We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers–Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated.
{"title":"Kramers–Wannier Duality and Random-Bond Ising Model","authors":"Chaoming Song","doi":"10.3390/e26080636","DOIUrl":"https://doi.org/10.3390/e26080636","url":null,"abstract":"We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on a planar graph and the corresponding dual graph, respectively, thereby explicitly demonstrating the Kramers–Wannier duality. The implications of our derived formula for the Random-Bond Ising Model are further elucidated.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Steven T. Homer, Nicholas Harley, Geraint A. Wiggins
We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it.
{"title":"Contrast Information Dynamics: A Novel Information Measure for Cognitive Modelling","authors":"Steven T. Homer, Nicholas Harley, Geraint A. Wiggins","doi":"10.3390/e26080638","DOIUrl":"https://doi.org/10.3390/e26080638","url":null,"abstract":"We present contrast information, a novel application of some specific cases of relative entropy, designed to be useful for the cognitive modelling of the sequential perception of continuous signals. We explain the relevance of entropy in the cognitive modelling of sequential phenomena such as music and language. Then, as a first step to demonstrating the utility of constrast information for this purpose, we empirically show that its discrete case correlates well with existing successful cognitive models in the literature. We explain some interesting properties of constrast information. Finally, we propose future work toward a cognitive architecture that uses it.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141786328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension.
{"title":"Optimized Tail Bounds for Random Matrix Series","authors":"Xianjie Gao, Mingliang Zhang, Jinming Luo","doi":"10.3390/e26080633","DOIUrl":"https://doi.org/10.3390/e26080633","url":null,"abstract":"Random matrix series are a significant component of random matrix theory, offering rich theoretical content and broad application prospects. In this paper, we propose modified versions of tail bounds for random matrix series, including matrix Gaussian (or Rademacher) and sub-Gaussian and infinitely divisible (i.d.) series. Unlike present studies, our results depend on the intrinsic dimension instead of ambient dimension. In some cases, the intrinsic dimension is much smaller than ambient dimension, which makes the modified versions suitable for high-dimensional or infinite-dimensional setting possible. In addition, we obtain the expectation bounds for random matrix series based on the intrinsic dimension.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Bernardo Araújo, João F. Teixeira, Joaquim Fonseca, Ricardo Cerqueira, Sofia C. Beco
Deep learning approaches have been gaining importance in several applications. However, the widespread use of these methods in safety-critical domains, such as Autonomous Driving, is still dependent on their reliability and trustworthiness. The goal of this paper is to provide a review of deep learning-based uncertainty methods and their applications to support perception tasks for Autonomous Driving. We detail significant Uncertainty Quantification and calibration methods, and their contributions and limitations, as well as important metrics and concepts. We present an overview of the state of the art of out-of-distribution detection and active learning, where uncertainty estimates are commonly applied. We show how these methods have been applied in the automotive context, providing a comprehensive analysis of reliable AI for Autonomous Driving. Finally, challenges and opportunities for future work are discussed for each topic.
{"title":"The Road to Safety: A Review of Uncertainty and Applications to Autonomous Driving Perception","authors":"Bernardo Araújo, João F. Teixeira, Joaquim Fonseca, Ricardo Cerqueira, Sofia C. Beco","doi":"10.3390/e26080634","DOIUrl":"https://doi.org/10.3390/e26080634","url":null,"abstract":"Deep learning approaches have been gaining importance in several applications. However, the widespread use of these methods in safety-critical domains, such as Autonomous Driving, is still dependent on their reliability and trustworthiness. The goal of this paper is to provide a review of deep learning-based uncertainty methods and their applications to support perception tasks for Autonomous Driving. We detail significant Uncertainty Quantification and calibration methods, and their contributions and limitations, as well as important metrics and concepts. We present an overview of the state of the art of out-of-distribution detection and active learning, where uncertainty estimates are commonly applied. We show how these methods have been applied in the automotive context, providing a comprehensive analysis of reliable AI for Autonomous Driving. Finally, challenges and opportunities for future work are discussed for each topic.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To describe the dark side of the universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time coincides with that in a conventional approach, although the cosmological “constant” in the Electromagnetic Accelerating Universe (EAU) Model shares a time dependence with the matter component. Its equation of state is ω ≡ P/ρ ≡ −1 within observational accuracy.
{"title":"Status of Electromagnetically Accelerating Universe","authors":"Paul H. Frampton","doi":"10.3390/e26080629","DOIUrl":"https://doi.org/10.3390/e26080629","url":null,"abstract":"To describe the dark side of the universe, we adopt a novel approach where dark energy is explained as an electrically charged majority of dark matter. Dark energy, as such, does not exist. The Friedmann equation at the present time coincides with that in a conventional approach, although the cosmological “constant” in the Electromagnetic Accelerating Universe (EAU) Model shares a time dependence with the matter component. Its equation of state is ω ≡ P/ρ ≡ −1 within observational accuracy.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lorenzo Di Meco, Mirko Degli Esposti, Federico Bellisardi, Armando Bazzani
The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network.
{"title":"Congestion Transition on Random Walks on Graphs","authors":"Lorenzo Di Meco, Mirko Degli Esposti, Federico Bellisardi, Armando Bazzani","doi":"10.3390/e26080632","DOIUrl":"https://doi.org/10.3390/e26080632","url":null,"abstract":"The formation of congestion on an urban road network is a key issue for the development of sustainable mobility in future smart cities. In this work, we propose a reductionist approach by studying the stationary states of a simple transport model using a random process on a graph, where each node represents a location and the link weights give the transition rates to move from one node to another, representing the mobility demand. Each node has a maximum flow rate and a maximum load capacity, and we assume that the average incoming flow equals the outgoing flow. In the approximation of the single-step process, we are able to analytically characterize the traffic load distribution on the single nodes using a local maximum entropy principle. Our results explain how congested nodes emerge as the total traffic load increases, analogous to a percolation transition where the appearance of a congested node is an independent random event. However, using numerical simulations, we show that in the more realistic case of synchronous dynamics for the nodes, entropic forces introduce correlations among the node states and favor the clustering of empty and congested nodes. Our aim is to highlight the universal properties of congestion formation and, in particular, to understand the role of traffic load fluctuations as a possible precursor of congestion in a transport network.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10−2. In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets.
{"title":"Breast Cancer Detection with Quanvolutional Neural Networks","authors":"Nadine Matondo-Mvula, Khaled Elleithy","doi":"10.3390/e26080630","DOIUrl":"https://doi.org/10.3390/e26080630","url":null,"abstract":"Quantum machine learning holds the potential to revolutionize cancer treatment and diagnostic imaging by uncovering complex patterns beyond the reach of classical methods. This study explores the effectiveness of quantum convolutional layers in classifying ultrasound breast images for cancer detection. By encoding classical data into quantum states through angle embedding and employing a robustly entangled 9-qubit circuit design with an SU(4) gate, we developed a Quantum Convolutional Neural Network (QCNN) and compared it to a classical CNN of similar architecture. Our QCNN model, leveraging two quantum circuits as convolutional layers, achieved an impressive peak training accuracy of 76.66% and a validation accuracy of 87.17% at a learning rate of 1 × 10−2. In contrast, the classical CNN model attained a training accuracy of 77.52% and a validation accuracy of 83.33%. These compelling results highlight the potential of quantum circuits to serve as effective convolutional layers for feature extraction in image classification, especially with small datasets.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chen Sun, Mengchao Yao, Ruiqi Xiong, Yang Su, Binglin Zhu, Yong-Cong Chen, Ping Ao
How did the complex structure of the telencephalon evolve? Existing explanations are based on phenomena and lack a first-principles account. The Darwinian dynamics and endogenous network theory—established decades ago—provides a mathematical and theoretical framework and a general constitutive structure for theory–experiment coupling for answering this question from a first-principles perspective. By revisiting a gene network that explains the anterior–posterior patterning of the vertebrate telencephalon, we found that upon increasing the cooperative effect within this network, fixed points gradually evolve, accompanied by the occurrence of two bifurcations. The dynamic behavior of this network is informed by the knowledge obtained from experiments on telencephalic evolution. Our work provides a quantitative explanation for how telencephalon anterior–posterior patterning evolved from the pre-vertebrate chordate to the vertebrate and provides a series of verifiable predictions from a first-principles perspective.
{"title":"Evolution of Telencephalon Anterior–Posterior Patterning through Core Endogenous Network Bifurcation","authors":"Chen Sun, Mengchao Yao, Ruiqi Xiong, Yang Su, Binglin Zhu, Yong-Cong Chen, Ping Ao","doi":"10.3390/e26080631","DOIUrl":"https://doi.org/10.3390/e26080631","url":null,"abstract":"How did the complex structure of the telencephalon evolve? Existing explanations are based on phenomena and lack a first-principles account. The Darwinian dynamics and endogenous network theory—established decades ago—provides a mathematical and theoretical framework and a general constitutive structure for theory–experiment coupling for answering this question from a first-principles perspective. By revisiting a gene network that explains the anterior–posterior patterning of the vertebrate telencephalon, we found that upon increasing the cooperative effect within this network, fixed points gradually evolve, accompanied by the occurrence of two bifurcations. The dynamic behavior of this network is informed by the knowledge obtained from experiments on telencephalic evolution. Our work provides a quantitative explanation for how telencephalon anterior–posterior patterning evolved from the pre-vertebrate chordate to the vertebrate and provides a series of verifiable predictions from a first-principles perspective.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
When a camera lens is directly faced with a strong light source, image flare commonly occurs, significantly reducing the clarity and texture of the photo and interfering with image processing tasks that rely on visual sensors, such as image segmentation and feature extraction. A novel flare removal network, the Sparse-UFormer neural network, has been developed. The network integrates two core components onto the UFormer architecture: the mixed-scale feed-forward network (MSFN) and top-k sparse attention (TKSA), creating the sparse-transformer module. The MSFN module captures rich multi-scale information, enabling the more effective addressing of flare interference in images. The TKSA module, designed with a sparsity strategy, focuses on key features within the image, thereby significantly enhancing the precision and efficiency of flare removal. Furthermore, in the design of the loss function, besides the conventional flare, background, and reconstruction losses, a structural similarity index loss has been incorporated to ensure the preservation of image details and structure while removing the flare. Ensuring the minimal loss of image information is a fundamental premise for effective image restoration. The proposed method has been demonstrated to achieve state-of-the-art performance on the Flare7K++ test dataset and in challenging real-world scenarios, proving its effectiveness in removing flare artefacts from images.
{"title":"Flare Removal Model Based on Sparse-UFormer Networks","authors":"Siqi Wu, Fei Liu, Yu Bai, Houzeng Han, Jian Wang, Ning Zhang","doi":"10.3390/e26080627","DOIUrl":"https://doi.org/10.3390/e26080627","url":null,"abstract":"When a camera lens is directly faced with a strong light source, image flare commonly occurs, significantly reducing the clarity and texture of the photo and interfering with image processing tasks that rely on visual sensors, such as image segmentation and feature extraction. A novel flare removal network, the Sparse-UFormer neural network, has been developed. The network integrates two core components onto the UFormer architecture: the mixed-scale feed-forward network (MSFN) and top-k sparse attention (TKSA), creating the sparse-transformer module. The MSFN module captures rich multi-scale information, enabling the more effective addressing of flare interference in images. The TKSA module, designed with a sparsity strategy, focuses on key features within the image, thereby significantly enhancing the precision and efficiency of flare removal. Furthermore, in the design of the loss function, besides the conventional flare, background, and reconstruction losses, a structural similarity index loss has been incorporated to ensure the preservation of image details and structure while removing the flare. Ensuring the minimal loss of image information is a fundamental premise for effective image restoration. The proposed method has been demonstrated to achieve state-of-the-art performance on the Flare7K++ test dataset and in challenging real-world scenarios, proving its effectiveness in removing flare artefacts from images.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As a severe inflammatory response syndrome, sepsis presents complex challenges in predicting patient outcomes due to its unclear pathogenesis and the unstable discharge status of affected individuals. In this study, we develop a machine learning-based method for predicting the discharge status of sepsis patients, aiming to improve treatment decisions. To enhance the robustness of our analysis against outliers, we incorporate robust statistical methods, specifically the minimum covariance determinant technique. We utilize the random forest imputation method to effectively manage and impute missing data. For feature selection, we employ Lasso penalized logistic regression, which efficiently identifies significant predictors and reduces model complexity, setting the stage for the application of more complex predictive methods. Our predictive analysis incorporates multiple machine learning methods, including random forest, support vector machine, and XGBoost. We compare the prediction performance of these methods with Lasso penalized logistic regression to identify the most effective approach. Each method’s performance is rigorously evaluated through ten iterations of 10-fold cross-validation to ensure robust and reliable results. Our comparative analysis reveals that XGBoost surpasses the other models, demonstrating its exceptional capability to navigate the complexities of sepsis data effectively.
{"title":"Machine Learning-Based Risk Prediction of Discharge Status for Sepsis","authors":"Kaida Cai, Yuqing Lou, Zhengyan Wang, Xiaofang Yang, Xin Zhao","doi":"10.3390/e26080625","DOIUrl":"https://doi.org/10.3390/e26080625","url":null,"abstract":"As a severe inflammatory response syndrome, sepsis presents complex challenges in predicting patient outcomes due to its unclear pathogenesis and the unstable discharge status of affected individuals. In this study, we develop a machine learning-based method for predicting the discharge status of sepsis patients, aiming to improve treatment decisions. To enhance the robustness of our analysis against outliers, we incorporate robust statistical methods, specifically the minimum covariance determinant technique. We utilize the random forest imputation method to effectively manage and impute missing data. For feature selection, we employ Lasso penalized logistic regression, which efficiently identifies significant predictors and reduces model complexity, setting the stage for the application of more complex predictive methods. Our predictive analysis incorporates multiple machine learning methods, including random forest, support vector machine, and XGBoost. We compare the prediction performance of these methods with Lasso penalized logistic regression to identify the most effective approach. Each method’s performance is rigorously evaluated through ten iterations of 10-fold cross-validation to ensure robust and reliable results. Our comparative analysis reveals that XGBoost surpasses the other models, demonstrating its exceptional capability to navigate the complexities of sepsis data effectively.","PeriodicalId":11694,"journal":{"name":"Entropy","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141782393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：