Figure 2.

The memory kernel, κ, is extracted from the noisy dwell time histogram, f. Left: A noisy dwell time histogram generated synthetically with 30% noise. Right: The resulting memory kernel. The green curve is the exact memory kernel (0% noise). The pink curve is obtained by direct brute force inversion of the data f. The brute force inversion produces a very noisy memory kernel. For this reason, we introduce a regularization method—detailed in the Appendix—to invert a kernel from the data. The red curve is the memory kernel obtained using this method with a prior shown as a blue dotted line. The prior—also detailed in the Appendix—is our guess as to what the memory kernel should look like in the absence of data. The memory kernel and the dwell time histogram are defined by eq 1.