nda(1) nda(1)NAMEnda - to do neighbor density analysis of point positions in planeSYNOPSISnda [-comfile filename] [graph options]DESCRIPTIONNDA is a program that performs "neighbor density analysis" of a pattern of points in a planar region. The key word in this name is "density". In one of its modes of operation, the program computes the average density of neighboring points as a function of radial distance from a point. This has several advantages. First, unlike a nearest neighbor analysis, NDA uses all of the information available about neighboring points, rather than just the distance to the nearest point. Second, the density values (in units of points per square micron or per square pixel) are intuitively meaningful. Third, a completely random distribution would give a flat curve of density versus distance, while the curve for a real distribution of points contains its own control or baseline region because it flattens out to the average density at large distances. Deviations from a flat density curve can be quantified by integrating the deviation from the baseline level. The program inte- grates in a special way to obtain the actual number of points that are extra or deficient, relative to the number expected with a random dis- tribution. Again, this kind of integral is an intuitively meaningful quantity. There are two ways to evaluate the significance of an apparent deviation from randomness. If the set of points is classified into two or more types, one way is simply to assign the points randomly to the various types. The second way is to generate a sample of randomly dis- tributed points within the region being analyzed, with the same number of points of each type as in the original data. One can require these points to be separated by a minimum distance. More realistically, one can specify a series of probabilities for various separations, so that the neighbor density can rise gradually rather than abruptly from zero back to the mean level. With either of these two forms of randomized data, the program can measure the statistical significance of devia- tions in the actual data. To do so, it draws many samples of random data, computes integrals for each sample, and thus determines how often randomly sampled data would give an integral as large as one obtained from the real data. Before using NDA, one must prepare an IMOD model file in which different types of points are each in a different object. For the most accurate density graphs, a single model contour should be drawn to enclose each area in which points are to be analyzed. The placement of the boundary contour is important because NDA uses a sophisticated edge correction method in order to compute densities only from the relevant areas inside the boundary. An arbitrarily shaped contour is allowed and, indeed, preferred. Draw the contour close to the outermost points in the region to be analyzed ("close" here means roughly at the pre- ferred spacing between points, if one is evident by inspection). NDA will automatically connect the first and last points of the boundary object to make a closed contour, so you do not need to make the last point superimpose the first one. If there are obvious regions lacking points inside the data area, try to draw a contour that excludes such regions. You can do this by tracing a path from the outer boundary of points to the hole inside, then drawing around the hole, then following nearly the same path back to the outside. Be careful that this tracing does not cross itself anywhere! If you make the boundary contour too big (leaving excessive space between it and the data points), or if you fail to eliminate significant interior holes, then you will get graphs of density that decline artifactually at larger distances. It is also possibly to analyze all points on a single section without drawing a boundary contour. You might want to do this for quick exploratory analysis, or if you need to average over so many sec- tions that it would be unduly burdensome to draw that many model con- tours. In the simplest form, you can make the boundary be the smallest square that encloses all of the points on the desired section. Or instead, you can have the program find the smallest convex polygon that encloses all of the points. A convex polygon is one with no indenta- tions, so that a straight line between any two points inside the poly- gon stays inside the polygon. This option is described more fully below at the point where the appropriate entries are described. NDA can make two kinds of density graphs. The first, referred to as a "radial" graph, shows the density of neighboring points as a func- tion of radial distance from a central point. The central point is referred to as a reference point. You can choose independently which types of points will be considered as reference points, and which types will be considered as neighbors to those reference points. The second kind of graph, the "angular" graph, shows density versus the angular separation between neighbors in an annulus around a reference point. This graph is more complicated in its complete generality, since it involves a distinction between two types of neighbors to a reference point: neighbors that are themselves considered reference points for the density graph, and "angular" neighbors whose density is measured as a function of angular separation from the "reference" neighbors. To make such a graph, you must choose the inner and outer radii of the annulus, the types of points to be considered reference points, the types to be considered as "reference" neighbors, and the types to be considered as "angular" neighbors. NDA takes several standard command-line options about the graphics win- dow, plus the option-comfilefollowed by the name of a file to take commands from, which works just like the first entry to the program described below. The graphics options are:-sfollowed by a window size in x and y,-pfollowed by a window position in x and y,-messagefollowed by a message to be shown in a message box,-tooltipfollowed by a tooltip for the graphics window, and-nographto disable the graphics window. The latter should be after a-comfileentry, if any. When you start NDA, you will make a standard series of entries until you get your first set of density graphs. Then you will have many options to choose from. The initial standard entries are now described in order. 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 standard 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 program. 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. 0 to get graphs displayed in a graphics window, or 1 to suppress graphs. Name of model file with points to be analyzed, or "Enter" to skip to the place where options are entered. If this model file does not have a pixel size defined, then enter 0 to not scale the data (distances will be in pixels and densities in points per square pixel), 1 to scale the data to microns (densities will be points per square micron), or -1 to specify some other scaling. IF you entered 1, next make two entries. For data digitized from film, enter: Magnification of the negatives, e.g. 15500 Scale during digitization, in microns per pixel For data acquired from CCD, enter: 1000 for the magnification the pixel size on the specimen in nanometers IF you entered -1, instead enter the desired multiplicative scaling factor. 0 for graphs of density versus radial distance from the average refer- ence point, or 1 for graphs of density versus the angular separation between neighbors in an annulus around a reference point. IMOD object number and contour number of the model contour that describes the boundary of the region to be analyzed, or for data read directly from a WIMP model file, the object number and 0. Enter 0,0 to analyze all points on a section, without using a model contour to spec- ify the boundary. (Enter -1,0 at this point to loop back and read a different model file.) IF you entered 0,0, the next line asks for two entries: the Z value of the section, numbered from 0; and either 0 to use the smallest rectangle that encloses all of the points on the section, or 1 to select some special options that would provide a fancier boundary than this, or -1 to use special options selected previously. The default for the Z value is one more than the Z value of the last area analyzed, so it is possible to analyze a series of sequential sections quickly by using , or / to take this default value. IF you enter 1 to select some special options, next make the following entries: A list of types of points to consider in selecting the boundary, or just Return to include all types of points. A distance to "pad" the boundary, so that it will always be at least this distance from any of the points to be included. Enter the distance in microns, or the negative of the number of pixels if you want that number to be scaled into microns. (If there is no scaling, just enter the number of pixels). 0 for a square boundary, or 1 for the smallest convex polygon (see above). IF you enter 1, next enter the fraction of points farthest from the rest to omit in finding the boundary, or just enter 0 to have a boundary that includes all of the points. At this point the program determines what points are within the bound- ary and types out the number and density of each type of point. The types are the object numbers from an IMOD file, or 256 minus the object color for a WIMP file. However, if a point comes from a WIMP object whose display is turned OFF, its type is the NEGATIVE of the object's color. Next you must specify the bin width and extent of the density graphs. For radial graphs, enter the bin width (the increment of radial distance over which a single value of density is computed) and the number of bins. The total radial extent of the graph is the product of the bin width and number of bins. The bin width should be in microns if the model file had a pixel size defined, or if you entered a pixel size as described above. For angular graphs, the extent of the graph is always 180 degrees. Enter the number of bins to divide this range into, and the inner and outer radii of the annulus within which to look for neighbors to a reference point. Next you must specify the graphs that you want to compute. First enter the number of graphs that you want. Then enter the following specifi- cations for each graph in turn: For radial graphs, which show the density of neighboring points around the average reference point, enter: A list of types of points to consider as reference points, or Return to include all types. Ranges may be entered, e.g., 250-252,255 A list of types of points to consider as neighboring points, or Return to include all types. For angular graphs, which show the density of "angular neighbor" points as a function of angular separation from a "reference neighbor" point, where both neighbors are within the specified annulus around a central reference point, enter: A list of types of points to consider as central reference points, or Return to include all types. A list of types of points to consider as reference neighboring points, or Return to include all types. A list of types of points to consider as angular neighbors to those neighboring points, or Return to include all types. Finally, your graphs are displayed and you are presented with the fol- lowing options: 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 graphics file to screen window/printer 12: Output single or average graph to file 45: Set PostScript filename 13: Loop back to specify model contour defining new area to analyze 14: Loop back to specify radial or angular graph and new boundary contour 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: Redo current region(s) with angular instead of radial graph or vice versa 18: Save bins of a graph to specify rejection probabilities for random points 19/26/20: Do current region(s) with shuffled/converted types or random points 21: Save current set of points and their types as an IMOD model 22/27/23: Do many sets with shuffled/converted types/random pnts for integrals 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 34/35: Set up special big array for plots/Plot all windows in array 37/38/39: Add list of graphs/Read list of graphs from file/Read&Add from file 42: Export graph values or points for drawing to file 43: Start or stop outputting all distances or angles to a file First note that the graphs are referred to by number, from 1 up to the total number that you computed. The first few graphs (up to 4 graphs) are displayed in the graphics window. There are 4 areas in this graphics window which are referred to as "windows"; each window shows both the window number and the number of the graph displayed there, with the format WINDOW # : GRAPH #. In some options, you refer to graphs by the graph number, while in other options, you refer to them by their window number. 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 points counted in each bin, rather than the density averaged over the reference points. 3: Use this option to integrate the number of neighboring points 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 points in that range of radial or angular distances. Otherwise, you will get the num- ber of points 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 end of this document 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 region to analyze; enter the object and contour numbers of the boundary contour, 0,0 for a whole section, or -1,0 to read in a different model file. If you have analyzed and aver- aged results from a series of regions, you will be warned that this option will destroy that list of regions, and you will have to confirm your desire to proceed. 14: Loop back to specify both whether you want radial or angular graphs and a new region to analyze. If you have analyzed and averaged results from a series of regions, you will be warned that this option will destroy that list of regions, and you will have to confirm your desire to proceed. 15: Analyze a new region and average its density graphs with those from previous analyzed region(s); enter the object and contour numbers of the new boundary contour, 0,0 for a whole section, or -1,0 to read in a different model file. The first time that you select this option after analyzing a single region, you will be told the graph numbers of the average graphs. If there are N kinds of graphs being built, then graphs for the newly analyzed region alone are referred to as 1 to N, and average graphs are referred to as N+1 to 2N. 16: Re-analyze the currently defined region(s) with different bin sizes, number of bins, 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 specify new types of graphs, or 0 to use the existing specifications. If several regions have been averaged together, then the program will automatically analyze and average all of those regions. 17: Re-analyze the currently defined region(s) with angular instead or radial graphs, or radial instead of angular graphs. You will have to enter new bin sizes, etc, as well as a complete new list of types for the various kinds of graphs that you want. If several regions have been averaged together, then the program will automatically analyze and average all of those regions. 18: Save the initial bins of a graph to use later as a list of proba- bilities for rejecting a randomly sampled point that is too close to another point. 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 probabili- ties 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 point types randomly shuffled. 26: Do the currently defined analysis on the currently defined region(s), but with some of the point randomly converted to other types. This option requires the following entries: Number of types to convert into other types For each of the types to be converted, then enter: The type to convert, the type to change it into, and the fraction of points of that type to convert 20: Do the currently defined analysis on the currently defined region(s), but select random points for each region. This option requires the following entries: Minimum allowed distance of the points from the boundary contour; to enter this distance in pixels, enter the negative of the desired distance (e.g., -10 for 10 pixels) IF you have previously saved probability values with option 18, enter 1 to use these values, or 0 not to. IF you are not using stored probability values, make the following entries: The number of bins of probability values to use for rejecting sampled points as being too close to other points, and the bin size (a radial distance). Enter 0,0 for no rejection of close points. The probability values (between 0 and 1) 21: Save the current set of points and their types as an IMOD model. Enter the model file name. Use this option to examine shuffled types or randomly sampled points. 22/27/23: Do a series of sets of randomly shuffled or converted types or randomly sampled points in order to obtain statistics on the signif- icance of integrated deficiencies or excesses in the real density graphs. If you select option 27, first enter 0 to use previously spec- ified conversions of types, or 1 to specify new conversions, 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 sampling of points. For all of the options, then make the following entries to control the computation of inte- grals: 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; otherwise 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. The program will next compute and type out the integral for each graph. It 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 deviation 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. 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. 34: To set up a big array of graphs on a page for printing. This requires the following entries: Number of columns and rows in the array 0 to fill one row after another, or 1 to fill one column after another Number of ticks along the X axis, number along the Y axis Size of gutter between graphs in X and in Y (/ for 0.20 0.20) A value to scale all graphs to on the Y axis, or 0 for no rescaling 35: To plot all of the currently displayed windows into the next free positions in the big array set up by 34. The program will tell you where each graph has been placed. 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. 43: Start or stop outputting all distances or angles to a file. Once you give this option to open a file for these data, every operation that computes a density graph versus distance will write each distance within the range of the graph to the file, on a line starting with point numbers for the reference point and the neighboring points. The point numbers are simply their index in the set of points abstracted for the current analysis; they might correspond to contour numbers for simple situations, but are otherwise not easily referenced back to the model. Similarly, when a graph of density versus angle between neigh- bors is computed, each angle will be written the file, preceded by the number of the reference point in the center of the annulus and the num- bers of the two neighbors separated by the angle. Select the option again and enter a blank line to stop saving to the file. 45: Set name of output file for PostScript graphics; this can include a relative or absolute path. If a graphics file has already been started, it will be closed, and the file entered here will opened for the next set of graphics output. If you have generated a random data set by randomizing types or by sampling random points, and there is only one region being analyzed, then when you invoke options 16 or 17, you have the option of analyzing either the random data or the original, real data. This allows you to examine a single random set in some detail. Also, if you have sampled random points with option 20 and you select option 19 to shuffle point types, you will have the option of shuffling the types of those random points or of the original, real data.MakingSpecialGraphswithGoodLabelsIf you used option 8 and entered a 0 to indicate that you wanted to specify all the characteristics of the graph, then you have many entries to make. If you are trying to make graphs for publication, it is much easier to set up a command file to do this. The file ndapltex- amp.dat (in the directory $IMOD_DIR/com) can be copied and modified for this use. Some guidance to the use of this file is given below, but first, here is a blow-by-blow description of the entries required after electing to specify the graph characteristics: The graph size in X and Y and coordinates of the lower-left corner in inches; there are 7.5 inches on the page and the lower-left corner of the page is at coordinates of (0,0). The number of divisions (ticks) along the X and Y axes, the tick size in inches, the line thickness (a small integer, 1 for ordinary lines), and 1 to enclose the graph in a box or 0 to omit the top and right axes. Use negative numbers of ticks and a negative tick size to get ticks that go outward from the graph only. Next, for the X axis, enter: # of ticks to label with numeric labels, and number of lines of text labels. IF you specified a nonzero number of ticks to label, next enter: If the ticks are to be labeled at regular intervals, enter the number of the first tick to label (first tick is #1) and the interval between labeled ticks (e.g. 2 for every other tick or enter 0,0 to specify a list of ticks to label. IF you entered 0,0, next enter the #'s of the ticks to label Labels for the ticks, in one line, separated by commas or spaces Numeric label size and separation from axis, in inches IF you specified a nonzero number of text labels, next enter for each label in turn: Text label size, separation from axis, and offset along axis between center of axis and center of text. Text label Next enter these parameters in the same order for the Y axis Finally, the program calls the IMMISC subroutine. Here, coordinates may be specified in one of three ways independently for each of the entries to the program. The coordinates may be in "user" units (the units of the numbers being graphed), in absolute units of inches on the plotter page, or in units relative to the frame of the graph (e.g. 0.1,0.9 for a position in the upper left corner, or 0.5,1.1 for a position centered above the graph frame). Enter the number of text labels, # of letters in circles, # of symbols in boxes, and # of dashed or solid lines to draw IF you entered a non-zero # of text labels, then for each, enter: X and Y position, and 0 for user or 1 for absolute or -1 for relative units 0 to center, -1 to left justify, or 1 to right justify the character string on this position Size of characters in inches, and orientation angle in degrees (usually 0 or 90) Text, on one line IF you entered a non-zero # of circled letters, then for each: X and Y position, and 0 for user or 1 for absolute or -1 for relative units Diameter of circle in inches, line thickness Size of character in inches Letter (upper case) IF you entered a non-zero # of boxed symbols, then for each: X and Y position, and 0 for user or 1 for absolute or -1 for relative units Symbol type (or 0 for no symbol), symbol size in inches, symbol thickness (a small integer), box size in inches (or 0 for no box), box line thickness IF you entered a non-zero # of lines, then for each, enter: 0 for user, 1 for absolute, or -1 for relative units A line specification as described above, in the units just indicated Here are some hints about using the ndapltexamp.dat file. 1) If you want to make several graphs on a page, you have two options: either make a command file for each graph, or combine all of the needed commands into a single file. 2) For the first graph placed into a new PostScript file, the pro- gram does not ask whether you want a new page; so for the first graph, you need to omit the line specifying whether to start a new page or not. 3) You need to decide how many divisions to divide the X and Y axes into, based upon the number of units displayed along the axes. 4) Negative numbers of ticks, and a negative tick size, as in the example, will produce tick marks that go only toward the outsides of the graph, which is preferable. 5) If you want neither numeric nor text labels for an axis, set the number of these labels to 0 and 0 and eliminate the following 5 lines. If you want only numeric labels, eliminate the two lines related to text labels; if you want only a text label, eliminate the three lines related to numeric labels. 6) You must list the desired numeric labels on a line, separated by commas. 7) Special characters can be placed into text labels. The example shows how to get a Greek micron and a superscript. There are three special codes: ^P to make the next character a superscript, ^B to make the next character a subscript, and ^S to make the next character be printed from the symbol font. (If you want more than one special char- acter in a row, each must be preceded by the nexessary code.) In the symbol font, letters map to Greek characters; some other useful entries are 260 for a degree symbol, 261 for +/-, and 264 for a times symbol (x). 8) If you want a single X text label to span two graphs that are side by side, label the X axis for the graph on the left and shift it to the right by the appropriate amount by putting in a positive "offset right from center". Similarly, to have one Y label for two graphs on top of each other, specify the label for the lower graph and shift it up with a positive "offset up from center". 9) The example provides for one line of text and one letter in a circle; you can easily add more lines of text. These items need not be placed inside the frame of the graph: the relative X and Y coordinates can be less than 0 or greater than 1 to place items outside the frame. 10) If you want no text labels, set the "# of lines of text" to 0 and eliminate the 4 lines related to the text line. If you want no letter in a circle, set the "# of letters in circles" to 0 and elimi- nate the 4 lines related to the letter in the circle. 11) If you want to plot more than one graph with a command file, put the appropriate NDA commands in place, then a new set of plotting commands, before returning to keyboard input with a 24.HISTORYWritten by David Mastronarde 7/31/90BUGSEmail bug reports to mast at colorado dot edu. IMOD 4.9.5 nda(1)