MS: ✗
BD: ✗

Time-Invariant Noise in Time-Invariant Signals

Work on this matter is being done by Saeed Mortezazadeh, post-doctoral fellow at the University of Lethbridge.

When performing equilibrium experiments, it is not possible to distinguish the time-invariant noise patterns from the signals due to the balancing of the sediment flux with the diffusion flux (Fick's Laws).

Solution 1: run empty cells and collect the intensity data patterns of each radial point and wavelength. The volume of the data collected must be significant (due to the presence of statistical noise in each scan) so that a time-invariant pattern can be averaged over all scans.

It is important to note that while the AUC Optima claims to emit light with a one nanometer resolution over a 190 nm to 700 nm range, different patterns can be observed in both the shape and intensity of scans. This is especially prevalent at lower wavelengths and it seems that the monochromatic optical system does not completely split the light, and as a result, the light emitted at a particular wavelength can be partially mixed with neighboring wavelengths.

The intensity of each scan is calculated by averaging the intensity of all radial points:

\[ \hat I = \frac{1}{N}\sum^{N}_{i=1} I (R_{i}). \]

The root mean square deviation (RMSD) is calculated to quantify the shape of each scan:

\[ \text{RMSD} = \sqrt{\frac{1}{N} \sum^{N}_{i=1}(I(R_{i}) - \hat I)^{2}}. \]

The mean and RMSD overlap of scans are clearly visible between neighboring wavelengths.

How do we determine which scan belongs to which wavelength?

  1. Calculate the histogram (probability distribution function) of the RMSD values for each wavelength using the core density equilibrium method.

  2. Scans with similar scans are consider to be in a cluster; histograms are used to cluster scans of all wavelengths.

  3. The main scans of corresponding scans are assumed to be the scans belonging to the cluster with the highest probability distribution.

  4. If the non-original clusters overlap with the main cluster of adjacent wavelengths, the corresponding scans are transferred to the adjacent wavelength.

The procedure for this method is imbedded in UltraScan, and the steps are outlined here.