Early warning signals in motion inference

Abstract

The ability to infer intention lies at the basis of many social interactions played out via motor actions. We consider a simple paradigm of this ability in humans using data from experiments simulating an antagonistic game between an Attacker and a Blocker. Evidence shows early inference of an Attacker move by as much as 100ms but the nature of the informational cues signaling the impending move remains unknown. We show that the transition to action has the hallmark of a critical transition that is accompanied by early warning signals. These early warning signals occur as much as 130 ms before motion ensues-showing a sharp rise in motion autocorrelation at lag-1 and a sharp rise in the autocorrelation decay time. The early warning signals further correlate strongly with Blocker response times. We analyze the variance of the motion near the point of transition and find that it diverges in a manner consistent with the dynamics of a fold-transition. To test if humans can recognize and act upon these early warning signals, we simulate the dynamics of fold-transition events and ask people to recognize the onset of directional motion: participants react faster to fold-transition dynamics than to its uncorrelated counterpart. Together, our findings suggest that people can recognize the intent and onset of motion by inferring its early warning signals.

Trial registration: ClinicalTrials.gov NCT00001360.

Fig 1. Experimental setup.

a) A schematic of an Attacker-Blocker trial. The Attacker starts a move towards either the right or left target at some instant of time, and the Blocker’s goal is to reach the same target as the Attacker as fast as possible, i.e. to minimize the delay t. b) Schematic of location of the seven sensors on the Attacker’s body.

Fig 2. The increase in the decay time of the autocorrelation signal predicts Attacker’s and Blocker’s motion onset.

a) Attacker’s finger motion onset timing as a function of the timing of the increase in the autocorrelation decay time. Inset, For the linear regression calculations, we focused on the highest density regions of the data points (covering 81% of the data points, see S1 Text for other thresholds). Shown are the regression line (solid blue), 50% CI (solid oragne) and 90% CI (solid green) lines. Δt: mean ± ste = 131 ± 2 ms. b) Blocker’s finger motion onset timing as a function of the timing of the increase in the autocorrelation decay time. Inset, For the linear regression calculations, we removed false positive events of the autocorrelation decay time rising earlier than 200 ms from the beginning of the trial and focused on the top highest density regions of the data points (covering 64% of the data points, see S1 Text). Shown are the regression line (solid blue), 50% CI (solid oragne) and 90% CI (solid green) lines. Δt: mean ± ste = 293 ± 2 ms.

Fig 3. Variance of the movement velocity diverges as one approaches the critical point following fold-transition characteristics.

An example of fitting model of log(σ²) = −log(b) + n log(t* − t) to a variance trajectory. Shown is the fit over a window of 12 consecutive time points (Red solid line). The fit parameter for the power-law (n) in this example is -0.53. Inset, Histogram of all fitted power-law parameters smaller than 1.5 (for the entire histogram, see S1 Text). Median fitted power-law is: n = -0.54, 95% CI = [-0.66, -0.5].

Fig 4. Participants act upon the early warning signals in fold-transition events.

a) Participants’ response times for motion of a fold-transition event (Eqn (6-7)) are significantly faster than their response to an uncorrelated version (Eq (8)) of the transition (Δt = 100ms±27ms, Mann-Whitney: U(143) = 20, p = 0.002, effect-size = 0.72). b) Participants’ response times distribution for the fold-transition (red) and uncorrelated transition (green). c) The shift function of decile differences between the fold-transition and uncorrelated transition response times distributions.