A Novel Robust Approach for Computing DE-9IM Matrices Based on Space Partition and Integer Coordinates

A novel approach for a robust computation of positional relations of two-dimensional geometric features is presented which guarantees reliable results, provided that the initial data is valid. The method is based on the use of integer coordinates and a method to generate a complete, gap-less and non-overlapping spatial decomposition. The spatial relationships of two geometric features are then represented using DE-9IM matrices. These allow the spatial relationships to be represented compactly. The DE-9IM matrices are based on the spatial decomposition using explicit neighborhood relations. No further geometric calculations are required for their computation. Based on comparative tests, it could be proven that this approach, up to a predictable limit, provides correct results and thus offers advantages over classical methods for the calculation of spatial relationships. This novel method can be used in all fields, especially where guaranteed reliable results are required.

A Viewpoint on Population Analyses

Population analyses have become an indispensable tool to computational chemists. Yet implementation within popular quantum chemistry software has buried the interesting philosophical choices made when partitioning the electron density into atomic contributions. There is further historical context that has significantly influenced common conceptions of chemical bonding and reactivity. This work reviews select aspects of orbital and spatial decomposition schemes of the density matrix, pointing out essential linear algebraic considerations and associated tools of shared interest to us and Prof. Mayer.

Comparison of Twelve Machine Learning Regression Methods for Spatial Decomposition of Demographic Data Using Multisource Geospatial Data: An Experiment in Guangzhou City, China

The spatial decomposition of demographic data at a fine resolution is a classic and crucial problem in the field of geographical information science. The main objective of this study was to compare twelve well-known machine learning regression algorithms for the spatial decomposition of demographic data with multisource geospatial data. Grid search and cross-validation methods were used to ensure that the optimal model parameters were obtained. The results showed that all the global regression algorithms used in the study exhibited acceptable results, besides the ordinary least squares (OLS) algorithm. In addition, the regularization method and the subsetting method were both useful for alleviating overfitting in the OLS model, and the former was better than the latter. The more competitive performance of the nonlinear regression algorithms than the linear regression algorithms implies that the relationship between population density and influence factors is likely to be non-linear. Among the global regression algorithms used in the study, the best results were achieved by the k-nearest neighbors (KNN) regression algorithm. In addition, it was found that multi-sources geospatial data can improve the accuracy of spatial decomposition results significantly, and thus the proposed method in our study can be applied to the study of spatial decomposition in other areas.

Programmable nonreciprocal meta-prism

Optical prisms are made of glass and map temporal frequencies into spatial frequencies by decomposing incident white light into its constituent colors and refract them into different directions. Conventional prisms suffer from their volumetric bulky and heavy structure and their material parameters are dictated by the Lorentz reciprocity theorem. Considering various applications of prisms in wave engineering and their growing applications in the invisible spectrum and antenna applications, there is a demand for compact apparatuses that are capable of providing prism functionality in a reconfigurable manner, with a nonreciprocal/reciprocal response. Here, we propose a nonreciprocal metasurface-based prism constituted of an array of phase- and amplitude-gradient frequency-dependent spatially variant radiating super-cells. In conventional optical prisms, nonreciprocal devices and metamaterials, the spatial decomposition and nonreciprocity functions are fixed and noneditable. Here, we present a programmable metasurface integrated with amplifiers to realize controllable nonreciprocal spatial decomposition, where each frequency component of the incident polychromatic wave can be transmitted under an arbitrary and programmable angle of transmission with a desired transmission gain. Such a polychromatic metasurface prism is constituted of frequency-dependent spatially variant transistor-based phase shifters and amplifiers for the spatial decomposition of the wave components. Interesting features include three-dimensional prism functionality with programmable angles of refraction, power amplification, and directive and diverse radiation beams. Furthermore, the metasurface prism can be digitally controlled via a field- programmable gate array (FPGA), making the metasurface a suitable solution for radars, holography applications, and wireless telecommunication systems.