Several studies have shown that our visual system may construct a “summary statistical representation” over groups of visual objects. Although there is a general understanding that human observers can accurately represent sets of a variety of features, many questions on how summary statistics, such as an average, are computed remain unanswered. This study investigated sampling properties of visual information used by human observers to extract two types of summary statistics of item sets, average and variance. We presented three models of ideal observers to extract the summary statistics: a global sampling model without sampling noise, global sampling model with sampling noise, and limited sampling model. We compared the performance of an ideal observer of each model with that of human observers using statistical efficiency analysis. Results suggest that summary statistics of items in a set may be computed without representing individual items, which makes it possible to discard the limited sampling account. Moreover, the extraction of summary statistics may not necessarily require the representation of individual objects with focused attention when the sets of items are larger than 4.

The supernumerary robotic limb system expands the motor function of human users by adding extra artificially designed limbs. It is important for us to embody the system as if it is a part of one’s own body and to maintain cognitive transparency in which the cognitive load is suppressed. Embodiment studies have been conducted with an expansion of bodily functions through a “substitution” and “extension”. However, there have been few studies on the “addition” of supernumerary body parts. In this study, we developed a supernumerary robotic limb system that operates in a virtual environment, and then evaluated whether the extra limb can be regarded as a part of one’s own body using a questionnaire and whether the perception of peripersonal space changes with a visuotactile crossmodal congruency task. We found that the participants can embody the extra-limbs after using the supernumerary robotic limb system. We also found a positive correlation between the perceptual change in the crossmodal congruency task and the subjective feeling that the number of one’s arms had increased (supernumerary limb sensation). These results suggest that the addition of an extra body part may cause the participants to feel that they had acquired a new body part that differs from their original body part through a functional expansion.

To overcome limitations in perceptual bandwidth, humans condense various features of the environment into summary statistics. Variance constitutes indices that represent diversity within categories and also the reliability of the information regarding that diversity. Studies have shown that humans can efficiently perceive variance for visual stimuli; however, to enhance perception of environments, information about the external world can be obtained from multisensory modalities and integrated. Consequently, this study investigates, through two experiments, whether the precision of variance perception improves when visual information (size) and corresponding auditory information (pitch) are integrated. In Experiment 1, we measured the correspondence between visual size and auditory pitch for each participant by using adjustment measurements. The results showed a linear relationship between size and pitch—that is, the higher the pitch, the smaller the corresponding circle. In Experiment 2, sequences of visual stimuli were presented both with and without linked auditory tones, and the precision of perceived variance in size was measured. We consequently found that synchronized presentation of audio and visual stimuli that have the same variance improves the precision of perceived variance in size when compared with visual-only presentation. This suggests that audiovisual information may be automatically integrated in variance perception.

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