Simulated data and relation between HRF-conv. GC and neural GC.

<p>A: Flowchart illustrating the process from neural to HRF-convolved neural to fMRI data. B: An example of the process in A where the neural time series (blue) was generated using AR(1) model and was convolved with a canonical HRF to yield the HRF-convolved neural time series (red), which, after down-sampling to TR = 2 s and addition of 20% white noise (SNR = 5), became the fMRI time series (Green). C: GC for HRF-convolved neural time series as a monotonically increasing function of neural GC where the slope of fitted linear trend is close to 1. D: HRF-conv. GC in the opposite direction is zero (unidirectional coupling).</p

Relation between fMRI GC and neural GC (unidirectional coupling).

<p>A: A typical experiment where fMRI GC is a monotonically increasing function of neural GC. B: fMRI GC and neural GC along opposite directions are uncorrelated. C: Distributions of correlation coefficients between neural GC and fMRI GC along the same direction (red) and along opposite directions (blue). D: TPR, FPR and TDR as functions of correlation significance threshold.</p

Effects of TR and noise.

<p>A: TDR, TPR and FPR as functions of fMRI TR. B: TDR, TPR and FPR as functions of the noise level.</p

Relation between fMRI GC and neural GC (bidirectional coupling).

<p>A: A typical experiment where fMRI GC is a monotonically increasing function of neural GC. B: fMRI GC and neural GC along opposite directions are uncorrelated. C: Distributions of correlation coefficients between neural GC and fMRI GC along the same direction (red) and along the opposite directions (blue). D: TPR, FPR and TDR as functions of correlation significance threshold.</p

Velocity Fluctuations in Helical Propulsion: How Small Can a Propeller Be

Helical propulsion is at the heart of locomotion strategies utilized by various natural and artificial swimmers. We used experimental observations and a numerical model to study the various fluctuation mechanisms that determine the performance of an externally driven helical propeller as the size of the helix is reduced. From causality analysis, an overwhelming effect of orientational noise at low length scales is observed, which strongly affects the average velocity and direction of motion of a propeller. For length scales smaller than a few micrometers in aqueous media, the operational frequency for the propulsion system would have to increase as the inverse cube of the size, which can be the limiting factor for a helical propeller to achieve locomotion in the desired direction