First, we smoothen time-series concentration data X M (t), and differentiate the resulting smoothing functions to obtain estimates of d X M (t)/ d t.
In the IPE implementation, we first smoothened the time series data using piecewise polynomial spline fitting, and subsequently differentiated the spline functions to obtain estimates of d X M (t)/ d t.
A new class of incremental parameter estimation methods has recently been proposed without the need to smoothen and differentiate noisy time series data [ 11- 13].
The lateral movement was estimated by Gaussian fitting of the peak of the cross-correlated images and the movement over time was smoothened with a low-pass Gaussian filter.
The derivative was computed after mild smoothening of the stimulus time course.
Upon mild smoothening of the stimulus time course trajectories with a Savitzky-Golay filter, the time derivative (gray) of the concentration profile is represented according to the y -axis on the right of the graph.
It demonstrates that the time for complete smoothening of the corrugation is finite, in sharp contrast with the previous treatments of the problem.
Partial dissolution of the oxide rings due to fluorine ions eventually re-shapes the NTs forming ribs, whereas excessive dissolution over extended anodizing times tends to smoothen the NTs and eventually leads to collapse of the NTs.
One might say that the GSDS excursional features may be potentially correlated with any of inclination lows in the previous East Asia records (see Additional file 1: Figure S1), given that post-depositional remanence lock-in can smoothen geomagnetic signals with durations on time scales of hundreds of years (e.g. Channell and Guyodo 2004; Roberts and Winklhofer 2004).
Comparing the outcomes of the IPE and SPE-slope methods using three different (s, o) combinations showed that the accuracy of the parameter estimates from these methods sensitively depends on the manner of which the time-series data are smoothen, especially for the IPE methods.
The average ratio of these voxels were smoothened using a 150 ms (three time points) rolling average, and the lowest 10% of the GCaMP3/mCherry ratio values were averaged to establish a ΔR/R (change in GCaMP3/mCherry fluorescence ratio/absolute ratio) baseline.
