Fig. 2
Statistical analysis and extraction of functionals for walking fruit fly experiments. a Single frame of 65 flies walking in a quasi 1D chamber of dimensions 10 cm × 0.8 cm divided into 48 bins with approximate area 0.15 cm2. Heat is applied on the right side of the chamber so that the temperature varies from 35 °C on the left to 50 °C on the right. b Averaged spatial correlation function. c Averaged temporal correlation function. d–e Probability distributions of the number of flies in the two bins outlined in a in red and magenta, respectively. f The “pseudo-free energy,” −ln(N!Pb(N)), for eight representative bins. The observed positive curvature indicates deviations from the Poisson form and repulsive interactions. g Frustration functional, fN, obtained from collapse of the pseudo-free energies for all 48 bins upon removal of the Poisson contributions. h Vexation for each bin as measured from the Poisson contributions to the pseudo-free energies. S.d. error bars in d–f computed from Bayesian posterior distribution assuming a Dirichlet prior. S.d. errors bars in g computed from linear propagation of errors displayed in f
