Self-consistent field method for open-shell systems within the density-matrix functional theory.

The unrestricted Hartree-Fock method is extended to correlation calculation within the density-matrix functional theory. The method is derived from an entropic cumulant functional for the correlation energy. The eigenvalue equations for the spin-orbitals are modified by the orbital occupation numbers. The Euler equation for the occupation numbers results in the Fermi-Dirac distribution, which is very efficient to update as soon as the orbital eigenvalue equations are solved. The method is demonstrated on the ground state of O 2 .

Development and application of a comprehensive evaluation index system for groundwater quality evolution patterns.

In recent years, driven by rapid socio-economic development and intensified human activities, the groundwater quality has exhibited a concerning trend of degradation. The challenge lies in integrating the impacts of both natural and anthropogenic factors to establish a scientific evaluation framework for the evolution of groundwater quality. This study adopts the model of driving forces - pressures - state - impacts - responses (DPSIR) proposed by the European Environment Agency, in conjunction with the Analytic Hierarchy Process (AHP) and Information Entropy Theory (IET), and the Water Quality Index (WQI) evaluation methods, to construct an evaluation index system for groundwater quality evolution that encompasses driving forces, state, and response systems. Initially, twelve indicators relevant to groundwater quality are quantified by screening across three systems, and a functional relationship between the categorization and scoring of each indicator is established. Subsequently, the weights for each system and indicator are obtained through the AHP, and the objective weights of the indicators are determined using the IET. The scores of each indicator are then comprehensively calculated. Finally, based on the defined types of groundwater quality evolution patterns, an integrated assessment of the evolution of groundwater quality over various time periods is conducted. Taking the Shijiazhuang region as a case study and analyzing the hydrochemical data of groundwater from 1985 to 2015, the results indicate a shift in the groundwater quality evolution pattern from one dominated by natural factors to one primarily influenced by human activities (The comprehensive score of the evaluation index system has increased from 1.84 to 3.25). Among these, the application of fertilizers emerges as the most important driving factors affecting groundwater quality. Particularly, nitrate and total hardness (TH) have emerged as the most salient indicators of quality degradation, with a significant escalation in their composite scores. At the outset, nitrate registered a score of 0.408, while TH scored 0.326; yet, these values have sharply ascended to 0.716 and 0.467, respectively, by the advanced stage. The study concludes with a discussion on the accuracy, strengths, limitations, and applicability of the evaluation index system. The establishment of this evaluation framework provides a scientific basis for the management and protection of groundwater resources and serves as a reference for identifying groundwater quality evolution patterns in other regions.

Green missing spots: Information entropy on greenhouse gas emission disclosure by Brazilian companies.

This study aims to address a critical gap in the literature by examining the incorporation of uncertainty in measuring carbon emissions using the greenhouse gas (GHG) Protocol methodology across all three scopes. By comprehensively considering the various dimensions of CO2 emissions within the context of organizational activities, our research contributes significantly to the existing body of knowledge. We address challenges such as data quality issues and a high prevalence of missing values by using information entropy, techniques for order preference by similarity to ideal solution (TOPSIS), and an artificial neural network (ANN) to analyze the contextual variables. Our findings, derived from the data sample of 56 companies across 18 sectors and 13 Brazilian states between 2017 and 2019, reveal that Scope 3 emissions exhibit the highest levels of information entropy. Additionally, we highlight the pivotal role of public policies in enhancing the availability of GHG emissions data, which, in turn, positively impacts policy-making practices. By demonstrating the potential for a virtuous cycle between improved information availability and enhanced policy outcomes, our research underscores the importance of addressing uncertainty in carbon emissions measurement for advancing effective climate change mitigation strategies.

Spatiotemporal dynamics of ecosystem supply service intensity in China: Patterns, drivers, and implications for sustainable development.

With the steady development of global economy and the rapid increase of population, it is of great significance to quantify the supply capacity of ecosystem services and reveal its driving factors for sustainable development. We quantify the ecosystem supply service intensity (ESSI) using multiple sources of natural and cultural data from 2000 to 2020. We then jointly analyze this data with the information entropy of the land to obtain the temporal and spatial evolution law of ESSI under multiple scales in China. At the same time, according to the spatial distribution of ESSI in China, the concept of China's ecosystem supply service intensity development equilibrium line (ESSIL) is innovatively put forward. The results show that the spatial distribution pattern of China's ESSI is symmetrical with the ESSIL which is nearly orthogonal to Hu Huanyong line. Because of the different regional development policies, different regions with different economic levels have different driving effects on land change. Furthermore, due to the country's large size, the primary ESSI drivers vary greatly throughout its various regions. The assessment of the ESSI changes in China from multi-scale, combined with the effects of land cover change, climate and human activities, and put forward a new pattern distribution mode of ESSI in China, which provides a new perspective for formulating ecologically sustainable development strategies in large-scale areas.

From field soil sampling to watershed model: Upscaling by integrating information entropy and interpolation method.

Soil property data plays a crucial role in watershed hydrology and non-point source (H/NPS) modeling, but how to improve modeling accuracy with affordable soil samplings and the effects of sampling information on H/NPS modeling remains to be further explored. In this study, the number of sampling points and soil properties were optimized by the information entropy and the spatial interpolation method. Then the sampled properties were parameterized and the effects of different parameterization schemes on H/NPS modeling were tested using the Soil and Water Assessment Tool (SWAT). The results indicated that the required sampling points increased successively for soil bulk density (SOL_BD), soil saturated hydraulic conductivity (SOL_K) and soil available water capacity (SOL_AWC). Compared to the traditional database (Harmonized world soil database), the NSE and R2 performance by new scheme increased by 22.8% and 10.5%, respectively. The entropy-based optimization reduced the sampling points by 13.2%, indicating a more cost-effective scheme. Compared to hydrological simulation, sampled properties showed greater effects on NPS modeling, especially for nitrogen. This proposed method/framework can be generalized to other watersheds by upscaling field soil sampling information to the watershed scale, thus improving H/NPS simulation.

Microbial entropy change and external dissipation process of urban sewer ecosystem.

As the initial stage of the sewage treatment system, the degradation of pollutants inevitably involves an entropy change process. Microorganisms play a vital role, where they interact with pollutants and constantly adjust own ecosystem. However, there is a lack of research on the entropy change and external dissipation processes within the sewer system. In this study, considering the characteristics of microbial population changes in the biofilm within the urban sewage pipe network, entropy theory is applied to characterize the attributes of different microorganisms. Through revealing the entropy change of the microbial population and chemical composition, a coupling relationship between the functional bacteria diversity, organic substances composition, and external dissipation in the pipeline network is proposed. The results show that the changes of nutrient availability, microbial community structure, and environmental conditions all affect the changes of information entropy in the sewer network. This study is critical for assessing the understanding of ecological dynamics and energy flows within these systems and can help researchers and operation managers develop strategies to optimize wastewater treatment processes, mitigate environmental impacts, and promote sustainable management practices.

Exploring the Diversity of Nuclear Density through Information Entropy.

This study explores the role of information entropy in understanding nuclear density distributions, including both stable configurations and non-traditional structures such as neutron halos and α-clustering. By quantifying the uncertainty and disorder inherent in nucleon distributions in nuclear many-body systems, information entropy provides a macroscopic measure of the physical properties of the system. A more dispersed and disordered density distribution results in a higher value of information entropy. This intrinsic relationship between information entropy and system complexity allows us to quantify uncertainty and disorder in nuclear structures by analyzing various geometric parameters such as nuclear radius, diffuseness, neutron skin, and cluster structural features.

Underwriter Discourse, IPO Profit Distribution, and Audit Quality: An Entropy Study from the Perspective of an Underwriter-Auditor Network.

Underwriters play a pivotal role in the IPO process. Information entropy, a tool for measuring the uncertainty and complexity of information, has been widely applied to various issues in complex networks. Information entropy can quantify the uncertainty and complexity of nodes in the network, providing a unique analytical perspective and methodological support for this study. This paper employs a bipartite network analysis method to construct the relationship network between underwriters and accounting firms, using the centrality of underwriters in the network as a measure of their influence to explore the impact of underwriters' influence on the distribution of interests and audit outcomes. The findings indicate that a more pronounced influence of underwriters significantly increases the ratio of underwriting fees to audit fees. Higher influence often accompanies an increase in abnormal underwriting fees. Further research reveals that companies underwritten by more influential underwriters experience a decline in audit quality. Finally, the study reveals that a well-structured audit committee governance and the rationalization of market sentiments can mitigate the negative impacts of underwriters' influence. The innovation of this paper is that it enriches the content related to underwriters by constructing the relationship network between underwriters and accounting firms for the first time using a bipartite network through the lens of information entropy. This conclusion provides new directions for thinking about the motives and possibilities behind financial institutions' cooperation, offering insights for market regulation and policy formulation.

Research on Risk Contagion in ESG Industries: An Information Entropy-Based Network Approach.

Sustainable development is a practical path to optimize industrial structures and enhance investment efficiency. Investigating risk contagion within ESG industries is a crucial step towards reducing systemic risks and fostering the green evolution of the economy. This research constructs ESG industry indices, taking into account the possibility of extreme tail risks, and employs VaR and CoVaR as measures of tail risk. The TENET network approach is integrated to to capture the structural evolution and direction of information flow among ESG industries, employing information entropy to quantify the topological characteristics of the network model, exploring the risk transmission paths and evolution patterns of ESG industries in an extreme tail risk event. Finally, Mantel tests are conducted to examine the existence of significant risk spillover effects between ESG and traditional industries. The research finds strong correlations among ESG industry indices during stock market crash, Sino-US trade frictions, and the COVID-19 pandemic, with industries such as the COAL, CMP, COM, RT, and RE playing key roles in risk transmission within the network, transmitting risks to other industries. Affected by systemic risk, the information entropy of the TENET network significantly decreases, reducing market information uncertainty and leading market participants to adopt more uniform investment strategies, thus diminishing the diversity of market behaviors. ESG industries show resilience in the face of extreme risks, demonstrating a lack of significant risk contagion with traditional industries.

Intelligent Fault Diagnosis Method for Rotating Machinery Based on Recurrence Binary Plot and DSD-CNN.

To tackle the issue of the traditional intelligent diagnostic algorithm's insufficient utilization of correlation characteristics within the time series of fault signals and to meet the challenges of accuracy and computational complexity in rotating machinery fault diagnosis, a novel approach based on a recurrence binary plot (RBP) and a lightweight, deep, separable, dilated convolutional neural network (DSD-CNN) is proposed. Firstly, a recursive encoding method is used to convert the fault vibration signals of rotating machinery into two-dimensional texture images, extracting feature information from the internal structure of the fault signals as the input for the model. Subsequently, leveraging the excellent feature extraction capabilities of a lightweight convolutional neural network embedded with attention modules, the fault diagnosis of rotating machinery is carried out. The experimental results using different datasets demonstrate that the proposed model achieves excellent diagnostic accuracy and computational efficiency. Additionally, compared with other representative fault diagnosis methods, this model shows better anti-noise performance under different noise test data, and it provides a reliable and efficient reference solution for rotating machinery fault-classification tasks.

Adaptive Space-Aware Infotaxis II as a Strategy for Odor Source Localization.

Mobile robot olfaction of toxic and hazardous odor sources is of great significance in anti-terrorism, disaster prevention, and control scenarios. Aiming at the problems of low search efficiency and easily falling into a local optimum of the current odor source localization strategies, the paper proposes the adaptive space-aware Infotaxis II algorithm. To improve the tracking efficiency of robots, a new reward function is designed by considering the space information and emphasizing the exploration behavior of robots. Considering the enhancement in exploratory behavior, an adaptive navigation-updated mechanism is proposed to adjust the movement range of robots in real time through information entropy to avoid an excessive exploration behavior during the search process, which may lead the robot to fall into a local optimum. Subsequently, an improved adaptive cosine salp swarm algorithm is applied to confirm the optimal information adaptive parameter. Comparative simulation experiments between ASAInfotaxis II and the classical search strategies are carried out in 2D and 3D scenarios regarding the search efficiency and search behavior, which show that ASAInfotaxis II is competent to improve the search efficiency to a larger extent and achieves a better balance between exploration and exploitation behaviors.

On Playing with Emotion: A Spatial Evolutionary Variation of the Ultimatum Game.

The Ultimatum Game is a simplistic representation of bargaining processes occurring in social networks. In the standard version of this game, the first player, called the proposer, makes an offer on how to split a certain amount of money. If the second player, called the responder, accepts the offer, the money is divided according to the proposal; if the responder declines the offer, both players receive no money. In this article, an agent-based model is employed to evaluate the performance of five distinct strategies of playing a modified version of this game. A strategy corresponds to instructions on how a player must act as the proposer and as the responder. Here, the strategies are inspired by the following basic emotions: anger, fear, joy, sadness, and surprise. Thus, in the game, each interacting agent is a player endowed with one of these five basic emotions. In the modified version explored in this article, the spatial dimension is taken into account and the survival of the players depends on successful negotiations. Numerical simulations are performed in order to determine which basic emotion dominates the population in terms of prevalence and accumulated money. Information entropy is also computed to assess the time evolution of population diversity and money distribution. From the obtained results, a conjecture on the emergence of the sense of fairness is formulated.

HAG-NET: Hiding Data and Adversarial Attacking with Generative Adversarial Network.

Recent studies on watermarking techniques based on image carriers have demonstrated new approaches that combine adversarial perturbations against steganalysis with embedding distortions. However, while these methods successfully counter convolutional neural network-based steganalysis, they do not adequately protect the data of the carrier itself. Recognizing the high sensitivity of Deep Neural Networks (DNNs) to small perturbations, we propose HAG-NET, a method based on image carriers, which is jointly trained by the encoder, decoder, and attacker. In this paper, the encoder generates Adversarial Steganographic Examples (ASEs) that are adversarial to the target classification network, thereby providing protection for the carrier data. Additionally, the decoder can recover secret data from ASEs. The experimental results demonstrate that ASEs produced by HAG-NET achieve an average success rate of over 99% on both the MNIST and CIFAR-10 datasets. ASEs generated with the attacker exhibit greater robustness in terms of attack ability, with an average increase of about 3.32%. Furthermore, our method, when compared with other generative stego examples under similar perturbation strength, contains significantly more information according to image information entropy measurements.

Global Semantic-Sense Aggregation Network for Salient Object Detection in Remote Sensing Images.

Salient object detection (SOD) aims to accurately identify significant geographical objects in remote sensing images (RSI), providing reliable support and guidance for extensive geographical information analyses and decisions. However, SOD in RSI faces numerous challenges, including shadow interference, inter-class feature confusion, as well as unclear target edge contours. Therefore, we designed an effective Global Semantic-aware Aggregation Network (GSANet) to aggregate salient information in RSI. GSANet computes the information entropy of different regions, prioritizing areas with high information entropy as potential target regions, thereby achieving precise localization and semantic understanding of salient objects in remote sensing imagery. Specifically, we proposed a Semantic Detail Embedding Module (SDEM), which explores the potential connections among multi-level features, adaptively fusing shallow texture details with deep semantic features, efficiently aggregating the information entropy of salient regions, enhancing information content of salient targets. Additionally, we proposed a Semantic Perception Fusion Module (SPFM) to analyze map relationships between contextual information and local details, enhancing the perceptual capability for salient objects while suppressing irrelevant information entropy, thereby addressing the semantic dilution issue of salient objects during the up-sampling process. The experimental results on two publicly available datasets, ORSSD and EORSSD, demonstrated the outstanding performance of our method. The method achieved 93.91% Sα, 98.36% Eξ, and 89.37% Fß on the EORSSD dataset.

Analysis of Vibration Characteristics of Bridge Structures under Seismic Excitation.

Bridges may undergo structural vibration responses when exposed to seismic waves. An analysis of structural vibration characteristics is essential for evaluating the safety and stability of a bridge. In this paper, a signal time-frequency feature extraction method (NTFT-ESVD) integrating standard time-frequency transformation, singular value decomposition, and information entropy is proposed to analyze the vibration characteristics of structures under seismic excitation. First, the experiment simulates the response signal of the structure when exposed to seismic waves. The results of the time-frequency analysis indicate a maximum relative error of only 1% in frequency detection, and the maximum relative errors in amplitude and time parameters are 5.9% and 6%, respectively. These simulation results demonstrate the reliability of the NTFT-ESVD method in extracting the time-frequency characteristics of the signal and its suitability for analyzing the seismic response of the structure. Then, a real seismic wave event of the Su-Tong Yangtze River Bridge during the Hengchun earthquake in Taiwan (2006) is analyzed. The results show that the seismic waves only have a short-term impact on the bridge, with the maximum amplitude of the vibration response no greater than 1 cm, and the maximum vibration frequency no greater than 0.2 Hz in the three-dimensional direction, indicating that the earthquake in Hengchun will not have any serious impact on the stability and security of the Su-Tong Yangtze River Bridge. Additionally, the reliability of determining the arrival time of seismic waves by extracting the time-frequency information from structural vibration response signals is validated by comparing it with results from seismic stations (SSE/WHN/QZN) at similar epicenter distances published by the USGS. The results of the case study show that the combination of dynamic GNSS monitoring technology and time-frequency analysis can be used to analyze the impact of seismic waves on the bridge, which is of great help to the manager in assessing structural seismic damage.

Avionics Module Fault Diagnosis Algorithm Based on Hybrid Attention Adaptive Multi-Scale Temporal Convolution Network.

Since the reliability of the avionics module is crucial for aircraft safety, the fault diagnosis and health management of this module are particularly significant. While deep learning-based prognostics and health management (PHM) methods exhibit highly accurate fault diagnosis, they have disadvantages such as inefficient data feature extraction and insufficient generalization capability, as well as a lack of avionics module fault data. Consequently, this study first employs fault injection to simulate various fault types of the avionics module and performs data enhancement to construct the P2020 communications processor fault dataset. Subsequently, a multichannel fault diagnosis method, the Hybrid Attention Adaptive Multi-scale Temporal Convolution Network (HAAMTCN) for the integrated functional circuit module of the avionics module, is proposed, which adaptively constructs the optimal size of the convolutional kernel to efficiently extract features of avionics module fault signals with large information entropy. Further, the combined use of the Interaction Channel Attention (ICA) module and the Hierarchical Block Temporal Attention (HBTA) module results in the HAAMTCN to pay more attention to the critical information in the channel dimension and time step dimension. The experimental results show that the HAAMTCN achieves an accuracy of 99.64% in the avionics module fault classification task which proves our method achieves better performance in comparison with existing methods.

Information Entropy Analysis of a PIV Image Based on Wavelet Decomposition and Reconstruction.

In particle image velocimetry (PIV) experiments, background noise inevitably exists in the particle images when a particle image is being captured or transmitted, which blurs the particle image, reduces the information entropy of the image, and finally makes the obtained flow field inaccurate. Taking a low-quality original particle image as the research object in this research, a frequency domain processing method based on wavelet decomposition and reconstruction was applied to perform particle image pre-processing. Information entropy analysis was used to evaluate the effect of image processing. The results showed that useful high-frequency particle information representing particle image details in the original particle image was effectively extracted and enhanced, and the image background noise was significantly weakened. Then, information entropy analysis of the image revealed that compared with the unprocessed original particle image, the reconstructed particle image contained more effective details of the particles with higher information entropy. Based on reconstructed particle images, a more accurate flow field can be obtained within a lower error range.

ESE-YOLOv8: A Novel Object Detection Algorithm for Safety Belt Detection during Working at Heights.

To address the challenges associated with supervising workers who wear safety belts while working at heights, this study proposes a solution involving the utilization of an object detection model to replace manual supervision. A novel object detection model, named ESE-YOLOv8, is introduced. The integration of the Efficient Multi-Scale Attention (EMA) mechanism within this model enhances information entropy through cross-channel interaction and encodes spatial information into the channels, thereby enabling the model to obtain rich and significant information during feature extraction. By employing GSConv to reconstruct the neck into a slim-neck configuration, the computational load of the neck is reduced without the loss of information entropy, allowing the attention mechanism to function more effectively, thereby improving accuracy. During the model training phase, a regression loss function named the Efficient Intersection over Union (EIoU) is employed to further refine the model's object localization capabilities. Experimental results demonstrate that the ESE-YOLOv8 model achieves an average precision of 92.7% at an IoU threshold of 50% and an average precision of 75.7% within the IoU threshold range of 50% to 95%. These results surpass the performance of the baseline model, the widely utilized YOLOv5 and demonstrate competitiveness among state-of-the-art models. Ablation experiments further confirm the effectiveness of the model's enhancements.

Evaluating the Attraction of Scenic Spots Based on Tourism Trajectory Entropy.

With the development of positioning technology and the widespread application of mobile positioning terminal devices, the acquisition of trajectory data has become increasingly convenient. Furthermore, mining information related to scenic spots and tourists from trajectory data has also become increasingly convenient. This study used the normalization results of information entropy to evaluate the attraction of scenic spots and the experience index of tourists. Tourists and scenic spots were chosen as the probability variables to calculate information entropy, and the probability values of each variable were calculated according to certain methods. There is a certain competitive relationship between scenic spots of the same type. When the distance between various scenic spots is relatively close (less than 8 km), a strong cooperative relationship can be established. Scenic spots with various levels of attraction can generally be classified as follows: cultural heritage, natural landscape, and leisure and entertainment. Scenic spots with higher attraction are usually those with a higher A-level and convenient transportation. A considerable number of tourists do not choose to visit crowded scenic destinations but choose some spots that they are more interested in according to personal preferences and based on access to free travel.

Infrared and Harsh Light Visible Image Fusion Using an Environmental Light Perception Network.

The complementary combination of emphasizing target objects in infrared images and rich texture details in visible images can effectively enhance the information entropy of fused images, thereby providing substantial assistance for downstream composite high-level vision tasks, such as nighttime vehicle intelligent driving. However, mainstream fusion algorithms lack specific research on the contradiction between the low information entropy and high pixel intensity of visible images under harsh light nighttime road environments. As a result, fusion algorithms that perform well in normal conditions can only produce low information entropy fusion images similar to the information distribution of visible images under harsh light interference. In response to these problems, we designed an image fusion network resilient to harsh light environment interference, incorporating entropy and information theory principles to enhance robustness and information retention. Specifically, an edge feature extraction module was designed to extract key edge features of salient targets to optimize fusion information entropy. Additionally, a harsh light environment aware (HLEA) module was proposed to avoid the decrease in fusion image quality caused by the contradiction between low information entropy and high pixel intensity based on the information distribution characteristics of harsh light visible images. Finally, an edge-guided hierarchical fusion (EGHF) module was designed to achieve robust feature fusion, minimizing irrelevant noise entropy and maximizing useful information entropy. Extensive experiments demonstrate that, compared to other advanced algorithms, the method proposed fusion results contain more useful information and have significant advantages in high-level vision tasks under harsh nighttime lighting conditions.