Narrow Results

With the rapid expansion of power grids and increasing user demand, effectively identifying and monitoring abnormal electricity consumption have become crucial for ensuring grid stability and operational efficiency. Traditional anomaly detection methods often struggle with scalability and accuracy, particularly as the volume and density of electricity data grow. To address these challenges, this paper introduces a novel electricity anomaly monitoring framework that integrates real-time data acquisition and advanced classification modeling techniques. Our approach leverages a parallel classification algorithm designed to efficiently handle large datasets and detect anomalies with high accuracy. Key features of abnormal user data are extracted using information entropy, and electricity consumption data are continuously collected through a wireless network. The proposed method then preprocesses and classifies the data, applying a random forest model to detect anomalies and monitor usage patterns. Experimental results indicate that our approach significantly enhances both the accuracy and efficiency of electricity anomaly detection, demonstrating its robustness and potential for large-scale deployment in power grid systems.

In this paper, we study the formation of Shannon information entropy in spin–orbit coupled (SOC) spin-1 antiferromagnetic dipolar Bose–Einstein condensates with external magnetic field. Our results show that, in the absence of magnetic field and with an increase in dipole–dipole interaction (DDI), information entropy in position space $S_r$ and momentum space $S_k$ remains almost unchanged and increases, respectively. Meanwhile, the order parameter $\delta$ decreases, which implies that the system develops toward a disorder state. With the increase of SOC strength, $S_r$, $S_k$ and $\delta$ show similar dynamics behavior. Whereas, in the presence of magnetic field, $S_k$ and $\delta$ are localized in the small scope by increasing the dipole and SOC strength. In addition, the value of $S_r$ is nearly the same in this process. These results embody that the introduction of external magnetic field suppresses the role of SOC and DDI, and impedes the condensates towards disorder state. At last, the influence of geometric structure and atom number on information entropy is investigated. It is seen that a narrower trap and fewer atom number make $S_r$ decrease and $S_k$ increase.

Operational risk capital is typically allocated on an annual timescale in extant research, while ignoring that the dependence between operational risk events may differ on different timescales, such as semi-annual and quarterly. This study examines whether operational risk dependence structures differ on multiple timescales and proposes an optimal timescale selection method based on information entropy theory to obtain more reasonable operational risk measurement results. Different dependence modeling methods, including linear correlation and copula functions, are employed to analyze the dependence structures on multiple timescales. The information changes between different timescales are calculated to select the optimal timescale. The empirical analysis is based on 2,024 operational risk events from 1994 to 2017 in the Chinese Operational Loss Database (COLD), which is one of the largest external operational risk datasets for the Chinese banking industry. The results reveal significant differences in operational risk dependence at different timescales which affect the operational risk measurement results. Crucially, the quarterly timescale should be considered for more reasonable measurements. The findings provide important insights for considering a more reasonable allocation of operational risk capital under multiple timescale dependence.

A modeling methodology for blog recommendation and forecasting based on information entropy is presented. With the increasing popularity of smartphones and the rapid development of the mobile Internet, the amount of user-generated content such as blogs is increasing daily. Valuable information, such as bloggers’ opinions, feelings, and attitudes, is often part of this content. Particularly in the context of an emergency, this information should also be used to facilitate decision making. The current blog recommendation model examines primarily users’ interests or content similarity, whereas in this paper, the value of the blog is considered. The primary contribution of this paper is the proposal of an information-entropy-based blog recommendation model for finding valuable blogs to facilitate decision-making in an emergency context. A series of indicators for evaluating a blog in an emergency context are proposed. Using the method of information entropy, a blog recommendation model is developed. The model can also be used to forecast the value of emergency blogs in the future. The model has been tested and validated using crawled data from the Sina Blog, and the results have demonstrated that the proposed model can effectively determine the value of emergency-related blogs.

The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of ${𝒫}{𝒯}$-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the ${𝒫}{𝒯}$-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, ${𝒫}{𝒯}$ phase transition conjectures the entropy squeezing in position space and momentum space.

The upper bound U_B(t) of the time derivative of entropy for a dynamical system driven by both additive colored noise and multiplicative colored noise with colored cross-correlation is investigated. Based on the Fokker–Planck equation, the effects of the parameters on U_B(t) are analyzed. The results show that: (i) α (the multiplicative noise intensity), D (the additive noise intensity) and τ₂ (the correlation time of the additive noise) always enhance U_B (t) monotonically; (ii) λ (the intensity of the cross-correlation between the multiplicative noise and the additive noise), τ₁ (the correlation time of the multiplicative noise), τ₃ (the correlation time of the cross-correlation) and γ (the dissipative constant) all possess a minimum, i.e., U_B (t) decreases for small values and increases for large values.

In this paper we have studied the dynamics of thermal broadband noise-driven dynamical system in terms of information entropy at both the nonstationary and stationary states. Here, a unified description of fluctuating force is considered in a thermodynamically closed system. Based on the Fokker–Planck description of stochastic processes and the entropy balance equation, we have calculated the time-dependence of the information entropy production and entropy flux in the presence and absence of nonequilibrium constraint. Our calculation considers how the time evolution of these quantities is affected if the characteristic of noise changes from white to red or green and red to green in a unified scheme.

In this paper we have studied information dynamics of both internal and external noises driven harmonic oscillator. Based on the Fokker–Planck description of the stochastic processes and the Schwarz inequality principle we have calculated upper bound of rate of change of information entropy with time and its deviation from the time derivative of the entropy. The bound and the deviation monotonically decreases to zero during the relaxation of a given nonequilibrium state to a stationery state. The relaxation time increase with increase of noise correlation time of the internal colored thermal noise but it is independent on the correlation time of the external colored noise. However, an extremum behavior appears in the variation of the bound as a function of parameter of the system such as damping strength, noise correlation time of thermal and nonthermal noises etc.

Compared with the low dimension chaotic systems (LDCS), the high dimension chaotic systems (HDCS) have many advantages as more complex mechanism, increasing the key space, more ruleless for the time series of the system variable, etc. Based on these reasons, a new encryption cryptosystem based on Lorenz system is proposed. The theoretical and experimental results show that, this algorithm can resist the local linear attack, the phase space reconstruct attack, the entropy attack, etc. The proposed cryptosystem has higher security.

In this paper, we study the properties of information entropy in spin–orbit coupled spin-1 Bose–Einstein condensates. Our discussion is divided into two parts, stationary state and dynamics. For the former, we find that the coordinate component S_r and total entropy S increase with the strength of the spin–orbit coupling $\kappa$. The momentum component S_k shows a discontinuity behavior, it increases with $\kappa$ when $\kappa$ is lesser than a critical value ${\kappa }_c$, while it decreases with $\kappa$ when $\kappa$ is greater than ${\kappa }_c$. In order to characterize the disorder-to-order transition, we introduce an order parameter $\eta$. Numerical results display that $\eta$ gradually increases with increasing $\kappa$ and reaches its saturation, which implies that the system becomes more and more ordered. For the latter, the S_r increases and S_k decreases with increasing $\kappa$ at the same time. The entropic uncertainty relation is well obeyed at fixed $\kappa$. Moreover, $\eta$ decreases as a function of t. The strength effect of spin–orbit coupling on order-to-disorder transition becomes weak.

Identifying the vital nodes in complex networks is essential in disease transmission control and network attack protection. In this paper, in order to identify the vital nodes, we define a centrality method named EMDC, which is based on information entropy, minimum dominating set (MDS) and the distance between node pairs. This method calculates the local spreading capability (LSC) of node by information entropy and selects that nodes have the largest value of LSC as core nodes by MDS. Then it defines the node’s spreading capability (SC) to use the sum of weighted distances from a node to the core nodes. Finally, the nodes are ranked by considering SC of their neighbors. The key nodes can be further identified in complex networks. In order to verify the effectiveness of this method, key nodes identification simulation experiments are carried out on 11 real networks, Scale-Free (BA) networks and Small-World (WS) networks, respectively. Experimental results show that this method can more effectively identify the influence of nodes in the networks.

Complex network is now widely used in a series of disciplines such as biology, physics, mathematics, sociology and so on. In this paper, we construct the stock price trend network based on the knowledge of complex network, and then propose a method based on information entropy to divide the stock network into some communities, that is, a gathering study of stock price trend. We construct time series networks for each stock in Chinese A-share market based on time series network model, and then use these networks to divide the stock market into communities. We find that the average trend of stocks in the same community is the same as the trend of market value weighting, but the average trend of stocks in different communities is quite different and the sequence correlation is low. This conclusion shows that stocks in the same community share the same price trend, while the stock trend in different communities varies. This paper is a successful application of complex network and information entropy in stock trend analysis, which mainly includes two contributions. First, the success of the visibility graph algorithm provides a new perspective for enriching stock price trend modeling. Second, our conclusion proves that the clustering based on information entropy theory is effective, which provides a new method for further research on stock price trend, portfolio construction and stock return prediction.

Link prediction is an important problem in complex network analysis, which can discover missing or possible future edges in the network. In recent years, link prediction methods based on network representation learning have made progress. But there are two problems with these methods. One is that neighborhood-based node sampling methods cannot handle the situation between two nodes that do not have any common neighbors. The other is the Skip-Gram-based embedding model that represents nodes as static vectors, which cannot reflect the various meanings of nodes. To overcome these two limitations, this paper proposes a method called AFS-BERT (Information entropy based Adaptive Fusion Sampling and BERT embedding model). First, this method defines a centrality score based on adjacency information entropy, which reflects the global and local importance of nodes. Second, we propose a sampling method that adaptively fuses two different strategies using the centrality score. Finally, the BERT-based embedding model is used to realize the low-dimensional dynamic vector representation of nodes. Experimental result on six real-world network datasets shows that AFS-BERT has better performance. Compared with methods of the same type, AFS-BERT achieves upto 6.7% improvement.

In this paper we study time evolution of configuration space in terms of information entropy flux and entropy production for colored cross-correlated noise-driven open systems. The effect of interference in additive and multiplicative white noises on entropy flux and entropy production is calculated based on the Fokker–Planck description of the stochastic process and information entropy balance equation. The variation of entropy production with the damping constant or strength of multiplicative noise reveals nonmonotonic behavior as a result of the interplay of deterministic and random forces.

The Wehrl classical information entropy of random phase negative binomial states (RPNBS) is investigated, and their Wigner function evolution in the thermal environment is also discussed. It is shown that the evolution of the RPNBS in the thermal channel can be roughly regarded as the shift of the parameters ε and α₀ of the RPNBS.

Diffusion processes have been widely investigated to understand some essential features of complex networks, and have attracted much attention from physicists, statisticians and computer scientists. In order to understand the evolution of the diffusion process and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the information entropy comprehending the structural characteristics and information propagation on the network. Based on the analysis of the diffusion process, we analyze the coupling impact of the structural factor and information propagating factor on the information entropy, where the analytical results fit well with the numerical ones on scale-free complex networks. The information entropy can better characterize the complex behaviors on networks and provides a new way to deepen the understanding of the diffusion process.

This paper proposes an image encryption algorithm based on a chaotic map and information entropy. Unlike Fridrich’s structure, the proposed method contains permutation, modulation, and diffusion (PMD) operations. This method avoids the shortcoming in traditional schemes of strictly shuffling the pixel positions before diffusion encryption. Information entropy is employed to influence the generation of the keystream. The initial keys used in the permutation and diffusion stages interact with each other. As a result, the algorithm acts as an indivisible entity to enhance security. Experimental results and security analyses demonstrate the good performance of the proposed algorithm as a secure and effective communication method for images.

As digital communication and storage continue to expand, the protection of image privacy information becomes increasingly critical. To safeguard sensitive visual information from unauthorized access, this paper proposes a novel image encryption scheme that integrates multiobjective Artificial Bee Colony (ABC) optimization algorithm and DNA coding. Multiple evaluation metrics including correlation relationship, Number of Pixel Change Rate (NPCR), Unified Average Changing Intensity (UACI), and information entropy are collaboratively optimized by the ABC algorithm. The proposed method begins with the application of the SHA-256 algorithm to generate keys and random sequences using chaotic systems. These sequences are then employed for shuffling, DNA coding, decoding, and diffusion, generating initial encrypted images. Subsequently, the encrypted images serve as individuals within the ABC algorithm to determine optimal parameters of the chaotic systems and the best ciphertext image. Simulation experiments demonstrate that the ciphertext images achieved excellent results in information entropy, pixel correlation coefficient, NPCR, and UACI. The integration of the multiobjective ABC optimization algorithm with DNA coding in our proposed image encryption scheme results in heightened security, as evidenced by superior performance in various metrics.

Peer-to-peer Grid (PG) is a new, promising approach for distributed computation that takes advantage of the huge amount of resources in grid computing. The purpose of PG is to support cooperative work between large-scale grid domains. In order to protect each domain's privilege and security, an efficient trust management mechanism is essential. Focusing on the requirement of large-scale PG computing, PG-Trust, a novel trust model is proposed based on trust relationships across domains. Firstly, a self-adaptive overall trust quantified framework is proposed based on the historical interaction records between participants, which not only can improve system efficiency, but also can solve trust computing problem when the direct evidence is sparse. Furthermore, the direct trust computing method based on attenuation function and the feedback trust mechanism based on direct trust tree (DTT) are introduced, which makes our model have a higher self-adaptability and a better scalability than previous studies. Through performance analyzing, the proposed model exhibits a strong self-adaptability in handling various dynamic behaviors of peers, and has a remarkable enhancement in the accuracy of trust evaluation.

Three measures of the information content of a probability distribution are briefly reviewed. They are applied to fractional occupation probabilities in light nuclei, taking into account short-range correlations. The effect of short-range correlations is to increase the information entropy (or disorder) of nuclei, comparing with the independent particle model. It is also indicated that the information entropy can serve as a sensitive index of order and short-range correlations in nuclei. It is concluded that increasing Z, the information entropy increases, i.e. the disorder of the nucleus increases for all measures of information considered in the present work.