Continuous Symmetry Analysis of the Effects of City Infrastructures on Invariant Metrics for House Market Volatilities

The invariant metrics of the effects of park size and distance to public transportation on housing value volatilities in Boston, Milwaukee, Taipei and Tokyo are investigated. They reveal a Cobb-Douglas-like behavior. The scale-invariant exponents corresponding to the percentage of a green area (a) are 7.4, 8.41, 14.1 and 15.5 for Boston, Milwaukee, Taipei and Tokyo, respectively, while the corresponding direct distances to the nearest metro station (d) are −5, −5.88, −10 and −10, for Boston, Milwaukee, Taipei and Tokyo, respectively. The multiphysics-based analysis provides a powerful approach for the symmetry characterization of market engineering. The scaling exponent ratio between park area percentages and distances to metro stations is approximately 3/2. The scaling exponent ratio expressed in the perceptual stimuli will remain invariant under group transformation. According to Stevens’ power law, the perception-dependent feature spaces for parks and public transportation can be described as two- and three-dimensional conceptual spaces. Based on the prolongation structure of the Schrödinger equation, the SL(2, R) models are used to analyze the house-price volatilities. Consistent with Shepard’s law, the rotational group leads to a Gaussian pattern, exhibiting an extension of the special linear group structure by embedding SO(3) ⊗ R(3) in SL(2, R). The influencing factors related to cognitive functioning exhibit substantially different scale-invariant characteristics corresponding to the complexity of the socio-economic features. Accordingly, the contour shapes of the price volatilities obtained from the group-theoretical analysis not only corroborate the impact of the housing pricing estimation in these cities but also reveal the invariant features of their housing markets are faced with the forthcoming sustainable development of big data technologies and computational urban science research.