Distances
Distances tab
This tab page deals with all methods that transform dipolar evolution data into a distance distribution.
There are three main options to perform that transform:
Model free (Makes no assumptions about the mathematical shape of the distance distribution)
Model Based (Assumes a distance distribution as a sum of simple line-shapes)
Tikhonov (A direct transform using linear algebra and related methods)
Model Free
Unlike the plain Tikhonov regularization that completes in milliseconds, model-free fitting uses advanced algorithms to determine a best fit distance distribution given non-negativity and smoothness constraints and is thus slower but still completes in seconds for typical data. For data with a huge number of points and/or many distance points it will be slower. The code is highly parallelized and can take advantage of all available CPU cores to speed up the process.
Simply press Fit! (Fitting can be interrupted by pressing the <Esc> Key). The fitting progress is shown by default in a small popup window.
My "smoothness" parameter is your friend. It acts similarly to the Tikhonov regularization parameter alpha but is named differently to avoid confusion but scales similar to alpha for comparable settings (data, time range, distance range, derivative, etc.). If the data is too spiky, just increase it, re-fit, and look at the results. You want the value to be as high as possible, but stop increasing once the fit and data no longer matches well (increase in the residual norm). There are seven buttons to quickly select from a few typical values. You can explore the performance of the algorithm by simulating some similar data (same dt, same number of points, similar noise, same expected peak widths etc.) to see how to get good agreement with simulation and fit for a given scenario. For more detailed exploration, use the tools on the L-curve tab.
Here is an animation (click image to play!), changing the smoothness for intentionally noisy simulated grid data:
Most of the time, the peaks are concentrated over a smaller distance range. You can greatly speed up the computations by dragging the right and left yellow cursor to restrict the number of distances used for fitting. These same limits are also used for the L-curve calculation (see below). Don't go too close to the data or you get bunching of spurious probabilities at the truncation points. If you see this, make the distance range a little wider. Press "reset cursors" to return to the full range.
The fitting results show some statistical parameters of the fit (distance location of maximum, median, width, and the location of some percentiles). They will probably not make a lot of sense for complicated distributions. The user can obtain more complex metrics by analyzing the saved data.
Model Based
For model based fitting, the distance distribution is assumed to be the sum of up to six mathematically defined lineshapes. A lineshape is enabled if the green bar is lit. Each line has a shape (Fn: gaussian, square, cosine, etc.), a central distance (D), a width (W), and a relative integrated area (A). Enabling a line will display it. Any change in parameters will cause a re-calculation so you can see how the dipolar data would look like under these assumptions. It is recommended to use the purple tikhonov distance distribution as a guide to place the initial line guesses, then simply press fit to have the program optimize the model to best fit the data. For each line, you can optionally fix any of the parameters and thus exclude them from fitting. For example if the width is poorly determined by the data (e.g. due to data truncation) you can fix the width at a reasonable value and fit only for the remaining parameters. To exclude a parameter, turn off the small green LED next to it. The results are given in the table. The parameter error is estimated from the covariance matrix according to the NIST procedure.
If the fitting fails, you should improve the starting guess, fix some parameters, or use fewer peaks.
Background co-fitting
There is a checkbox to "Refine Background". Enabling "Refine background" will include the background parameters in the fit (model-free(!!!) or model-based). This can further improve background determination over the estimate obtained on the background tab. It is often a good idea to co-fit the background. Note that model-free and model-based fitting have their own checkbox to enable co-fitting of the background. The text below the fit button shows the current setting for the current fit mode as a reminder.
Tikhonov
Tikhonov regularization is always performed and is by default non-negative (changeable on the settings tab). Play with alpha to see how things change. A very small value will introduce noise while a very large value causes excessive broadening of the distance distribution.
The fitting results show some statistical parameters of the Tikhonov regularization (distance location of maximum, median, width, and the location of some percentiles). They will probably not make a lot of sense for complicated distributions. The user can obtain more complex metrics by analyzing the saved data.
Saving and printing a fit
Pressing “save” will generate a set of output files as described here. Additional save options are available in the settings tab.
If there is no valid fit result, the Tikhonov regularization is saved.
*To enable experimental features, go to the "Settings" tab and check the box.
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