The human brain has been described as a complex system. Its study by means of neurophysiological signals has revealed the presence of linear and nonlinear interactions. In this context, entropy metrics have been used to uncover brain behavior in the presence and absence of neurological disturbances. Entropy mapping is of great interest for the study of progressive neurodegenerative diseases such as Alzheimer’s disease. The aim of this study was to characterize the dynamics of brain oscillations in such disease by means of entropy and amplitude of low frequency oscillations from Bold signals of the default network and the executive control network in Alzheimer’s patients and healthy individuals, using a database extracted from the Open Access Imaging Studies series. The results revealed higher discriminative power of entropy by permutations compared to low-frequency fluctuation amplitude and fractional amplitude of low-frequency fluctuations. Increased entropy by permutations was obtained in regions of the default network and the executive control network in patients. The posterior cingulate cortex and the precuneus showed differential characteristics when assessing entropy by permutations in both groups. There were no findings when correlating metrics with clinical scales. The results demonstrated that entropy by permutations allows characterizing brain function in Alzheimer’s patients, and also reveals information about nonlinear interactions complementary to the characteristics obtained by calculating the amplitude of low frequency oscillations.

Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

Based on 898 English documents and 363 Chinese documents citing the Rising of Network Society, it studied that the knowledge contribution of citation content analysis and citation context analysis methods, and the knowledge contribution of Chinese and foreign quotations to human geography. The study found that “mobile space” is the most quoted theoretical view in domestic and foreign literature, and the proportion of domestic research is significantly higher than foreign research; the focus of domestic and foreign research focuses on the external spatial form and its transformation, while foreign research pays more attention on the internal spatial dynamics of network society and three types of knowledge contributions, reflecting the influence of “network social theory” on human geography. Among them, critical references reveal the shortcomings of “network social theory” point out the abstraction of “spatial duality” the importance of local space, and the limitations of research data, methods, and time background, which provides new enlightenment for the future application and innovation of “network social theory” in the field of human geography.

The influence of mining activity on the environment on the environment belongs to the most negative industrial influences. Mine subsidence on the surface can be a result of many deep underground mining activities. The present study offers the theory to the specific case of the deformation vectors solution in a case of disruption of the data homogeneity of the geodetic network structure in the monitoring station during periodical measurements in mine subsidence. The theory was developed for the mine subsidence at the abandoned magnesite mine of Košice-Bankov near the city of Košice in East Slovakia. The outputs from the deformation survey were implemented into geographical information system (GIS) applications to a process of gradual reclamation of whole mining landscape in the magnesite mine vicinity. After completion of the mining operations and liquidation of the mine company, it was necessary to determine the exact edges of the mine subsidence of Košice-Bankov with the zones of residual ground motion in order to implement a comprehensive reclamation of the devastated mining landscape. Requirement of knowledge about stability of the former mine subsidence was necessary for starting the reclamation work. Outputs from the present specific solutions of the deformation vectors confirmed the multi-year stability of the mine subsidence in the area of interest. Some numerical and graphical results from the deformation vectors survey in the abandoned magnesite mine of Košice-Bankov are presented. The obtained results were transformed into GIS for the needs of the municipality of Košice City to the implementation of the reclamation activities in the mining territory of Košice-Bankov.

Aiming at the problem of road network multi-scale matching, a multi-scale road matching method under the constraint of road mesh of small-scale data has been proposed. First, two road meshes with different scale data are constructed; Secondly, under the constraint of the small-scale road mesh, the composite mesh composed of several road meshes in the large-scale road is extracted, and the mesh matching with the small-scale road mesh is completed; Then, many-to-many matching of road meshes with different scales is realized; finally, the matching relationship between composite mesh and small-scale road mesh is transformed into the matching between multi-scale road mesh boundary roads and internal roads, and the matching of the whole road network is completed. The experimental results show that this method can better realize the matching of multi-scale road network.