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.

[Objective]In order to explore the sustainable food security level in the Yangtze River Economic Belt, ensure food security and sustainable development of agricultural modernization, it is necessary to establish a scientific food security evaluation system to safeguard local food security.[Methods]This paper takes the food system of the Yangtze River Economic Belt in China as the research object, based on the food security research results at home and abroad, based on sustainable development thinking, combined with a new perspective of dynamic equilibrium research: Beginning with food normalcy, a comprehensive analysis of food production, food economy, social development, ecological security, and technical support for sustainable development is presented using the entropy-weighted TOPSIS model to build a food security evaluation system for sustainable development. [Conclusion]After systematic analysis, it is concluded that (1) the average value of food security score of the Yangtze River Economic Belt from 2008 to 2021 is 0.429, and the overall food in the Yangtze River Economic Belt is in general security level (0.400 ≤ Q1 ≤ 0.600), and the overall situation of food security is not optimistic, (2) from the segmentation of the Yangtze River Economic Belt, the high and low level of food security are divided into sections: midstream > downstream > upstream, and each province and city is slowly rising to different degrees. In this way, we propose general countermeasures to ensure local food security from the perspective of sustainable development.

The world has changed to a massive degree in the past thousands of years. Most of the time, the amount of carbon dioxide in the atmosphere remains constant. In the late 18th century, according to the sources of CDIAC and NOOA, the level of carbon dioxide began to rise, and then in the 20th century, it went through the roof, reaching levels that had not been seen in nature for millions of years. The increase in carbon in the atmosphere is the major contributing factor to climate change. The key to reversing the damage is restoring the earth’s delicate, balanced carbon cycle. As carbon cycle depicts the way carbon moves around the earth. It consists of sources that emit the carbon component into the atmosphere. The biological side of the carbon cycle is well balanced due to respiration, where carbon dioxide is released into the atmosphere, then plants, bacteria, and algae take carbon dioxide out of the atmosphere during photosynthesis and the process they use to generate chemical energy. On the other hand, oceans are the best sources and sinks; carbon dioxide is endlessly being absorbed into the ocean and released from the oceans almost exactly at the same rate, which is rapidly influencing the carbon cycle. Similarity is a methodology that has many applications in the real world. The current research article is destined to study how statistics of carbon emission metrics are alike and belong to one cluster. In the current study, the research is destined to derive a similarity analysis of several countries’ carbon emission metrics that are alike and often fall in the range of [0, 1]. And deriving the proximity of the carbon emission metrics leading to similarity or dissimilarity. In the current context of data matrices of numerical data, an Euclidian measure of distance between two data elements will yield a degree of similarity. The current research article is destined to study the similarity analysis of carbon emission metrics through fuzzy entropy clustering.

Assessment of water resources carrying capacity (WRCC) is of great significance for understanding the status of regional water resources, promoting the coordinated development of water resources with environmental, social and economic development, and promoting sustainable development. This study focuses on the Longdong Loess Plateau region and utilized panel data spanning from 2010 to 2020, established a three-dimensional evaluation index system encompassing water resources, economic, and ecological dimensions, uses the entropy-weighted TOPSIS model coupled with global spatial autocorrelation analysis (Global Moran’s I) and the hot spot analysis (Getis-Ord Gi* index) method to comprehensively evaluate the spatial distribution of the WRCC in the study region. It can provide scientific basis and theoretical support for decision-making on sustainable development strategies in the Longdong Loess Plateau region and other regions of the world.From 2010 to 2020, the overall WRCC of the Longdong Loess Plateau area show some fluctuations but maintained overall growth. The WRCC in each county and district predominantly fell within level III (normal) and level IV (good). The spatial distribution of the WRCC in each county and district is featured by clustering pattern, with neighboring counties displaying similar values, resulting in a spatial distribution pattern characterized by high carrying capacity in the south and low carrying capacity in the north. Based on these findings, our study puts forth several recommendations for enhancing the WRCC in the Longdong Loess Plateau area.