Entropy

10 pages, 273 KiB

Open AccessArticle

Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition

by Chao Tian and Shlomo Shamai (Shitz)

Entropy 2025, 27(3), 310; https://doi.org/10.3390/e27030310 (registering DOI) - 15 Mar 2025

Partial information decomposition has recently found applications in biological signal processing and machine learning. Despite its impacts, the decomposition was introduced through an informal and heuristic route, and its exact operational meaning is unclear. In this work, we fill this gap by connecting [...] Read more.

Partial information decomposition has recently found applications in biological signal processing and machine learning. Despite its impacts, the decomposition was introduced through an informal and heuristic route, and its exact operational meaning is unclear. In this work, we fill this gap by connecting partial information decomposition to the capacity of the broadcast channel, which has been well studied in the information theory literature. We show that the synergistic information in the decomposition can be rigorously interpreted as the cooperative gain, or a lower bound of this gain, on the corresponding broadcast channel. This interpretation can help practitioners to better explain and expand the applications of the partial information decomposition technique. Full article

(This article belongs to the Special Issue Semantic Information Theory)

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22 pages, 429 KiB

Open AccessArticle

Restart Mechanisms for the Successive-Cancellation List–Flip Decoding of Polar Codes

by Charles Pillet, Ilshat Sagitov, Alexios Balatsoukas-Stimming and Pascal Giard

Entropy 2025, 27(3), 309; https://doi.org/10.3390/e27030309 - 14 Mar 2025

Abstract

Polar codes concatenated with a cyclic redundancy check (CRC) code have been selected in the 5G standard with the successive-cancellation list (SCL) of list size L = 8 as the baseline algorithm. Despite providing great error-correction performance, a large list size increases the [...] Read more.

Polar codes concatenated with a cyclic redundancy check (CRC) code have been selected in the 5G standard with the successive-cancellation list (SCL) of list size L = 8 as the baseline algorithm. Despite providing great error-correction performance, a large list size increases the hardware complexity of the SCL decoder. Alternatively, flip decoding algorithms were proposed to improve the error-correction performance with a low-complexity hardware implementation. The combination of list and flip algorithms, the successive-cancellation list flip (SCLF) and dynamic SCLF (DSCLF) algorithms, provides error-correction performance close to SCL-32 with a list size L = 2 and

T_{\max}

= 300 maximum additional trials. However, these decoders have a variable execution time, a characteristic that poses a challenge to some practical applications. In this work, we propose a restart mechanism for list–flip algorithms that allows us to skip parts of the decoding computations without affecting the error-correction performance. We show that the restart location cannot realistically be allowed to occur at any location in a codeword as it would lead to an unreasonable memory overhead under DSCLF. Hence, we propose a mechanism where the possible restart locations are limited to a set and propose various construction methods for that set. The construction methods are compared, and the tradeoffs are discussed. For a polar code of length N = 1024 and rate

M M 1 / 4

, under DSCLF decoding with a list size L = 2 and a maximum number of trials

T_{\max}

= 300, our proposed approach is shown to reduce the average execution time by 41.7% with four restart locations at the cost of approximately 1.5% in memory overhead. Full article

(This article belongs to the Special Issue Advances in Modern Channel Coding)

42 pages, 3012 KiB

Open AccessArticle

Optimal Power Procurement for Green Cellular Wireless Networks Under Uncertainty and Chance Constraints

by Nadhir Ben Rached, Shyam Mohan Subbiah Pillai and Raúl Tempone

Entropy 2025, 27(3), 308; https://doi.org/10.3390/e27030308 - 14 Mar 2025

Abstract

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, [...] Read more.

Given the increasing global emphasis on sustainable energy usage and the rising energy demands of cellular wireless networks, this work seeks an optimal short-term, continuous-time power-procurement schedule to minimize operating expenditure and the carbon footprint of cellular wireless networks equipped with energy-storage capacity, and hybrid energy systems comprising uncertain renewable energy sources. Despite the stochastic nature of wireless fading channels, the network operator must ensure a certain quality-of-service (QoS) constraint with high probability. This probabilistic constraint prevents using the dynamic programming principle to solve the stochastic optimal control problem. This work introduces a novel time-continuous Lagrangian relaxation approach tailored for real-time, near-optimal energy procurement in cellular networks, overcoming tractability problems associated with the probabilistic QoS constraint. The numerical solution procedure includes an efficient upwind finite-difference solver for the Hamilton–Jacobi–Bellman equation corresponding to the relaxed problem, and an effective combination of the limited memory bundle method (LMBM) for handling nonsmooth optimization and the stochastic subgradient method (SSM) to navigate the stochasticity of the dual problem. Numerical results, based on the German power system and daily cellular traffic data, demonstrate the computational efficiency of the proposed numerical approach, providing a near-optimal policy in a practical timeframe. Full article

(This article belongs to the Special Issue Stochastic Models and Statistical Inference: Analysis and Applications)

25 pages, 2080 KiB

Open AccessArticle

Multilabel Classification for Entry-Dependent Expert Selection in Distributed Gaussian Processes

by Hamed Jalali and Gjergji Kasneci

Entropy 2025, 27(3), 307; https://doi.org/10.3390/e27030307 - 14 Mar 2025

Abstract

By distributing the training process, local approximation reduces the cost of the standard Gaussian process. An ensemble method aggregates predictions from local Gaussian experts, each trained on different data partitions, under the assumption of perfect diversity among them. While this assumption ensures tractable [...] Read more.

By distributing the training process, local approximation reduces the cost of the standard Gaussian process. An ensemble method aggregates predictions from local Gaussian experts, each trained on different data partitions, under the assumption of perfect diversity among them. While this assumption ensures tractable aggregation, it is frequently violated in practice. Although ensemble methods provide consistent results by modeling dependencies among experts, they incur a high computational cost, scaling cubically with the number of experts. Implementing an expert-selection strategy reduces the number of experts involved in the final aggregation step, thereby improving efficiency. However, selection approaches that assign a fixed set of experts to each data point cannot account for the unique properties of individual data points. This paper introduces a flexible expert-selection approach tailored to the characteristics of individual data points. To achieve this, we frame the selection task as a multi-label classification problem in which experts define the labels, and each data point is associated with specific experts. We discuss in detail the prediction quality, efficiency, and asymptotic properties of the proposed solution. We demonstrate the efficiency of the proposed method through extensive numerical experiments on synthetic and real-world datasets. This strategy is easily extendable to distributed learning scenarios and multi-agent models, regardless of Gaussian assumptions regarding the experts. Full article

(This article belongs to the Special Issue Gaussian Fields and Their Application in Computational Engineering and Mathematical Physics)

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19 pages, 1138 KiB

Open AccessArticle

Democratic Thwarting of Majority Rule in Opinion Dynamics: 1. Unavowed Prejudices Versus Contrarians

by Serge Galam

Entropy 2025, 27(3), 306; https://doi.org/10.3390/e27030306 - 14 Mar 2025

Abstract

I study the conditions under which the democratic dynamics of a public debate drives a minority-to-majority transition. A landscape of the opinion dynamics is thus built using the Galam Majority Model (GMM) in a 3-dimensional parameter space for three different sizes, [...] Read more.

I study the conditions under which the democratic dynamics of a public debate drives a minority-to-majority transition. A landscape of the opinion dynamics is thus built using the Galam Majority Model (GMM) in a 3-dimensional parameter space for three different sizes,

r = 2, 3, 4

, of local discussion groups. The related parameters are

(p_{0}, k, x)

, the respective proportions of initial agents supporting opinion A, unavowed tie prejudices breaking in favor of opinion A, and contrarians. Combining k and x yields unexpected and counterintuitive results. In most of the landscape the final outcome is predetermined, with a single-attractor dynamics, independent of the initial support for the competing opinions. Large domains of

(k, x)

values are found to lead an initial minority to turn into a majority democratically without any external influence. A new alternating regime is also unveiled in narrow ranges of extreme proportions of contrarians. The findings indicate that the expected democratic character of free opinion dynamics is indeed rarely satisfied. The actual values of

(k, x)

are found to be instrumental to predetermining the final winning opinion independently of

p_{0}

. Therefore, the conflicting challenge for the predetermined opinion to lose is to modify these values appropriately to become the winner. However, developing a model which could help in manipulating public opinion raises ethical questions. This issue is discussed in the Conclusions. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics II)

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20 pages, 19302 KiB

Open AccessArticle

Variability Identification and Uncertainty Evolution Characteristic Analysis of Hydrological Variables in Anhui Province, China

by Xia Bai, Jinhuang Yu, Yule Li, Juliang Jin, Chengguo Wu and Rongxing Zhou

Entropy 2025, 27(3), 305; https://doi.org/10.3390/e27030305 - 14 Mar 2025

Abstract

Variability identification and uncertainty characteristic analysis, under the impacts of climate change and human activities, is beneficial for accurately predicting the future evolution trend of hydrological variables. In this study, based on the evolution trend and characteristic analyses of historical precipitation and temperature [...] Read more.

Variability identification and uncertainty characteristic analysis, under the impacts of climate change and human activities, is beneficial for accurately predicting the future evolution trend of hydrological variables. In this study, based on the evolution trend and characteristic analyses of historical precipitation and temperature sequences from monthly, annual, and interannual scales through the Linear Tendency Rate (LTR) index, as well as its variability point identification using the M–K trend test method, we further utilized three cloud characteristic parameters comprising the average Ex, entropy En, and hyper-entropy He of the Cloud Model (CM) method to quantitatively reveal the uncertainty features corresponding to the diverse cloud distribution of precipitation and temperature sample scatters. And then, through an application analysis of the proposed research framework in Anhui Province, China, the following can be summarized from the application results: (1) The annual precipitation of Anhui Province presented a remarkable decreasing trend from south to north and an annual increasing trend from 1960 to 2020, especially in the southern area, with the LTR index equaling 55.87 mm/10a, and the annual average temperature of the entire provincial area also presented an obvious increasing trend from 1960 to 2020, with LTR equaling about 0.226 °C/10a. (2) The uncertainty characteristic of the precipitation series was evidently intensified after the variability points in 2013 and 2014 in the southern and provincial areas, respectively, according to the derived values of entropy En and hyper-entropy He, which are basically to the contrary for the historical annual average temperature series in southern Anhui Province. (3) The obtained result was basically consistent with the practical statistics of historical hydrological and disaster data, indicating that the proposed research methodologies can be further applied in related variability diagnosis analyses of non-stationary hydrological variables. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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22 pages, 4990 KiB

Open AccessArticle

Edge-Centric Embeddings of Digraphs: Properties and Stability Under Sparsification

by Ahmed Begga, Francisco Escolano Ruiz and Miguel Ángel Lozano

Entropy 2025, 27(3), 304; https://doi.org/10.3390/e27030304 - 14 Mar 2025

Abstract

In this paper, we define and characterize the embedding of edges and higher-order entities in directed graphs (digraphs) and relate these embeddings to those of nodes. Our edge-centric approach consists of the following: (a) Embedding line digraphs (or their iterated versions); (b) Exploiting [...] Read more.

In this paper, we define and characterize the embedding of edges and higher-order entities in directed graphs (digraphs) and relate these embeddings to those of nodes. Our edge-centric approach consists of the following: (a) Embedding line digraphs (or their iterated versions); (b) Exploiting the rank properties of these embeddings to show that edge/path similarity can be posed as a linear combination of node similarities; (c) Solving scalability issues through digraph sparsification; (d) Evaluating the performance of these embeddings for classification and clustering. We commence by identifying the motive behind the need for edge-centric approaches. Then we proceed to introduce all the elements of the approach, and finally, we validate it. Our edge-centric embedding entails a top-down mining of links, instead of inferring them from the similarities of node embeddings. This analysis is key to discovering inter-subgraph links that hold the whole graph connected, i.e., central edges. Using directed graphs (digraphs) allows us to cluster edge-like hubs and authorities. In addition, since directed edges inherit their labels from destination (origin) nodes, their embedding provides a proxy representation for node classification and clustering as well. This representation is obtained by embedding the line digraph of the original one. The line digraph provides nice formal properties with respect to the original graph; in particular, it produces more entropic latent spaces. With these properties at hand, we can relate edge embeddings to node embeddings. The main contribution of this paper is to set and prove the linearity theorem, which poses each element of the transition matrix for an edge embedding as a linear combination of the elements of the transition matrix for the node embedding. As a result, the rank preservation property explains why embedding the line digraph and using the labels of the destination nodes provides better classification and clustering performances than embedding the nodes of the original graph. In other words, we do not only facilitate edge mining but enforce node classification and clustering. However, computing the line digraph is challenging, and a sparsification strategy is implemented for the sake of scalability. Our experimental results show that the line digraph representation of the sparsified input graph is quite stable as we increase the sparsification level, and also that it outperforms the original (node-centric) representation. For the sake of simplicity, our theorem relies on node2vec-like (factorization) embeddings. However, we also include several experiments showing how line digraphs may improve the performance of Graph Neural Networks (GNNs), also following the principle of maximum entropy. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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17 pages, 498 KiB

Open AccessArticle

Minimizing System Entropy: A Dual-Phase Optimization Approach for EV Charging Scheduling

by Wenpeng Yuan and Lin Guan

Entropy 2025, 27(3), 303; https://doi.org/10.3390/e27030303 - 14 Mar 2025

Abstract

To address the electric vehicle (EV) charging scheduling problem in rural distribution networks, this study proposes a novel two-phase optimization strategy that combines particle swarm optimization (PSO) and Q-learning for global optimization and real-time adaptation. In the first stage, PSO is used to [...] Read more.

To address the electric vehicle (EV) charging scheduling problem in rural distribution networks, this study proposes a novel two-phase optimization strategy that combines particle swarm optimization (PSO) and Q-learning for global optimization and real-time adaptation. In the first stage, PSO is used to generate an initial charging plan that minimizes voltage deviations and line overloads while maximizing user satisfaction. In the second phase, a Q-learning approach dynamically adjusts the plan based on real-time grid conditions and feedback. The strategy reduces the system’s entropy by minimizing the uncertainty and disorder in power distribution caused by variable EV charging loads. Experimental results on a 33-bus distribution system under baseline and high-load scenarios demonstrate significant improvements over conventional dispatch methods, with voltage deviation reduced from 5.8% to 1.9%, maximum load factor reduced from 95% to 82%, and average customer satisfaction increased from 75% to 88%. While the computation time increases compared to standalone PSO (66 min vs. 34 min), the enhanced grid stability and customer satisfaction justify the trade-off. By effectively minimizing system entropy and balancing grid reliability with user convenience, the proposed two-phase strategy offers a practical and robust solution for integrating EVs into rural power systems. Full article

(This article belongs to the Section Multidisciplinary Applications)

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14 pages, 653 KiB

Open AccessArticle

A Consistent Approach to Modeling Quantum Observers

by David W. Ring

Entropy 2025, 27(3), 302; https://doi.org/10.3390/e27030302 - 14 Mar 2025

Abstract

A number of no-go theorems have shown that Wigner’s Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers [...] Read more.

A number of no-go theorems have shown that Wigner’s Friend scenarios combined with various metaphysical assumptions lead to contradictions in any version of quantum theory. We present an alternative constructive approach that only assumes that agents make properly qualified true statements. Quantum observers are modeled rigorously, although simplistically, using quantum circuits. Terminology is suggested to help avoid contradictions. Our methodology is applied to the Frauchiger-Renner paradox and results in statements by all agents that are both true and consistent. Quantum theory evades the no-go theorems because they make an incorrect implicit assumption about how quantum agents behave. Full article

(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)

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11 pages, 548 KiB

Open AccessArticle

Enhancing Visual-Language Prompt Tuning Through Sparse Knowledge-Guided Context Optimization

by Qiangxing Tian and Min Zhang

Entropy 2025, 27(3), 301; https://doi.org/10.3390/e27030301 - 14 Mar 2025

Abstract

Prompt tuning visual-language models (VLMs) for specialized tasks often involves leveraging task-specific textual tokens, which can tailor the pre-existing, broad capabilities of a VLM to more narrowly focused applications. This approach, exemplified by CoOp-based methods, integrates mutable textual tokens with categorical tokens to [...] Read more.

Prompt tuning visual-language models (VLMs) for specialized tasks often involves leveraging task-specific textual tokens, which can tailor the pre-existing, broad capabilities of a VLM to more narrowly focused applications. This approach, exemplified by CoOp-based methods, integrates mutable textual tokens with categorical tokens to foster nuanced textual comprehension. Nonetheless, such specialized textual insights often fail to generalize beyond the scope of familiar categories, as they tend to overshadow the versatile, general textual knowledge intrinsic to the model’s wide-ranging applicability. Addressing this base-novel dilemma, we propose the innovative concept of SparseKnowledge-guided Context Optimization (Sparse-KgCoOp). This technique aims to fortify the adaptable prompts’ capacity to generalize to categories yet unencountered. The cornerstone of Sparse-KgCoOp is based on the premise that reducing the differences between adaptive prompt and their hand-crafted counterparts through sparsification operations can mitigate the erosion of fundamental knowledge. Specifically, Sparse-KgCoOp seeks to narrow the gap between the textual embeddings produced by both the dynamic prompts and the manually devised ones, thus preserving the foundational knowledge while maintaining adaptability. Extensive experiments of several benchmarks demonstrate that the proposed Sparse-KgCoOp is an efficient method for prompt tuning. Full article

(This article belongs to the Section Multidisciplinary Applications)

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13 pages, 447 KiB

Open AccessArticle

Biswas–Chatterjee–Sen Model Defined on Solomon Networks in (1 ≤ D ≤ 6)-Dimensional Lattices

by Gessineide Sousa Oliveira, David Santana Alencar, Tayroni Alencar Alves, José Ferreira da Silva Neto, Gladstone Alencar Alves, Antônio Macedo-Filho, Ronan S. Ferreira, Francisco Welington Lima and João Antônio Plascak

Entropy 2025, 27(3), 300; https://doi.org/10.3390/e27030300 - 14 Mar 2025

Abstract

The discrete version of the Biswas–Chatterjee–Sen model, defined on D-dimensional hypercubic Solomon networks, with

1 \leq D \leq 6

, has been studied by means of extensive Monte Carlo simulations. Thermodynamic-like variables have been computed as a function of the external noise [...] Read more.

The discrete version of the Biswas–Chatterjee–Sen model, defined on D-dimensional hypercubic Solomon networks, with

1 \leq D \leq 6

, has been studied by means of extensive Monte Carlo simulations. Thermodynamic-like variables have been computed as a function of the external noise probability. Finite-size scaling theory, applied to different network sizes, has been utilized in order to characterize the phase transition of the system in the thermodynamic limit. The results show that the model presents a phase transition of the second order for all considered dimensions. Despite the lower critical dimension being zero, this dynamical system seems not to have any upper critical dimension since the critical exponents change with D and go away from the expected mean-field values. Although larger networks could not be simulated because the number of sites drastically increases with the dimension D, the scaling regime has been achieved when computing the critical exponent ratios and the corresponding critical noise probability. Full article

(This article belongs to the Special Issue Entropy-Based Applications in Sociophysics II)

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25 pages, 37855 KiB

Open AccessArticle

Hyperchaotic System-Based PRNG and S-Box Design for a Novel Secure Image Encryption

by Erman Özpolat, Vedat Çelik and Arif Gülten

Entropy 2025, 27(3), 299; https://doi.org/10.3390/e27030299 - 13 Mar 2025

Abstract

A hyperchaotic system was analyzed in this study, and its hyperchaotic behavior was confirmed through dynamic analysis. The system was utilized to develop a pseudo-random number generator (PRNG), whose statistical reliability was validated through NIST SP800-22 tests, demonstrating its suitability for cryptographic applications. [...] Read more.

A hyperchaotic system was analyzed in this study, and its hyperchaotic behavior was confirmed through dynamic analysis. The system was utilized to develop a pseudo-random number generator (PRNG), whose statistical reliability was validated through NIST SP800-22 tests, demonstrating its suitability for cryptographic applications. Additionally, a 16 × 16 S-box was constructed based on the hyperchaotic system, ensuring high nonlinearity and strong cryptographic performance. A comparative analysis revealed that the proposed S-box structure outperforms existing designs in terms of security and efficiency. A new image encryption algorithm was designed using the PRNG and S-box, and its performance was evaluated on 512 × 512 grayscale images, including the commonly used baboon and pepper images. The decryption process successfully restored the original images, confirming the encryption scheme’s reliability. Security evaluations, including histogram analysis, entropy measurement, correlation analysis, and resistance to differential and noise attacks, were conducted. The findings showed that the suggested encryption algorithm outperforms current techniques in terms of security and efficiency. This study contributes to the advancement of robust PRNG generation, secure S-box design, and efficient image encryption algorithms using hyperchaotic systems, offering a promising approach for secure communication and data protection. Full article

(This article belongs to the Section Information Theory, Probability and Statistics)

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17 pages, 9871 KiB

Open AccessArticle

HA: An Influential Node Identification Algorithm Based on Hub-Triggered Neighborhood Decomposition and Asymmetric Order-by-Order Recurrence Model

by Min Zhao, Junhan Ye, Jiayun Li, Yuzhuo Dai, Tianze Zhao and Gengchen Zhang

Entropy 2025, 27(3), 298; https://doi.org/10.3390/e27030298 - 13 Mar 2025

Abstract

In recent years, the rise of power network security incidents caused by malicious attacks has drawn considerable attention to identifying influential nodes in power networks. Power networks are a special class of complex networks characterized by a high relative clustering coefficient, which reflects [...] Read more.

In recent years, the rise of power network security incidents caused by malicious attacks has drawn considerable attention to identifying influential nodes in power networks. Power networks are a special class of complex networks characterized by a high relative clustering coefficient, which reflects a more intricate connection between nodes. This paper proposes a novel node influence evaluation algorithm based on hub-triggered neighborhood decomposition and asymmetric order-by-order recurrence model. First, the concepts of network directionalization strategy and hub-triggered neighborhood decomposition are introduced to distinguish the functional differences among nodes in the virus-spreading process. Second, this paper proposes the concepts of infected and infecting potential, then constructs a calculation model with asymmetric characteristics based on the order-by-order recurrence method to fully use the information in the connection structure of the adjacent neighborhood. Finally, the influence of the hub node is evaluated by integrating the infected potential and infecting potential of neighbors of multiple orders. We compare our method with the traditional and state-of-the-art algorithms on six power networks regarding Susceptible–Infected–Recovered (SIR) correlation coefficients, imprecision functions, and algorithmic resolution. The experimental results show that the algorithm proposed in this paper is superior in the above aspects. Full article

(This article belongs to the Section Complexity)

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22 pages, 7837 KiB

Open AccessArticle

Online Monitoring and Fault Diagnosis for High-Dimensional Stream with Application in Electron Probe X-Ray Microanalysis

by Tao Wang, Yunfei Guo, Fubo Zhu and Zhonghua Li

Entropy 2025, 27(3), 297; https://doi.org/10.3390/e27030297 - 13 Mar 2025

Abstract

This study introduces an innovative two-stage framework for monitoring and diagnosing high-dimensional data streams with sparse changes. The first stage utilizes an exponentially weighted moving average (EWMA) statistic for online monitoring, identifying change points through extreme value theory and multiple hypothesis testing. The [...] Read more.

This study introduces an innovative two-stage framework for monitoring and diagnosing high-dimensional data streams with sparse changes. The first stage utilizes an exponentially weighted moving average (EWMA) statistic for online monitoring, identifying change points through extreme value theory and multiple hypothesis testing. The second stage involves a fault diagnosis mechanism that accurately pinpoints abnormal components upon detecting anomalies. Through extensive numerical simulations and electron probe X-ray microanalysis applications, the method demonstrates exceptional performance. It rapidly detects anomalies, often within one or two sampling intervals post-change, achieves near 100% detection power, and maintains type-I error rates around the nominal 5%. The fault diagnosis mechanism shows a 99.1% accuracy in identifying components in 200-dimensional anomaly streams, surpassing principal component analysis (PCA)-based methods by 28.0% in precision and controlling the false discovery rate within 3%. Case analyses confirm the method’s effectiveness in monitoring and identifying abnormal data, aligning with previous studies. These findings represent significant progress in managing high-dimensional sparse-change data streams over existing methods. Full article

(This article belongs to the Special Issue Statistical Methods for Modeling High-Dimensional and Complex Data: Second Edition)

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19 pages, 709 KiB

Open AccessArticle

Design Particularities of Quadrature Chaos Shift Keying Communication System with Enhanced Noise Immunity for IoT Applications

by Darja Cirjulina, Ruslans Babajans and Deniss Kolosovs

Entropy 2025, 27(3), 296; https://doi.org/10.3390/e27030296 - 12 Mar 2025

Abstract

This article is devoted to the investigation of synchronization noise immunity in quadrature chaos shift keying (QCSK) communication systems and its profound impact on system performance. The study focuses on Colpitts and Vilnius chaos oscillators in different synchronization configurations, and the reliability of [...] Read more.

This article is devoted to the investigation of synchronization noise immunity in quadrature chaos shift keying (QCSK) communication systems and its profound impact on system performance. The study focuses on Colpitts and Vilnius chaos oscillators in different synchronization configurations, and the reliability of the system in the particular configuration is assessed using the bit error rate (BER) estimation. The research considers synchronization imbalances and demonstrates their effect on the accuracy of data detection and overall transmission stability. The article proposes an approach for optimal bit detection in the case of imbalanced synchronization and correlated chaotic signals in data transmission. The study practically shows the importance of the proposed decision-making technique, revealing that certain adjustments can significantly enhance system noise resilience. Full article

(This article belongs to the Special Issue Multimedia Data Security and Privacy Protection Based on Chaotic Systems and Compressive Sensing)

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23 pages, 11439 KiB

Open AccessArticle

Enterprise Digital Transformation Strategy: The Impact of Digital Platforms

by Qiong Huang and Yifan Tang

Entropy 2025, 27(3), 295; https://doi.org/10.3390/e27030295 - 12 Mar 2025

Abstract

The development of the digital economy is a strategic choice for seizing new opportunities in the latest wave of technological revolution and industrial transformation. As a critical tool for driving the digital transformation of enterprises, digital platforms play a pivotal role in this [...] Read more.

The development of the digital economy is a strategic choice for seizing new opportunities in the latest wave of technological revolution and industrial transformation. As a critical tool for driving the digital transformation of enterprises, digital platforms play a pivotal role in this process. This study employs the evolutionary game theory of complex networks to develop a game model for the digital transformation of enterprises and utilizes the Fermi rule from sociophysics to characterize the evolution of enterprise strategies. Throughout this process, the interactive behaviors and strategic choices of enterprises embody the features of information flow and dynamic adjustment within the network. These features are crucial for elucidating the complexity and uncertainty inherent in strategic decision-making. The research findings indicate that digital platforms, through the provision of high-quality services and the implementation of effective pricing strategies, can significantly reduce the costs associated with digital transformation, thereby enhancing operational efficiency and innovation capacity. Moreover, the model reveals the competitive relationships between enterprises and their impact on transformation strategies, offering theoretical insights for policymakers. Based on these findings, the paper proposes policy recommendations such as strengthening infrastructure, implementing differentiated service strategies, and enhancing decision-making capability training, with the aim of supporting the digital transformation of enterprises across various industries and promoting sustainable development. Full article

(This article belongs to the Special Issue Entropy, Econophysics, and Complexity)

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20 pages, 754 KiB

Open AccessArticle

ESfix: An Embedded Program Repair Tool for Effective Removal of Concurrency Defects

by Jingwen Zhao, Yanxia Wu, Yan Fu and Shuyong Liu

Entropy 2025, 27(3), 294; https://doi.org/10.3390/e27030294 - 12 Mar 2025

Abstract

Embedded programs are not only inseparable from our daily lives but are also widely used in aerospace, medical devices, and other fields that require very high security and stability. The uncertainty and randomness of the large amount of data generated by these systems [...] Read more.

Embedded programs are not only inseparable from our daily lives but are also widely used in aerospace, medical devices, and other fields that require very high security and stability. The uncertainty and randomness of the large amount of data generated by these systems during operation can be quantified by entropy. Traditional repair methods for concurrency defects may introduce new issues such as deadlocks, original semantic destruction, and high performance overhead. To overcome the limitations of the existing methods and help developers reduce the time and effort spent on fixing software defects, this paper proposes ESfix, a defect fixing technique applied to embedded software. ESfix first utilizes the bug information reported by the defect detection tool to locate the repair region and extracts the node information corresponding to the defective code. Then, ESfix optimizes the interrupt disable/enable strategies and lock strategies to repair data race and reduce bugs in information transmission, thereby reducing system entropy and improving data certainty and reliability. Finally, ESfix repairs atomicity violation defects using the reordering repair strategy, reducing information entropy by adjusting the order of information to ensure its integrity and consistency. ESfix conducts semantic analysis by analyzing the dependency graph in the control flow graph (CFG) to ensure that no new defects are introduced during the repair process, and to maintain the efficiency and accuracy of information transmission between different parts of the code. We evaluate the effectiveness of repair strategies through information entropy, and the experimental results show that ESfix not only improves performance but also reduces potential risks and losses. Full article

(This article belongs to the Special Issue Information Security and Data Privacy)

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12 pages, 689 KiB

Open AccessArticle

Modeling Diffusion of Elongated Particles Through a Narrowing Channel

by Anna Strzelewicz, Michał Cieśla, Bartłomiej Dybiec and Monika Krasowska

Entropy 2025, 27(3), 293; https://doi.org/10.3390/e27030293 - 12 Mar 2025

Abstract

Simulations of the Brownian dynamics of diffusing particles in complex environments provide important information about the characteristics of the medium and the properties of biological processes. Notable examples include the diffusion of ions and macromolecular solutes through channels of varying cross-section, such as [...] Read more.

Simulations of the Brownian dynamics of diffusing particles in complex environments provide important information about the characteristics of the medium and the properties of biological processes. Notable examples include the diffusion of ions and macromolecular solutes through channels of varying cross-section, such as pores in biological membranes, living tissues, zeolites, carbon nanotubes, and synthetic porous materials. In these systems, the observed diffusion can exhibit anomalous behavior characterized by a nonlinear increase in the mean squared displacement. In this article, we present a toy model of the diffusion of rod-shaped particles through a narrowing, conical pore with a trapezoidal longitudinal cross-section. Particles of different sizes undergo a random walk due to interactions with the environment (modeled as noise). We study how the diffusion properties change with particle size as a function of pore width. The numerical analysis of diffusion-driven transport through narrowing conical channels reveals its effective subdiffusive, i.e., anomalous, character. Full article

(This article belongs to the Collection Disorder and Biological Physics)

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26 pages, 481 KiB

Open AccessArticle

Controlled Double-Direction Cyclic Quantum Communication of Arbitrary Two-Particle States

by Nueraminaimu Maihemuti, Zhanheng Chen, Jiayin Peng, Yimamujiang Aisan and Jiangang Tang

Entropy 2025, 27(3), 292; https://doi.org/10.3390/e27030292 - 11 Mar 2025

Abstract

With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains [...] Read more.

With the rapid development of quantum communication technologies, controlled double-direction cyclic (CDDC) quantum communication has become an important research direction. However, how to choose an appropriate quantum state as a channel to achieve double-direction cyclic (DDC) quantum communication for multi-particle entangled states remains an unresolved challenge. This study aims to address this issue by constructing a suitable quantum channel and investigating the DDC quantum communication of two-particle states. Initially, we create a 25-particle entangled state using Hadamard and controlled-NOT (CNOT) gates, and provide its corresponding quantum circuit implementation. Based on this entangled state as a quantum channel, we propose two new four-party CDDC schemes, applied to quantum teleportation (QT) and remote state preparation (RSP), respectively. In both schemes, each communicating party can synchronously transmit two different arbitrary two-particle states to the other parties under supervisory control, achieving controlled quantum cyclic communication in both clockwise and counterclockwise directions. Additionally, the presented two schemes of four-party CDDC quantum communication are extended to situations where

n > 3

communicating parties. In each proposed scheme, we provide universal analytical formulas for the local operations of the sender, supervisor, and receiver, demonstrating that the success probability of each scheme can reach 100%. These schemes only require specific two-particle projective measurements, single-particle von Neumann measurements, and Pauli gate operations, all of which can be implemented with current technologies. We have also evaluated the inherent efficiency, security, and control capabilities of the proposed schemes. In comparison to earlier methods, the results demonstrate that our schemes perform exceptionally well. This study provides a theoretical foundation for bidirectional controlled quantum communication of multi-particle states, aiming to enhance security and capacity while meeting the diverse needs of future network scenarios. Full article

(This article belongs to the Special Issue Classical and Quantum Networks: Theory, Modeling and Optimization)

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