Figure 3
From: Downstream network transformations dissociate neural activity from causal functional contributions
Difference between causal contributions and activity profiles in three toy examples. (A) We first produced 30 sinusoidal waves with various frequencies and amplitudes. We called these time series building blocks. (B) For the first example, we summed the building blocks that resulted in a new time series that we called the combined time series (teal). (C) Employing MSA showed that the causal contributions (red) and the activity profiles (the building blocks; deep blue) are indistinguishable. Summing the contributions resulted in the combined time series (gray) since no downstream transformation was applied. (D) For the second example, we multiplied the combined time series by a factor of two, which generated a new time series with a larger amplitude. (E) Using MSA, we uncovered the causal contributions and found them to be twice as large as the building blocks, yet retaining a perfect linear relationship (purple), since the structure of the time series remained unchanged. Here, summing contributions resulted in the combined time series with a larger amplitude due to the downstream multiplication operation. (F) For the last example, we passed the combined time series through a nonlinear function that resulted in a warped signal. (G) with MSA, we found the causal contributions to be also warped. Consequently, the trajectory in the contribution-activity space is more complex. In this case, summing the contributions reconstructed the warped time series.
