ROC analysis was used to assess the responses evoked by odors. ROCs were implemented in MatLab software. The auROC is a nonparametric measure of the discriminability of two distributions. We used auROC to assess the neural responses to 8 odors. The value of auROC was defined as ranging from 0 to 1. A value of 0.5 indicates completely overlapping distributions, whereas a value of 1 indicates perfect discriminability. auROC values <0.25 were defined as inhibitory responses; auROC values >0.75 were defined as excitatory responses; 0.25 < auROC values < 0.75 were defined as no significant response. The latency of the response onset, the latency of the peak response, and the response duration were calculated from the auROC values (Fig. (Fig.3A–C).3A–C). Onset latency was defined as the time at which the odor-induced response began (auROC <0.25 or >0.75). Peak latency was defined as the time at which the odor-induced response reached its maximum or minimum point. Response duration was defined as the time from the start to the end of the odor-induced response.

Odor-evoked temporal characteristics of the Ca2+ signals and electrophysiological signals. AC Histograms and cumulative probability for onset latency (A1A4), peak latency (B1B4), and response duration (C1C4) of the Ca2+ signal, beta oscillations, high-gamma oscillations, and spikes from all the mouse/cell–odor pairs (n = 68, 43, 69, and 299 for Ca2+, beta, high-gamma, and spikes, respectively). DF Line charts of the cumulative probabilities for onset latency, peak latency, and response duration (two-sample K–S test, ***P <0.001). Bar charts (inset) show the mean values for onset latency, peak latency, and response duration (Kruskal-Wallis test, ***P <0.001). Ca, calcium; HG, high gamma.

AuROC was also used to calculate the difference between two odor-induced responses. Two responses were randomly selected from 8 odor-induced responses in the same animal. auROC values were positively correlated with the difference in odor-induced responses (Fig. (Fig.6A,6A, B).

Decoding ability of the Ca2+ and electrophysiological signals. A1A4 Heat maps (upper panels, 20 trials) and trial-averaged traces (lower panels) showing the Ca2+ signal, power in the beta and high gamma bands, and spikes evoked by a pair of odors (isoamyl acetate vs n-heptane) in a representative mouse. B auROC analysis of the difference in ΔF/F, normalized LFP band power, and MFR induced by the two odors shown in A. C, D auROC analysis of all mouse/cell–odor pairs (C: Kruskal–Wallis test, ***P <0.001; D: two-sample K–S test, ***P <0.001; for spikes: n = 1652 pairs from 11 mice; for Ca2+, beta and high-gamma, n = 308 pairs from 11 mice). E Performance of the logistic regression classifiers on odor-pair discrimination for ΔF/F, normalized LFP band power, and MFR processed by subtracting the baseline. F Statistical analyses of the accuracy of all odor pairs when time = 5 s as in E (Kruskal–Wallis test, ***P <0.001; for spikes, sample size = 75 from 11 mice for each of the 8 odors; for Ca2+ signals, sample size = 220 from 11 mice for each odor; for beta and high-gamma oscillations, sample size = 200 from 11 mice for each odor). Ca, calcium; HG, high gamma

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