Entropy最新文献

{"title":"Lower Limit of Percolation Threshold on Square Lattice with Complex Neighborhoods.","authors":"Antoni Piotr Ciepłucha, Marcin Utnicki, Maciej Wołoszyn, Krzysztof Malarz","doi":"10.3390/e27040361","DOIUrl":"https://doi.org/10.3390/e27040361","url":null,"abstract":"<p><p>In this paper, the 60-year-old concept of long-range interaction in percolation problems introduced by Dalton, Domb and Sykes is reconsidered. With Monte Carlo simulation-based on the Newman-Ziff algorithm and the finite-size scaling hypothesis-we estimate 64 percolation thresholds for a random site percolation problem on a square lattice with neighborhoods that contain sites from the seventh coordination zone. The percolation thresholds obtained range from 0.27013 (for the neighborhood that contains only sites from the seventh coordination zone) to 0.11535 (for the neighborhood that contains all sites from the first to the seventh coordination zone). Similarly to neighborhoods with smaller ranges, the power-law dependence of the percolation threshold on the effective coordination number with an exponent close to -1/2 is observed. Finally, we empirically determine the limit of the percolation threshold on square lattices with complex neighborhoods. This limit scales with the inverse square of the mean radius of the neighborhood. The boundary of this limit is touched for threshold values associated with extended (compact) neighborhoods.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025640/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144062843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"LOMDP: Maximizing Desired Opinions in Social Networks by Considering User Expression Intentions.","authors":"Xuan Wang, Bin Wu, Tong Wu","doi":"10.3390/e27040360","DOIUrl":"https://doi.org/10.3390/e27040360","url":null,"abstract":"<p><p>To address the problem of maximizing desired opinions in social networks, we present the Limited Opinion Maximization with Dynamic Propagation Optimization framework, which is grounded in information entropy theory. Innovatively, we introduce the concept of node expression capacity, which quantifies the uncertainty of users' expression intentions via entropy and effectively identifies the impact of silent nodes on the propagation process. Based on this, in terms of seed node selection, we develop the Limited Opinion Maximization algorithm for multi-stage seed selection, which dynamically optimizes the seed distribution among communities through a multi-stage seeding approach. In terms of node opinion changes, we establish the LODP dynamic opinion propagation model, reconstructing the node opinion update mechanism and explicitly modeling the entropy-increasing effect of silent nodes on the information propagation path. The experimental results on four datasets show that LOMDP outperforms six baseline algorithms. Our research effectively resolves the problem of maximizing desired opinions and offers insights into the dynamics of information propagation in social networks from the perspective of entropy and information theory.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025780/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143990745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring Word-Adjacency Networks with Multifractal Time Series Analysis Techniques.","authors":"Jakub Dec, Michał Dolina, Stanisław Drożdż, Robert Kluszczyński, Jarosław Kwapień, Tomasz Stanisz","doi":"10.3390/e27040356","DOIUrl":"https://doi.org/10.3390/e27040356","url":null,"abstract":"<p><p>A novel method of exploring linguistic networks is introduced by mapping word-adjacency networks to time series and applying multifractal analysis techniques. This approach captures the complex structural patterns of language by encoding network properties-such as clustering coefficients and node degrees-into temporal sequences. Using Alice's Adventures in Wonderland by Lewis Carroll as a case study, both traditional word-adjacency networks and extended versions that incorporate punctuation are examined. The results indicate that the time series derived from clustering coefficients, when following the natural reading order, exhibits multifractal characteristics, revealing inherent complexity in textual organization. Statistical validation confirms that observed multifractal properties arise from genuine correlations rather than from spurious effects. Extending this analysis by taking into account punctuation equally with words, however, changes the nature of the global scaling to a more convolved form that is not describable by a uniform multifractal. An analogous analysis based on the node degrees does not show such rich behaviors, however. These findings reveal a new perspective for quantitative linguistics and network science, providing a deeper understanding of the interplay between text structure and complex systems.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025806/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143985710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Hyperbolic Sum Rule for Probability: Solving Recursive (\"Chicken and Egg\") Problems.","authors":"Michael C Parker, Chris Jeynes, Stuart D Walker","doi":"10.3390/e27040352","DOIUrl":"https://doi.org/10.3390/e27040352","url":null,"abstract":"<p><p>We prove that the probability of \"<i>A</i> or <i>B</i>\", denoted as <i>p</i>(<i>A</i> or <i>B</i>), where <i>A</i> and <i>B</i> are events or hypotheses that may be recursively dependent, is given by a \"Hyperbolic Sum Rule\" (<b>HSR</b>), which is relationally isomorphic to the hyperbolic tangent double-angle formula. We also prove that this HSR is Maximum Entropy (<b>MaxEnt</b>). Since this recursive dependency is commutative, it maintains the symmetry between the two events, while the recursiveness also represents temporal symmetry within the logical structure of the HSR. The possibility of recursive probabilities is excluded by the \"Conventional Sum Rule\" (<b>CSR</b>), which we have also proved to be MaxEnt (with lower entropy than the HSR due to its narrower domain of applicability). The concatenation property of the HSR is exploited to enable analytical, consistent, and scalable calculations for multiple hypotheses. Although they are intrinsic to current artificial intelligence and machine learning applications, such calculations are not conveniently available for the CSR, moreover they are presently considered intractable for analytical study and methodological validation. Where, for two hypotheses, we have <i>p</i>(<i>A</i>|<i>B</i>) > 0 and <i>p</i>(<i>B</i>|<i>A</i>) > 0 together (where \"<i>A</i>|<i>B</i>\" means \"<i>A</i> given <i>B</i>\"), we show that <i>either</i> {<i>A</i>,<i>B</i>} is independent <i>or</i> {<i>A</i>,<i>B</i>} is recursively dependent. In general, recursive relations cannot be ruled out: the HSR should be used by default. Because the HSR is isomorphic to other physical quantities, including those of certain components that are important for digital signal processing, we also show that it is as reasonable to state that \"<i>probability is physical</i>\" as it is to state that \"<i>information is physical</i>\" (which is now recognised as a truism of communications network engineering); probability is <i>not</i> merely a mathematical construct. We relate this treatment to the physics of Quantitative Geometrical Thermodynamics, which is defined in complex hyperbolic (Minkowski) spacetime.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12026390/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143956819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"InfoMat: Leveraging Information Theory to Visualize and Understand Sequential Data.","authors":"Dor Tsur, Haim Permuter","doi":"10.3390/e27040357","DOIUrl":"https://doi.org/10.3390/e27040357","url":null,"abstract":"<p><p>Despite the widespread use of information measures in analyzing probabilistic systems, effective visualization tools for understanding complex dependencies in sequential data are scarce. In this work, we introduce the information matrix (InfoMat), a novel and intuitive matrix representation of information transfer in sequential systems. InfoMat provides a structured visual perspective on mutual information decompositions, enabling the discovery of new relationships between sequential information measures and enhancing interpretability in time series data analytics. We demonstrate how InfoMat captures key sequential information measures, such as directed information and transfer entropy. To facilitate its application in real-world datasets, we propose both an efficient Gaussian mutual information estimator and a neural InfoMat estimator based on masked autoregressive flows to model more complex dependencies. These estimators make InfoMat a valuable tool for uncovering hidden patterns in data analytics applications, encompassing neuroscience, finance, communication systems, and machine learning. We further illustrate the utility of InfoMat in visualizing information flow in real-world sequential physiological data analysis and in visualizing information flow in communication channels under various coding schemes. By mapping visual patterns in InfoMat to various modes of dependence structures, we provide a data-driven framework for analyzing causal relationships and temporal interactions. InfoMat thus serves as both a theoretical and empirical tool for data-driven decision making, bridging the gap between information theory and applied data analytics.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12026351/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143974651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiscale Sample Entropy-Based Feature Extraction with Gaussian Mixture Model for Detection and Classification of Blue Whale Vocalization.","authors":"Oluwaseyi Paul Babalola, Olayinka Olaolu Ogundile, Vipin Balyan","doi":"10.3390/e27040355","DOIUrl":"https://doi.org/10.3390/e27040355","url":null,"abstract":"<p><p>A multiscale sample entropy (MSE) algorithm is presented as a time domain feature extraction method to study the vocal behavior of blue whales through continuous acoustic monitoring. Additionally, MSE is applied to the Gaussian mixture model (GMM) for blue whale call detection and classification. The performance of the proposed MSE-GMM algorithm is experimentally assessed and benchmarked against traditional methods, including principal component analysis (PCA), wavelet-based feature (WF) extraction, and dynamic mode decomposition (DMD), all combined with the GMM. This study utilizes recorded data from the Antarctic open source library. To improve the accuracy of classification models, a GMM-based feature selection method is proposed, which evaluates both positively and negatively correlated features while considering inter-feature correlations. The proposed method demonstrates enhanced performance over conventional PCA-GMM, DMD-GMM, and WF-GMM methods, achieving higher accuracy and lower error rates when classifying the non-stationary and complex vocalizations of blue whales.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025404/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143985659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Model for the Formation of Beliefs and Social Norms Based on the Satisfaction Problem (SAT).","authors":"Bastien Chopard, Franck Raynaud, Julien Stalhandske","doi":"10.3390/e27040358","DOIUrl":"https://doi.org/10.3390/e27040358","url":null,"abstract":"<p><p>We propose a numerical representation of beliefs in social systems based on the so-called SAT problem in computer science. The main idea is that a belief system is a set of true/false values associated with claims or propositions. Each individual assigns these values according to its cognitive system in order to minimize logical contradictions, thus trying to solve a satisfaction problem. Social interactions between agents that disagree on a proposition can be introduced in order to see how, in the long term, social norms and competing belief systems build up in a population. Among other metrics, entropy is used to characterize the diversity of belief systems.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025432/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143992345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Causal Artificial Intelligence in Legal Language Processing: A Systematic Review.","authors":"Philippe Prince Tritto, Hiram Ponce","doi":"10.3390/e27040351","DOIUrl":"https://doi.org/10.3390/e27040351","url":null,"abstract":"<p><p>Recent advances in legal language processing have highlighted limitations in correlation-based artificial intelligence approaches, prompting exploration of Causal Artificial Intelligence (AI) techniques for improved legal reasoning. This systematic review examines the challenges, limitations, and potential impact of Causal AI in legal language processing compared to traditional correlation-based methods. Following the Joanna Briggs Institute methodology, we analyzed 47 papers from 2017 to 2024 across academic databases, private sector publications, and policy documents, evaluating their contributions through a rigorous scoring framework assessing Causal AI implementation, legal relevance, interpretation capabilities, and methodological quality. Our findings reveal that while Causal AI frameworks demonstrate superior capability in capturing legal reasoning compared to correlation-based methods, significant challenges remain in handling legal uncertainty, computational scalability, and potential algorithmic bias. The scarcity of comprehensive real-world implementations and overemphasis on transformer architectures without causal reasoning capabilities represent critical gaps in current research. Future development requires balanced integration of AI innovation with law's narrative functions, particularly focusing on scalable architectures for maintaining causal coherence while preserving interpretability in legal analysis.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025529/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143974648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Information-Theoretic Measures of Metacognitive Efficiency: Empirical Validation with the Face Matching Task.","authors":"Daniel Fitousi","doi":"10.3390/e27040353","DOIUrl":"https://doi.org/10.3390/e27040353","url":null,"abstract":"<p><p>The ability of participants to monitor the correctness of their own decisions by rating their confidence is a form of metacognition. This introspective act is crucial for many aspects of cognition, including perception, memory, learning, emotion regulation, and social interaction. Researchers assess the quality of confidence ratings according to <i>bias</i>, <i>sensitivity</i>, and <i>efficiency</i>. To do so, they deploy quantities such as meta-d'-d' or the M-ratio These measures compute the expected accuracy level of performance in the primary task (Type 1) from the secondary confidence rating task (Type 2). However, these measures have several limitations. For example, they are based on unwarranted parametric assumptions, and they fall short of accommodating the granularity of confidence ratings. Two recent papers by Dayan and by Fitousi have proposed information-theoretic measures of metacognitive efficiency that can address some of these problems. Dayan suggested meta-I and Fitousi proposed meta-U, meta-KL, and meta-J. These authors demonstrated the convergence of their measures on the notion of metacognitive efficiency using simulations, but did not apply their measures to real empirical data. The present study set to test the construct validity of these measures in a concrete behavioral task-the face-matching task. The results supported the viability of these novel indexes of metacognitive efficiency, and provide substantial empirical evidence for their convergence. The results also adduce considerable evidence that participants in the face-matching task acquire valuable metaknowledge about the correctness of their own decisions in the task.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025997/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143979035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Design and Implementation of Low-Complexity Multiple Symbol Detection Algorithm Using Hybrid Stochastic Computing in Aircraft Wireless Communications.","authors":"Yukai Liu, Rongke Liu, Kairui Tian, Zheng Lu, Ling Zhao","doi":"10.3390/e27040359","DOIUrl":"https://doi.org/10.3390/e27040359","url":null,"abstract":"<p><p>The Multiple Symbol Detection (MSD) algorithm can effectively lower the demodulation threshold in Frequency Modulation (FM) technology, which is widely used in aircraft wireless communications due to its insensitivity to large Doppler shifts. However, the high computational complexity of the MSD algorithm leads to considerable hardware resource overhead. In this paper, we propose a novel MSD architecture based on hybrid stochastic computing (SC), which allows for accurate signal detection while maintaining low hardware complexity. Given that the correlation calculation dominates the computational load in the MSD algorithm, we develop an SC-based, low-complexity unit to perform complex correlation operations using simple hardware circuits, significantly reducing the hardware overhead. Particularly, we integrate a flexible and scalable stochastic adder in the SC-based correlation calculation, which incorporates an adjustable scaling factor to enable high distinguishability in all possible correlation results. Additionally, for the symbol decision process of the MSD algorithm, we design a binary computing-based pipeline architecture to execute the computing process serially, which leverages the inherent low update rate of SC-based correlation results to further reduce the overall resource overhead. Experimental results show that, compared to an 8-bit quantization MSD implementation, our proposed hybrid SC-based MSD architecture achieves a comparable bit error rate while reducing the hardware resources to 69%, 45%, and 36% of those required for the three-, five-, and seven-symbol MSD algorithms, respectively.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025373/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143973472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}