Department of Electrical Engineering, National Taiwan Ocean University, Keelung City, Taiwan, Republic of China.
Department of Computer Science, National Taipei University of Education, Taipei City, Taiwan, Republic of China.
PLoS One. 2021 Aug 5;16(8):e0255233. doi: 10.1371/journal.pone.0255233. eCollection 2021.
Due to the complexity of socio-economic-related issues, people thought of housing market as a chaotic nucleus situated at the intersection of neighboring sciences. It has been known that the dependence of house features on the residential property value can be estimated employing the well-established hedonic regression analysis method in teams of location characteristic, neighborhood characteristic and structure characteristic. However, to further assess the roles of urban infrastructures in housing markets, we proposed a new kind of volatility measure for house prices utilizing the Lie symmetry analysis of quantum theory based on Schrödinger equation, mainly focusing on the effects of transportation systems and public parks on residential property values. Based on the municipal open government data regularly collected for four cities, including Boston, Milwaukee, Taipei and Tokyo, and all spatial sampling sites were featured by United States Geological Survey (USGS) National Map, transportation and park were modelled as perturbations to the quantum states generated by the feature space in response to the environmental amenities with different spatial extents. In an attempt to ascertain the intrinsic impact of the location-dependent price information obtained, the similarity functions associated with the Schrödinger equation were considered to facilitate revealing the city amenities capitalizing into house prices. By examining the spatial spillover phenomena of house prices in the four cities investigated, it was found that the mass transit systems and the public green lands possessed the infinitesimal generators of Lie point symmetries Y2 and Y5, respectively. Compared statistically with the common performance criteria, including mean absolute error (MAE), mean squared error (MSE) and, root mean squared error (RMSE) obtained by hedonic pricing model, the Lie symmetry analysis of the Schrödinger equation approach developed herein was successfully carried out. The invariant-theoretical characterizations of economics-related phenomena are consonant with the observed residential property values of the cities internationally, ultimately leading to develop a new perspective in the global financial architecture.
由于与社会经济相关问题的复杂性，人们认为住房市场是一个位于相邻科学交叉点的混沌核心。众所周知，可以使用成熟的特征价格回归分析方法，根据位置特征、邻里特征和结构特征来估计房屋特征对住宅物业价值的依赖性。然而，为了进一步评估城市基础设施在住房市场中的作用，我们利用基于薛定谔方程的量子理论的李对称分析，提出了一种新的房价波动率度量方法，主要关注交通系统和公园对住宅物业价值的影响。
基于波士顿、密尔沃基、台北和东京四个城市定期收集的市政公开数据，并且所有空间采样点都具有美国地质调查局（USGS）国家地图的特征，交通和公园被建模为对特征空间生成的量子态的微扰，以响应具有不同空间范围的环境设施。为了确定获得的位置相关价格信息的内在影响，考虑了与薛定谔方程相关的相似函数，以方便揭示利用房价的城市设施资本。通过检查在所研究的四个城市中房价的空间溢出现象，发现大众运输系统和公共绿地分别拥有李点对称的无穷小生成元 Y2 和 Y5。
与基于特征价格模型获得的常用性能标准（包括平均绝对误差（MAE）、均方误差（MSE）和均方根误差（RMSE））进行统计比较，成功地进行了薛定谔方程李对称分析方法的开发。经济相关现象的不变量理论特征与国际上城市的住宅物业价值观察结果一致，最终为全球金融架构的发展提供了一个新视角。
