Quantifying long-range correlations and 1/f patterns in a minimal experiment of social interaction

Abstract

In recent years, researchers in social cognition have found the "perceptual crossing paradigm" to be both a theoretical and practical advance toward meeting particular challenges. This paradigm has been used to analyze the type of interactive processes that emerge in minimal interactions and it has allowed progress toward understanding of the principles of social cognition processes. In this paper, we analyze whether some critical aspects of these interactions could not have been observed by previous studies. We consider alternative indicators that could complete, or even lead us to rethink, the current interpretation of the results obtained from both experimental and simulated modeling in the fields of social interactions and minimal perceptual crossing. In particular, we discuss the possibility that previous experiments have been analytically constrained to a short-term dynamic type of player response. Additionally, we propose the possibility of considering these experiments from a more suitable framework based on the use and analysis of long-range correlations and fractal dynamics. We will also reveal evidence supporting the idea that social interactions are deployed along many scales of activity. Specifically, we propose that the fractal structure of the interactions could be a more adequate framework to understand the type of social interaction patterns generated in a social engagement.

Keywords: 1/f noise; long-term correlations; multifractality; multiscale interaction; perceptual crossing; social engagement.

Figure 1

Cumulative probability density function of the time between collisions for different types of opponents aggregated among participants and trials. Values for the regions illustrated are: (dotted line) human vs. oscillatory agent, (dashed line) human vs. shadow agent, (solid line) both participants are human players.

Figure 2

Probability density function of the time between stimulations for different types of opponents aggregated among participants and trials. Values for the regions illustrated are: (A) human vs. oscillatory agent (“vs. oscillator”), (B) human vs. shadow agent (“vs. shadow”), (C) both participants are human players (“vs. human”).

Figure 3

Example of statistical comparison between two multiscale systems. In case 2.a the behavior is statistically different from 1 at scale s₂ because the intrinsic levels of activity at this scale have been increased. However, in case 2.b the statistical differences respect to 1 at scale x₂ is not due to any intrinsic change in x₂ but instead to a change in the relation between x₂ and x₁, that now presents a phase modulation from slower to fastest frequencies.

Figure 4

Fractal analysis calculated on interactive patterns between two participants. Values for the regions illustrated are: (A) human vs. oscillatory agent (“vs. oscillator”), (B) human vs. shadow agent (“vs. shadow”), (C) both participants are human players (“vs. human”). The examples are representative cases of the three kinds of populations in the experiment.

Figure 5

(A) Boxplots distribution of β and, (B) width of the multifractal spectrum Δh in the time series of the relative velocity between participants. Values illustrated refer to interactions between: a human and a oscillatory agent (“vs. oscillator”), a human and a shadow agent (“vs. shadow”) and two human participants (“vs. human”).

Figure 6

Boxplots distribution of β (left side) and width of the multifractal spectrum (right side) in the velocity of the players. The upper figures (A,B) represent the fractal and multifractal analysis when we take the velocity of the player. The bottom figures (C,D) represent the case when we analyze the velocity of the opponent. Values illustrated refer to interactions between: a human and a oscillatory agent (“vs. oscillator”), a human and a shadow agent (“vs. shadow”) and two human participants (“vs. human”).