Mapping internal states to formal systems: modeling human numerosity estimation

Whether estimating the size of a crowd, thinking about how heavy something will be before trying to lift it, or reviewing a restaurant on a five-star scale, the modern world frequently requires us to navigate between subjective sensory experiences and shared formal systems. This entails mapping internal variables onto a common scale. Here we ask how people manage this in the case of estimating number. We present people with arrays of dots and ask them to report how many dots there are. In Experiment 1, we test predictions made by existing models of how people map from internal representations of numerosity to verbal estimates. We find that people’s estimates do not have a stable coefficient of variation at higher magnitudes, as has previously been suggested, and that the likely cause of this is a “drift” in people’s estimate calibration over many trials. Building on these results, we present a model of the mapping function from subjective numerosity to formal number estimates which relies only on a limited set of previous estimates and a rough sensitivity to the distribution of numbers in the world. Our model is able to generate an accurate mapping with limited data, as well as reproduce the notable aspects of human estimation described in our experimental results, namely humanlike patterns of underestimation, individual variability, and dynamic miscalibration at higher magnitudes.

Simultaneous Floating-Base Estimation of Human Kinematics and Joint Torques

The paper presents a stochastic methodology for the simultaneous floating-base estimation of the human whole-body kinematics and dynamics (i.e., joint torques, internal and external forces). The paper builds upon our former work where a fixed-base formulation had been developed for the human estimation problem. The presented approach is validated by presenting experimental results of a health subject equipped with a wearable motion tracking system and a pair of shoes sensorized with force/torque sensors while performing different motion tasks, e.g., walking on a treadmill. The results show that joint torque estimates obtained by using floating-base and fixed-base approaches match satisfactorily, thus validating the present approach.