FIGURE

Figure 4.

ID
ZDB-FIG-230511-20
Publication
Wolf et al., 2023 - Emergence of time persistence in a data-driven neural network model
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Figure 4.

Mean-field approximation of the inferred Ising model.

(A) Schematic view of the mean-field Ising model. (B) Examples of simulated π‘šπΏ and π‘šπ‘… signals of the mean-field dynamical equations for two sets of parameters that correspond to fish ID #5 at two water temperatures (22Β°C and 30Β°C), see Appendix 2β€”table 2. (C) Free-energy landscapes in the (π‘šπΏ,π‘šπ‘…) plane computed with the mean-field model. These data correspond to the same sets of parameters as in panel (B). Colored circles denote metastable states, and the line of black arrows indicates the optimal path between (π‘šπ‘™π‘œπ‘€,π‘šπ‘™π‘œπ‘€) and (π‘šπ‘™π‘œπ‘€,π‘šβ„Žπ‘–π‘”β„Ž) states. (D) Schematic view of the free energy along the π‘šπ‘… axes. The arrows denote the energy barriers Ξ”β„± associated with the various transitions. The dark green arrow denotes Ξ”β„±((π‘šβ„Žπ‘–π‘”β„Ž,π‘šπ‘™π‘œπ‘€)β†’(π‘šπ‘™π‘œπ‘€,π‘šπ‘™π‘œπ‘€)); the purple arrow denotes Ξ”β„±((π‘šπ‘™π‘œπ‘€,π‘šπ‘™π‘œπ‘€)β†’(π‘šβ„Žπ‘–π‘”β„Ž,π‘šπ‘™π‘œπ‘€)). (E) Values of the free-energy barriers as a function of temperature. Error bars are standard error of the mean (32 recordings, n = 13 fish at 5 different water temperatures). (F) Persistence time of the mean-field anterior rhombencephalic turning region (ARTR) model for all fish and runs at different experimental temperatures. Each dot refers to one fish at one temperature; colors encode temperature.

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