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Innovation is a key factor for a country's overall national strength and core competitiveness. The spatial pattern of innovation reflects the regional differences of innovation development, which can provide guidance for the regional allocation of innovation resources. Most studies on the spatial pattern of innovation are at urban and above spatial scale, but studies at urban internal scale are insufficient. The precision and index of the spatial pattern of innovation in the city needs to be improved. This study proposes to divide spatial units based on geographic coordinates of patents, designs the innovation capability and innovation structure index of a spatial unit and their calculation methods, and then reveals the spatial patterns of innovation and their evolutionary characteristics in Shenzhen during 2000–2018. The results show that: (1) The pattern of innovation capacity of secondary industry exhibited a pronounced spatial spillover effect with a positive spatial correlation. The innovation capacity and innovation structure index of the secondary industry evolved in a similar manner; i.e., they gradually extended from the southwest area to the north over time, forming a tree-like distribution pattern with the central part of the southwest area as the "root" and the northwest and northeast areas as the "canopy". (2) The pattern of innovation capacity of tertiary industry also had a significant spatial spillover effect with a positive spatial correlation. There were differences between the evolutions of innovation capacity and innovation structure index of tertiary industry. Specifically, its innovation capacity presented a triangular spatial distribution pattern with three groups in the central and eastern parts of the southwest area and the south-eastern part of the northwest area as the vertices, while its innovative structure showed a radial spatial distribution pattern with the southwestern part of the southwest area as the source and a gradually sparse distribution toward the northeast. (3) There were differences between the evolution modes of secondary and tertiary industries. Areas with high innovation capacity in the secondary industry tended to be more balanced, while areas with high innovation capacity in the tertiary industry did not necessarily have a balanced innovation structure. Through the method designed in this paper, the spatial pattern of urban innovation can be more precise and comprehensive revealed, and provide useful references for the development of urban innovation. [ABSTRACT FROM AUTHOR]

Based on the significant hotspots analysis method (Getis-Ord Gi* significance statistics), space-time cube model (STC) and the Mann–Kendall trend test method, this paper proposes a G-STC-M spatio-temporal analysis method based on Archaeological Sites. This method can integrate spatio-temporal data variable analysis and the space-time cube model to explore the spatio-temporal distribution of Archaeological Sites. The G-STC-M method was used to conduct time slice analysis on the data of Archaeological Sites in the study area, and the spatio-temporal variation characteristics of Archaeological Sites in East China from the Tang Dynasty to the Qing Dynasty were discussed. The distribution of Archaeological Sites has temporal hotspots and spatial hotspots. Temporally, the distribution of Archaeological Sites showed a gradual increasing trend, and the number of Archaeological Sites reached the maximum in the Qing Dynasty. Spatially, the hotspots of Archaeological Sites are mainly distributed in Jiangsu (30°~33° N, 118°~121° E) and Anhui (29°~31° N, 117°~119° E) and the central region of Zhejiang (28°~31° N, 118°~121° E). Temporally and spatially, the distribution of Archaeological Sites is mainly centered in Shanghai (30°~32° N, 121°~122° E), spreading to the southern region. [ABSTRACT FROM AUTHOR]

Maintaining topological consistency is a crucial issue for 3D cadastral modeling as this helps to represent the cadastral boundary clearly and accurately. As a result, 3D cadastral data models are mainly built on the basis of topological models that allow topology to be expressed clearly. However, topological models in Euclidean space cannot directly represent objects' geometric information. As geometric information is important in 3D spatial analysis, 3D cadastral data models based on topological models cannot realize topological calculation and analysis. Previous research has proved that geometric and topological information for cadastral objects can be integrated and represented by conformal geometric algebra (CGA) expressions. This paper aims to realize 3D topological analysis in the cadastral field using CGA's advantages in geometric relations computation. A calculation framework is designed on the basis of the outer product to achieve the purpose of multidimensional unity for 3D cadastral topological analysis in this paper. A calculation framework of topological relations between a boundary point (or a boundary line) and a cadastral parcel is developed. A total of 13 types of topological relations between a boundary point and a cadastral parcel and 48 types of topological relations between a boundary line and a cadastral parcel are obtained. The study indicates that the advantages of CGA in multidimensional unified representation and calculation can be used to solve problems encountered by topological models in Euclidean space. [ABSTRACT FROM AUTHOR]