Entropy最新文献

{"title":"Mean Field Initialization of the Annealed Importance Sampling Algorithm for an Efficient Evaluation of the Partition Function Using Restricted Boltzmann Machines.","authors":"Arnau Prat Pou, Enrique Romero, Jordi Martí, Ferran Mazzanti","doi":"10.3390/e27020171","DOIUrl":"10.3390/e27020171","url":null,"abstract":"<p><p>Probabilistic models in physics often require the evaluation of normalized Boltzmann factors, which in turn implies the computation of the partition function <i>Z</i>. Obtaining the exact value of <i>Z</i>, though, becomes a forbiddingly expensive task as the system size increases. A possible way to tackle this problem is to use the Annealed Importance Sampling (AIS) algorithm, which provides a tool to stochastically estimate the partition function of the system. The nature of AIS allows for an efficient and parallel implementation in Restricted Boltzmann Machines (RBMs). In this work, we evaluate the partition function of magnetic spin and spin-like systems mapped into RBMs using AIS. So far, the standard application of the AIS algorithm starts from the uniform probability distribution and uses a large number of Monte Carlo steps to obtain reliable estimations of <i>Z</i> following an annealing process. We show that both the quality of the estimation and the cost of the computation can be significantly improved by using a properly selected mean-field starting probability distribution. We perform a systematic analysis of AIS in both small- and large-sized problems, and compare the results to exact values in problems where these are known. As a result, we propose two successful strategies that work well in all the problems analyzed. We conclude that these are good starting points to estimate the partition function with AIS with a relatively low computational cost. The procedures presented are not linked to any learning process, and therefore do not require a priori knowledge of a training dataset.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11853956/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143500022","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":"Critical Relaxation in the Quantum Yang-Lee Edge Singularity.","authors":"Yue-Mei Sun, Xinyu Wang, Liang-Jun Zhai","doi":"10.3390/e27020170","DOIUrl":"10.3390/e27020170","url":null,"abstract":"<p><p>We study the relaxation dynamics near the critical points of the Yang-Lee edge singularities (YLESs) in the quantum Ising chain in an imaginary longitudinal field with a polarized initial state. We find that scaling behaviors are manifested in the relaxation process after a non-universal transient time. We show that for the paramagnetic Hamiltonian, the magnetization oscillates periodically with the period being inversely proportional to the gap between the lowest energy level; for the ferromagnetic Hamiltonian, the magnetization decays to a saturated value; while for the critical Hamiltonian, the magnetization increases linearly. A scaling theory is developed to describe these scaling properties. In this theory, we show that for a small- and medium-sized system, the scaling behavior is described by the (0+1)-dimensional YLES.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11853887/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499362","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":"Fault Diagnosis of Semi-Supervised Electromechanical Transmission Systems Under Imbalanced Unlabeled Sample Class Information Screening.","authors":"Chaoge Wang, Pengpeng Jia, Xinyu Tian, Xiaojing Tang, Xiong Hu, Hongkun Li","doi":"10.3390/e27020175","DOIUrl":"10.3390/e27020175","url":null,"abstract":"<p><p>In the health monitoring of electromechanical transmission systems, the collected state data typically consist of only a minimal amount of labeled data, with a vast majority remaining unlabeled. Consequently, deep learning-based diagnostic models encounter the challenge of scarcity in labeled data and abundance in unlabeled data. Traditional semi-supervised deep learning methods based on pseudo-label self-training, while alleviating the issue of labeled data scarcity to some extent, neglect the reliability of pseudo-label information, the accuracy of feature extraction from unlabeled data, and the imbalance in sample selection. To address these issues, this paper proposes a novel semi-supervised fault diagnosis method under imbalanced unlabeled sample class information screening. Firstly, an information screening mechanism for unlabeled data based on active learning is established. This mechanism discriminates based on the variability of intrinsic feature information in fault samples, accurately screening out unlabeled samples located near decision boundaries that are difficult to separate clearly. Then, combining the maximum membership degree of these unlabeled data in the classification space of the supervised model and interacting with the active learning expert system, label information is assigned to the screened unlabeled data. Secondly, a cost-sensitive function driven by data imbalance is constructed to address the class imbalance problem in unlabeled sample screening, adaptively adjusting the weights of different class samples during model training to guide the training of the supervised model. Ultimately, through dynamic optimization of the supervised model and the feature extraction capability of unlabeled samples, the recognition ability of the diagnostic model for unlabeled samples is significantly enhanced. Validation through two datasets, encompassing a total of 12 experimental scenarios, demonstrates that in scenarios with only a small amount of labeled data, the proposed method achieves a diagnostic accuracy increment exceeding 10% compared to existing typical methods, fully validating the effectiveness and superiority of the proposed method in practical applications.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854703/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499918","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":"Multi-Space Feature Fusion and Entropy-Based Metrics for Underwater Image Quality Assessment.","authors":"Baozhen Du, Hongwei Ying, Jiahao Zhang, Qunxin Chen","doi":"10.3390/e27020173","DOIUrl":"10.3390/e27020173","url":null,"abstract":"<p><p>In marine remote sensing, underwater images play an indispensable role in ocean exploration, owing to their richness in information and intuitiveness. However, underwater images often encounter issues such as color shifts, loss of detail, and reduced clarity, leading to the decline of image quality. Therefore, it is critical to study precise and efficient methods for assessing underwater image quality. A no-reference multi-space feature fusion and entropy-based metrics for underwater image quality assessment (MFEM-UIQA) are proposed in this paper. Considering the color shifts of underwater images, the chrominance difference map is created from the chrominance space and statistical features are extracted. Moreover, considering the information representation capability of entropy, entropy-based multi-channel mutual information features are extracted to further characterize chrominance features. For the luminance space features, contrast features from luminance images based on gamma correction and luminance uniformity features are extracted. In addition, logarithmic Gabor filtering is applied to the luminance space images for subband decomposition and entropy-based mutual information of subbands is captured. Furthermore, underwater image noise features, multi-channel dispersion information, and visibility features are extracted to jointly represent the perceptual features. The experiments demonstrate that the proposed MFEM-UIQA surpasses the state-of-the-art methods.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854840/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143500054","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":"Statistical Characteristics of Strong Earthquake Sequence in Northeastern Tibetan Plateau.","authors":"Ying Wang, Rui Wang, Peng Han, Tao Zhao, Miao Miao, Lina Su, Zhaodi Jin, Jiancang Zhuang","doi":"10.3390/e27020174","DOIUrl":"10.3390/e27020174","url":null,"abstract":"<p><p>As the forefront of inland extension on the Indian plate, the northeastern Tibetan Plateau, marked by low strain rates and high stress levels, is one of the regions with the highest seismic risk. Analyzing seismicity through statistical methods holds significant scientific value for understanding tectonic conditions and assessing earthquake risk. However, seismic monitoring capacity in this region remains limited, and earthquake frequency is low, complicating efforts to improve earthquake catalogs through enhanced identification and localization techniques. Bi-scale empirical probability integral transformation (BEPIT), a statistical method, can address these data gaps by supplementing missing events shortly after moderate to large earthquakes, resulting in a more reliable statistical data set. In this study, we analyzed six earthquake sequences with magnitudes of <i>M</i>_S ≥ 6.0 that occurred in northeastern Tibet since 2009, following the upgrade of the regional seismic network. Using BEPIT, we supplemented short-term missing aftershocks in these sequences, creating a more complete earthquake catalog. ETAS model parameters and <i>b</i> values for these sequences were then estimated using maximum likelihood methods to analyze parameter variability across sequences. The findings indicate that the <i>b</i> value is low, reflecting relatively high regional stress. The background seismicity rate is very low, with most mainshocks in these sequences being background events rather than foreshock-driven events. The p-parameter of the ETAS model is high, indicating that aftershocks decay relatively quickly, while the α-parameter is also elevated, suggesting that aftershocks are predominantly induced by the mainshock. These conditions suggest that earthquake prediction in this region is challenging through seismicity analysis alone, and alternative approaches integrating non-seismic data, such as electromagnetic and fluid monitoring, may offer more viable solutions. This study provides valuable insights into earthquake forecasting in the northeastern Tibetan Plateau.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11853782/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499733","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":"R Version of the Kedem-Katchalsky-Peusner Equations for Liquid Interface Potentials in a Membrane System.","authors":"Andrzej Ślęzak, Sławomir M Grzegorczyn","doi":"10.3390/e27020169","DOIUrl":"10.3390/e27020169","url":null,"abstract":"<p><p>Peusner's network thermodynamics (PNT) is an important way of describing processes in nonequilibrium thermodynamics. PNT allows energy transport and conversion processes in membrane systems to be described. This conversion concerns internal energy transformation into free and dissipated energies linked with the membrane transport of solutes. A transformation of the Kedem-Katchalsky (K-K) equations into the R variant of Kedem-Katchalsky-Peusner (K-K-P) equations was developed for the transport of binary electrolytic solutions through a membrane. The procedure was verified for a system in which a membrane Ultra Flo 145 Dialyser separated aqueous NaCl solutions. Peusner coefficients were calculated by the transformation of the K-K coefficients. Next, the coupling coefficients of the membrane processes and energy fluxes for electrolyte solutions transported through the membrane were calculated based on the Peusner coefficients. The efficiency of energy conversion in the membrane transport processes was estimated, and this coefficient increased nonlinearly with the increase in the solute concentration in the membrane. In addition, the energy fluxes as functions of ionic current density for constant solute fluxes were also investigated for membrane transport processes in the Ultra Flo 145 Dialyser membrane.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854436/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143500076","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":"Dynamical Complexity in Geomagnetically Induced Current Activity Indices Using Block Entropy.","authors":"Adamantia Zoe Boutsi, Constantinos Papadimitriou, Georgios Balasis, Christina Brinou, Emmeleia Zampa, Omiros Giannakis","doi":"10.3390/e27020172","DOIUrl":"10.3390/e27020172","url":null,"abstract":"<p><p>Geomagnetically Induced Currents (GICs) are a manifestation of space weather events at ground level. GICs have the potential to cause power failures in electric grids. The GIC index is a proxy of the ground geoelectric field derived solely from geomagnetic field data. Information theory can be used to shed light on the dynamics of complex systems, such as the coupled solar wind-magnetosphere-ionosphere-ground system. We performed block entropy analysis of the GIC activity indices at middle-latitude European observatories around the St. Patrick's Day March 2015 intense magnetic storm and Mother's Day (or Gannon) May 2024 superintense storm. We found that the GIC index values were generally higher for the May 2024 storm, indicating elevated risk levels. Furthermore, the entropy values of the SYM-H and GIC indices were higher in the time interval before the storms than during the storms, indicating transition from a system with lower organization to one with higher organization. These findings, including the temporal dynamics of the entropy and GIC indices, highlight the potential of this method to reveal pre-storm susceptibility and relaxation processes. This study not only adds to the knowledge of geomagnetic disturbances but also provides valuable practical implications for space weather forecasting and geospatial risk assessment.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11853915/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499683","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":"The Information Loss Problem and Hawking Radiation as Tunneling.","authors":"Baocheng Zhang, Christian Corda, Qingyu Cai","doi":"10.3390/e27020167","DOIUrl":"10.3390/e27020167","url":null,"abstract":"<p><p>In this paper, we review some methods that have tried to solve the information loss problem. In particular, we revisit the solution based on Hawking radiation as tunneling and provide a detailed statistical interpretation of the black hole entropy in terms of the quantum tunneling probability of Hawking radiation from the black hole. In addition, we show that black hole evaporation is governed by a time-dependent Schrödinger equation that sends pure states into pure states rather than into mixed states (Hawking had originally established that the final result would be mixed states). This is further confirmation of the fact that black hole evaporation is unitary.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854280/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499838","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":"Perceptual Complexity as Normalized Shannon Entropy.","authors":"Norberto M Grzywacz","doi":"10.3390/e27020166","DOIUrl":"10.3390/e27020166","url":null,"abstract":"<p><p>Complexity is one of the most important variables in how the brain performs decision making based on esthetic values. Multiple definitions of perceptual complexity have been proposed, with one of the most fruitful being the Normalized Shannon Entropy one. However, the Normalized Shannon Entropy definition has theoretical gaps that we address in this article. Focusing on visual perception, we first address whether normalization fully corrects for the effects of measurement resolution on entropy. The answer is negative, but the remaining effects are minor, and we propose alternate definitions of complexity, correcting this problem. Related to resolution, we discuss the ideal spatial range in the computation of spatial complexity. The results show that this range must be small but not too small. Furthermore, it is suggested by the analysis of this range that perceptual spatial complexity is based solely on translational isometry. Finally, we study how the complexities of distinct visual variables interact. We argue that the complexities of the variables of interest to the brain's visual system may not interact linearly because of interclass correlation. But the interaction would be linear if the brain weighed complexities as in Kempthorne's λ-Bayes-based compromise problem. We finish by listing several experimental tests of these theoretical ideas on complexity.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854106/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143500065","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":"Crack-Detection Algorithm Integrating Multi-Scale Information Gain with Global-Local Tight-Loose Coupling.","authors":"Yun Bai, Zhiyao Li, Runqi Liu, Jiayi Feng, Biao Li","doi":"10.3390/e27020165","DOIUrl":"10.3390/e27020165","url":null,"abstract":"<p><p>In this study, an improved target-detection model based on information theory is proposed to address the difficulties of crack-detection tasks, such as slender target shapes, blurred boundaries, and complex backgrounds. By introducing a multi-scale information gain mechanism and a global-local feature coupling strategy, the model has significantly improved feature extraction and expression capabilities. Experimental results show that, on a single-crack dataset, the model's mAP@50 and mAP@50-95 are 1.6% and 0.8% higher than the baseline model RT-DETR, respectively; on a multi-crack dataset, these two indicators are improved by 1.2% and 1.0%, respectively. The proposed method shows good robustness and detection accuracy in complex scenarios, providing new ideas and technical support for in-depth research in the field of crack detection.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 2","pages":""},"PeriodicalIF":2.1,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11854598/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143499413","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}