 stimuli was confirmed using a digital oscilloscope (DS-5424A, Iwatsu, Suginami-ku/ Japan). The experiment was conducted in a dimly darkened room with 39.8 dB (A) of background noise. Participants viewed the monitor binocularly at a distance of 70 cm with their heads stabilized on a chin rest.
Stimuli. Visual stimuli were Gabor patches ( Figure 1A) of two SFs, 1.0 and 5.0 cycles per degree (c/deg). The size of the visual stimulus was approximately 2.0 in diameter, and the luminance was 3.29 to 122.02 cd/m 2 with a duration of 50 ms. The fixation point was a white cross (159.51 cd/m 2 ) that was 1.1 in diameter. These stimuli were presented on a gray background (29.37 cd/m 2 ). The auditory stimulus was a pure tone of 500 Hz with a duration of 50 ms (including ramp times of 5 ms at the beginning and end of the sound wave envelope), and the sound pressure level was 55 dB (A). There were 10 SOAs between visual and auditory stimuli: AE510, AE260, AE130, AE50, and AE0 ms (negative SOAs indicate that the auditory stimulus was presented before the visual stimulus and vice versa). Figure 1B. Trials were initiated by pressing the 0 on the keyboard. Each trial consisted of a 500-ms fixation followed by blank and visual stimulus presentations. The duration of the blank displays was randomized (500-1010 ms). Visual stimulus was presented for 50 ms accompanying an auditory stimulus randomly selected from the range of SOAs. After presenting the visual stimulus, participants were instructed to judge whether the presentation of the visual and auditory stimuli was simultaneous by pressing 1 for simultaneity and 3 for asynchrony. This SJ task consisted of two sessions, each comprising three blocks. One block consisted of 100 trials and there were 10 trials for each SOA condition. Half the trials of one block had the 1.0 c/deg Gabor patch presented, while the remaining half had the 5.0 c/deg Gabor patch presented. Therefore, each participant completed a total of 600 trials. After completing the SJ task, each participant performed a simple RT task for both Gabor patches to confirm the SF-based difference in neural processing speed (Breitmeyer, 1975). The trial sequence is displayed in Figure 1C. A fixation cross was presented at the center of the screen (for 500 ms), followed by a blank display (randomized duration, 500-1010 ms). Then, the visual stimulus was presented until a response was made. Participants were instructed to press the 5 key as soon as the visual stimulus was presented. Each participant completed a total of 60 trials: 30 trials for each SF stimulus.

Results
The proportion of simultaneous responses was calculated for each condition. Two participants were excluded from further analysis, as their SJs were over 25% in the À510 ms or þ510 ms SOA condition. To compute the amplitude, PSS, and sigma values, a threeparameter Gaussian function was fitted to each participant's data based on minimization of the root-mean-square-error (RMSE): The SOA parameter was equal to that of the experimental condition (from À510 to þ510 ms). The parameters of amplitude, PSS, and sigma values were estimated, and the amplitude and sigma values were restricted to greater than 0. The mean estimated PSS and sigma values are shown in Figure 2A and 2B (1.0 c/deg: mean RMSE ¼ 0.06 AE 0.03; 5.0 c/deg: mean RMSE ¼ 0.06 AE 0.03). The PSS was larger for the 5.0 c/deg visual stimulus than for the 1.0 c/deg visual stimulus, t(30) ¼ 2.33, p <.05, d ¼ 0.20, whereas the sigma did not differ between SFs, t(30) ¼ 1.14, p ¼.26, d ¼ 0.06. Moreover, the average RT was computed for each SF using data between 200 and 1000 ms (5.05% of the data were excluded). The results are shown in Figure 2C. A two-tailed t test on the RT data confirmed that processing speed was slower for the 5.0 c/deg visual stimulus than for the 1.0 c/deg visual stimulus, t(30) ¼ 4.88, p <.001, d ¼ 0.45.
An intertrial analysis was conducted to examine whether the modality order on a given previous trial (tÀ1) affected the distribution of simultaneity responses in the current trial (t). Furthermore, the distribution of perceived simultaneity as a function of SOA was compiled for each participant and each SF and trial tÀ1SF separately, given that in some cases trial tÀ1 exhibited either a negative SOA (i.e., audition leads) or positive SOA (i.e., vision leads). The synchrony distributions were then fitted with the above Gaussian function-1.    Figure 3A and 3B. A two-way analysis of variance (ANOVA) with the SF (2) Â the SF on trial tÀ1 (2) was conducted, for the recalibration effect and the simultaneity bandwidth. For the recalibration effect, neither the main effects of SF, F(1, 30) ¼ 0.14, p ¼.71, g p 2 ¼.005, and of SF on trial tÀ1, F(1, 30) ¼ 0.05, p ¼.83, g p 2 ¼.002, nor the interaction, F(1, 30) ¼ 0.46, p ¼.50, g p 2 ¼.02, were significant. In addition, for the simultaneity bandwidth, neither the main effects of the SF, F(1, 30) ¼ 0.39, p ¼.54, g p 2 ¼.01, and of the SF on trial tÀ1, F(1, 30) ¼ 0.02, p ¼.90, g p 2 <¼.001, nor the interaction, F(1, 30) ¼ 2.38, p ¼.13, g p 2 ¼.07, were significant. In follow-up analyses, I examined whether the PSS varied as a function of the SOA on trial tÀ1. By performing this analysis, we aimed to confirm that the PSS depends on the modality order (i.e., SOAs) on the preceding trial. Figure 3C illustrated how the mean PSS varies as a function of the SOA on trial tÀ1. A two-way ANOVA with the SF (2) Â the SOA on trial tÀ1 (9) was conducted. The results revealed a significant main effect of the SOA on trial tÀ1, F(8, 240) ¼ 4.58, p <.001, g p 2 ¼.13. Neither the main effect of the SF, F(1, 30) ¼ 0.001, p ¼.97, g p 2 <¼.001, nor the interaction was significant, F(8, 240) ¼ 0.97, p ¼.46, g p 2 ¼.03.

Experiment 2
Experiment 1 did not show that differences in SF of the current trial modulate the magnitude of rapid recalibration. Furthermore, the magnitudes of rapid recalibration were almost the same regardless of the difference in SF of visual stimuli between the preceding and current trials. In Experiment 2, I replicated that the difference in SF of visual stimuli did not affect the rapid recalibration. However, Gabor patches of either SFs were repeatedly presented in one session in this experiment. The adaptation to a single SF by repeated presentation may affect the rapid recalibration magnitude. Experiment 2 investigated the effects of repeated presentations of the same SF Gabor patch on the rapid recalibration.

Method
Participants. A total of 32 individuals (18 women and 14 men; mean age ¼ 20.56 AE 2.19 years) participated in this experiment. All participants orally reported normal or corrected-to-normal vision and normal hearing and provided written informed consent before participation.
Stimuli. The audiovisual stimuli and experimental conditions were the same as that used in Experiment 1.
Procedure. The trial sequence and task were the same as that in Experiment 1. Participants completed two sessions. Each session comprised three blocks; one block consisted of 100 trials and there were 10 trials for each SOA condition. Therefore, each participant completed a total of 600 trials. Unlike Experiment 1, in one session, either of the two Gabor patches was presented. The order of sessions was counterbalanced across participants. After completing the SJ task, each participant performed a simple RT task for each Gabor patch as in Experiment 1.

Results
The proportion of simultaneous responses was calculated for each condition. Four participants were excluded from further analysis, as their SJs were over 25% in the À510 ms or þ510 ms SOA condition. To compute the amplitude, PSS, and sigma values, a threeparameter Gaussian function was fitted to each participant's data as in Experiment 1. The mean estimated PSS and sigma are shown in Figure 4A and 4B (1.0 c/deg: mean RMSE ¼ 0.07 AE 0.03; 5.0 c/deg: mean RMSE ¼ 0.07 AE 0.03). The PSS was larger for the 5.0 c/deg visual stimulus than for the 1.0 c/deg visual stimulus, t(27) ¼ 2.83, p <.01, d ¼ 0.24, whereas the sigma value did not