use for each of the other objects that dis-
       tances
          are going to be checked against.

          Maximum distance to shift objects outside the bounding box of the
          original data, i.e., the maximum extent in X, Y, Z and Z of the
          unshifted model.

          Object number of an object with contours that surround the allowed
          volume within which shifted entities must lie.  If the model doesnot
          uniformly fill its bounding box, bounding contours can be used to
          place tighter constraints on the shifted objects and avoid having
       them
          placed preferentially in empty areas of the volume.

          1 to check a potentially shifted item against both items that have
          been shifted and items yet to be shifted, or 0 to check them only
          against items yet to be shifted (as well as against the other
       objects
          that you specified).  If there is a substantial failure rate in
          shifting items, checking against unshifted items will make the
          spacings between all items be legal after shifting, but it might
          increase the difficulty in finding shifted positions.

          Maximum total number of trials or attempts to shift an entity.

          Number of trials per cycle and factor by which to increase the maxi-
       mum
          allowed shifts on each cycle.

       40: Unshift an object that has been shifted.  Enter the object number
       to unshift.  The program will remember which entities were successfully
       shifted, so you can then do an analysis of actual distances from items
       for just the items that were shifted.

       41: Toggle between including and excluding items that failed to shift
       from an analysis.  Originally all items are included; excluding ones
       that failed to shift allows you to do a density graph based on the sub-
       set that shifted, then unshift them and get a completely comparable
       density graph.

       22/27/23: Do a series of sets of items randomly shuffled or converted
       between objects or randomly shifted in order to obtain statistics on
       the significance of integrated deficiencies or excesses in the real
       density graphs.  If you select option 27, first enter 0 to use previ-
       ously specified conversions of objects, or 1 to specify new conver-
       sions, in which case you would then make the entries listed under
       option 26 above.  If you select option 23, first make the entries
       described above under option 20 to control the shifting of objects.
       For all of the options, then make the following entries to control the
       computation of integrals:

          0 to make a separate specification for each graph of the bins to use
       in
          computing the integral, or 1 to use the same specification for all
       graphs

          IF you entered 0, make the following entries for each graph; other-
       wise
          just make these entries once:

             Starting and ending bins of the peak or deficiency to integrate

             Starting and ending bins to compute a baseline density from, or
       0,0 to
                use a fixed value for the baseline instead of computing it
       from
                each graph

             IF you entered 0,0, then enter the fixed baseline density value.

          1 to accumulate mean and standard deviation graphs, or 0 not to.
       This
          question appears after the program computes and types out the inte-
       gral
          for each graph.

       The program will then ask you for the number of control sets to run.
       It will do these control sets, and type out the mean and standard devi-
       ation of the integral for each graph, and the number of sets whose
       integrals exceed the integral of the real data.  You can specify a new
       number of sets to run, whose results will be accumulated with existing
       results, or you can enter 0 to return to selecting options.

       21: can be used to save the current model, which can be either the
       original model or a model after shuffling or converting lines or points
       among objects or shifting lines or points objects randomly.  (Random
       shifts of meshed objects will not be reflected in the output model.)
       If you have run an analysis on this model with limits set for storing
       information on closest approaches, then two new objects will be created
       in the model, one with connecting lines between the two items making a
       selected close approach, and one for scattered points at the middle of
       each connecting line. You can also transfer the contours or surfaces
       that made a close approach within the specified limits into new
       objects.   This will work for line objects, for meshed objects, and for
       point objects if every point is in a separate contour.  With a meshed
       object, all contours associated with a surface having a close approach
       will be transferred.  After entering the output file name, enter a list
       of objects for which you want to transfer a contour to a new object, or
       Return for no such transfers.

       24: Take input from a command file; enter the file name or Return to
       continue or resume input from the keyboard.  The file should end with a
       24 and a blank line to resume input from the keyboard, or a 25 to exit
       the program.

       28:  Save a graph in an "extra" graph location.  An extra location is
       any graph location up to 50; it may already contain a graph.  Enter the
       graph number, and the number of the graph location to save it into.

       29:  Average two graphs into an extra graph location.  The program will
       average the two graphs by computing the total point count and the total
       area occupied by each bin and deriving the density from these values.
       Enter the numbers of the two graphs to average and the number of the
       graph location (any number of 50) in which to place the result.

       30:  Linearly combine two graphs into an extra graph location.  This
       will form a weighed sum of two graphs.  Enter the numbers of the two
       graphs, the coefficients to apply to each, and the number of the loca-
       tion to place the result in.

       31:  Save a graph in a file, in a form that can be easily retrieved and
       redisplayed.  First enter the number of the graph to save.  Then enter
       the name of the file to save it in, or Return to add it to the cur-
       rently open file if graphs have already been saved into that file.

       32:  Read a graph from a file that was saved with option 31.  First
       enter the number of the graph location to read the graph into (any
       value up to 50).  Then enter the name of the file to read from, or
       return to read from a file that has been read from before.  Then enter
       the number of the graph in the file to read.

       33:  Replace some sets of bins by their averages.  In its simplest
       form, this option allows you to combine bins into larger bins and get
       the same graph you would have gotten if you had run the analysis with
       the larger bin size. However, you can choose to combine only selected
       sets of bins, thus allowing you to have a single graph with narrow bins
       in some places and apparently broader bins elsewhere.  Also, you can
       have the program automatically figure out which bins to combine where,
       so that the densities in all of the new apparent bins are based on
       roughly the same amount of area.  This will give you a graph with a
       noise level that is nearly constant across the graph, and may help you
       distinguish signal from noise.  For simple combination of bins, enter
       the number of bins to be averaged together in each replacement, and the
       starting and ending bin numbers to replace (e.g., 3,1,12 will replace
       bins 1, 2, and 3 by their average, 4, 5, and 6 by their average, and
       7-9 and 10-12 by their averages).  For automatic optimal combination of
       bins, enter the NEGATIVE of the desired number of apparent bins to end
       up with over the range of bins being replaced, and the starting and
       ending bin numbers to replace.  For example, -5,1,20 will divide the 20
       bins from 1 to 20 into 5 sets that have, as nearly as possibly, the
       same amount of area for the density calculation.  The program will then
       replace the bins in each set by that set's average.
            After this first entry, next enter a list of graphs to apply the
       replacement to, or Return to apply it to all graphs.  Although you can
       validly run the option first on one set of bins and then again on a
       non-overlapping set of bins, do not run the option more than once on
       the same set of bins.  To experiment with combining bins in different
       ways, copy the desired graph into an extra graph location and combine
       the bins of that copy.  To get the best results from the automatic com-
       bination of bins, start with bins that are much smaller than the final
       desired bin size.

       37: Add a list of graphs into an extra graph loaction.  First enter the
       list of graphs to add together, then enter the location in which to
       place the sum.

       38: Read a list of graphs from a file and place each in a separate
       extra graph location.  First enter the list of graph numbers in the
       file, then enter the list of graph locations in which to place them,
       then enter the name of the graph file from which to read the graphs.

       39: Add together a list of graphs from a file.  First enter an extra
       location in which to place the final sum, and an extra location to be
       used for temporary storage.  Then enter the list of graph numbers in
       the file.  Finally enter the name of the graph file.

       42: Export a graph to a file; i.e., output the graph information in a
       format suitable for importing into a spreadsheet or graphing program.
       First enter the number of the graph to save.  Then enter the name of
       the file to save it in (only one graph can be saved per file).  Then
       enter 0 to output the density values or 1 to output raw counts in each
       bin.  Finally, enter 1 to output points that could be connected to draw
       a histogram, or 2 to output the starting distance and bin value for
       each bin, 3 for the midpoint distance and bin value of each bin, or 4
       for the starting and ending distance and bin value for each bin.

       44: Toggle between recording distances to all and nearest neighbors.
       Initially, the program records in the graphs the distances between each
       reference item and all of its neighbors.  This option switches it to
       recording only the distance to the nearest neighbor for each reference
       item, or back again.  With nearest neighbor distances, the vertical
       scale of the graph is the fraction of reference items that have a near-
       est neighbor at the given distance; the initial power entry has no
       effect on the graph scaling.

HISTORY
              Written by David Mastronarde,  November 1991
               Expanded to full 3-D analysis, March 2000
               Documented, August 2003

BUGS
       Email bug reports to mast at colorado dot edu.



BL3DEMC                              4.7.3                              mtk(1)