Asymptote

  •   FIND ASYMPTOTE...   3  This is an application of first-order kinetics, in which data approach a stable plateau (asymptote) according to a rate constant (this means that the fractional rate of approach to the asymptote is constant over time).  Some examples include heating and cooling (the "Newtonian" model) and gas mixing and washout characteristics (and many other physical phenomena).

    The program uses an iterative method to find the best-fit asymptote for a selected block of data, according to the simple model: Y = ln (asymptote - data).  You can chose any number of iterations between 6 and 50.  Using a lot of iterations might increase the accuracy of the estimate (this doesn't always occur), but will also increase the analysis time.  In practice, you usually don't need to use more than 6 to 10 iterations for good accuracy.  Note that the algorithm isn't terribly 'smart':   if you give it 'messy' data that do not conform reasonably well to first-order kinetics, the program may take a long time to produce an estimate, and that estimate may have fairly glaring errors (GIGO: garbage in, garbage out).

    After completing the analysis, LabAnalyst shows the asymptote, the coefficient of determination or C.D. (an estimate of the precision of the fit of the data to the model, and hence the precision of the estimated asymptote), the slope of the ln-transformed data, the rate constant (the fraction of the change between a starting value and the asymptote that is completed during 1 time unit), and the time to complete a fraction of the total change between a starting value and the asymptote (values from 1% to 99% are selectable from a pop-up menu).  You can use your choice of time units (seconds, minutes, hours, or days) for slopes and rate constants.

    LabAnalyst also draws a goodness-of-fit plot that illustrates how closely the model matches the data.  Points are plotted in yellow as the log (base e) of the absolute difference between the model predictions and the data:

    Y value = ln (abs(asymptote - data))

    Individual points are shown only if the total number of points in the plot is less than 60.  The line predicted by the model is shown in white. In this example (not the same as for the previous figure), the analysis contained 31 points ranging in value from about 31.1 to slightly less than 0, with a predicted asymptote of -0.05.  If you are analyzing less than 200,000 points, you can also plot the residuals from this regression.

    Some additional considerations:

    • The time needed for finding an asymptote increases with the size of the data block (as well as the number of iterations).  On a typical machine, a block containing several thousand data points will be analyzed within a second or so.
    • You cannot send results to disk or printer by hitting the 'p' key, as usual.  Instead, use the 'print' button (this button is available only if output has been selected from the FILE menu).
    • This option DOES NOT print to a tabular file (the output format is incompatible). 

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