Physica A: Statistical Mechanics and its Applications最新文献

{"title":"Randomized Gauss–Seidel iterative algorithms for Extreme Learning Machines","authors":"Chinnamuthu Subramani ,&nbsp;Ravi Prasad K. Jagannath ,&nbsp;Venkatanareshbabu Kuppili","doi":"10.1016/j.physa.2025.130515","DOIUrl":"10.1016/j.physa.2025.130515","url":null,"abstract":"<div><div>Extreme Learning Machines (ELMs) are a class of single hidden-layer feedforward neural networks known for their rapid training process, structural simplicity, and strong generalization capabilities. ELM training requires solving a system of linear equations, where solution accuracy directly impacts model performance. However, conventional ELMs rely on the Moore–Penrose inverse, which is computationally expensive, memory-intensive, and numerically unstable in ill-conditioned problems. Additionally, stabilizing matrix inversion requires a hyperparameter, whose optimal selection further increases computational complexity. Iterative numerical techniques offer a promising alternative; however, the stochastic nature of the feature matrix challenges deterministic methods, while stochastic gradient approaches are hyperparameter-sensitive and prone to local minima. To address these limitations, this study introduces randomized iterative algorithms that solve the original linear system without requiring matrix inversion or full-system computation, instead leveraging random subsets of data in a hyperparameter-free framework. Although these methods incorporate randomness, they are not arbitrary but remain system-dependent, dynamically adapting to the structure of the feature matrix. Theoretical analysis establishes upper bounds on the expected number of iterations, expressed in terms of statistical properties of the feature matrix, providing insights into near-singularity, condition number, and network size. Empirical evaluations on classification datasets demonstrate that the proposed methods consistently outperform conventional ELM, deterministic solvers, and gradient descent-based methods in accuracy, efficiency, and robustness. Statistical validation using Friedman’s rank test and Wilcoxon post-hoc analysis confirms the superior performance and reliability of these randomized algorithms, establishing them as a computationally efficient and numerically stable alternative to existing approaches.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130515"},"PeriodicalIF":2.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681478","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}

{"title":"Robust analysis of spatio-temporal inequality with Inverse entropy","authors":"Miguel Ángel Ruiz Reina","doi":"10.1016/j.physa.2025.130532","DOIUrl":"10.1016/j.physa.2025.130532","url":null,"abstract":"<div><div>This study introduces Inverse entropy, a novel metric for spatio-temporal inequality that extends traditional measures such as Shannon entropy and the Gini coefficient. Unlike dispersion-based indices, it focuses on temporal concentration and employs a decomposition framework to disentangle structural, transversal, and allocative components, offering deeper insights into inequality dynamics. Monte Carlo simulations validate its robustness across skewed and noisy distributions, demonstrating superior sensitivity, monotonicity, and scalability compared to traditional inequality and concentration measures. An empirical analysis of 106 Spanish tourism destinations (2005–2019) reveals significant temporal disparities, with transversal components emerging as key drivers of seasonal demand variability. The results provide actionable insights for policymakers, addressing structural dependencies and allocative inefficiencies to optimise resource allocation. The computational implementation ensures reproducibility using R, enabling large-scale analyses. Beyond tourism, Inverse entropy is applicable to energy demand, transportation, and retail forecasting.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130532"},"PeriodicalIF":2.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143642069","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}

{"title":"Gap solitons of spin–orbit coupled Bose–Einstein condensates with Rabi coupling in twisted-bilayer optical lattices","authors":"Pu Tu ,&nbsp;Jin-Ping Ma ,&nbsp;Xi Zhao ,&nbsp;Bao-Long Xi ,&nbsp;Kai-Hua Shao ,&nbsp;Xiao-Fei Zhang ,&nbsp;Yu-Ren Shi","doi":"10.1016/j.physa.2025.130504","DOIUrl":"10.1016/j.physa.2025.130504","url":null,"abstract":"<div><div>We consider the gap solitons of a two-component Bose–Einstein condensate with spin–orbit coupling and Rabi coupling confined in twisted-bilayer optical lattices. Our results show that the band structure of the twisted-bilayer optical lattices exhibits flattening one, which shows strong dependence not only on the amplitude of sublattice and the twist angle, but also on the spin–orbit coupling and Rabi coupling. We also find a series of solutions of gap solitons existing in the Bloch band gap, and its shapes show strongly dependence on the chemical potential, spin–orbit coupling and Rabi couplings. Finally, the stability of such gap solitons is analyzed using the non-linear methods, and the results show that both the spin–orbit coupling and Rabi coupling play significant roles on the stability of the gap solitons.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130504"},"PeriodicalIF":2.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628741","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}

{"title":"Tactical analysis of football games by vector calculus of last-pass performance","authors":"Tenpei Morishita ,&nbsp;Yuji Aruga ,&nbsp;Masao Nakayama ,&nbsp;Akifumi Kijima ,&nbsp;Hiroyuki Shima","doi":"10.1016/j.physa.2025.130507","DOIUrl":"10.1016/j.physa.2025.130507","url":null,"abstract":"<div><div>The traditional approach to analyzing football (soccer) gameplay is to observe the movements of the ball and players closely to gain insight into the tactics and interactions between players. This study introduces a more advanced mathematical approach based on observational data to elucidate typical game patterns and tactical characteristics. Specifically, we applied vector analysis to the direction and length of the last-passes observed in numerous games and derived potential fields from the last-pass vector fields. Our approach allows for the visualization of natural pass flows along the gradient of the potential and the tactical characteristics of the last-passes that do not follow the gradient. Vector analysis also revealed the spontaneous formation of low-potential areas where passes were concentrated in front of the goal area, visualizing the typicality of crosses near the penalty area. Additionally, a detailed analysis of vector components not aligned with the gradient revealed the tactical characteristics of attacks or responses to defenders in the central and side areas. The outcomes of this study provide useful insights into tactical analysis and strategy optimization in matches, offering new perspectives in sports science.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130507"},"PeriodicalIF":2.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143681435","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}

{"title":"Spatial structures of wind farms: Correlation analysis of the generated electrical power","authors":"Edgar Jungblut ,&nbsp;Henrik M. Bette,&nbsp;Thomas Guhr","doi":"10.1016/j.physa.2025.130508","DOIUrl":"10.1016/j.physa.2025.130508","url":null,"abstract":"<div><div>We investigate the interaction of many wind turbines in a wind farm with a focus on their electrical power production. The operational data of two offshore wind farms with a ten minute and a ten second time resolution, respectively, are analyzed. For the correlations of the active power between turbines over the entire wind farms, we find a dominant collective behavior. We manage to subtract the collective behavior and find a significant dependence of the correlation structure on the spatial structure of the wind farms. We further show a connection between the observed correlation structures and the prevailing wind direction. We attribute the differences between the two wind farms to the differences in the turbine spacing within the two wind farms.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130508"},"PeriodicalIF":2.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628739","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":"Uniform transformation and collective degree analysis on higher-order networks","authors":"Ke Zhang ,&nbsp;Jingyu Gao ,&nbsp;Haixing Zhao ,&nbsp;Wenjun Hu ,&nbsp;Minmin Miao ,&nbsp;Zi-Ke Zhang","doi":"10.1016/j.physa.2025.130512","DOIUrl":"10.1016/j.physa.2025.130512","url":null,"abstract":"<div><div>Hypergraphs provide crucial and potent mathematical models for accurately describing the intricate high-order interactions prevalent in real-world systems. To advance the research landscape of hypergraph theory and deepen its applications, a systematic investigation into the group properties of high-order networks that model these systems is imperative. In this context, we introduce an innovative method for transforming general non-uniform hypergraphs into uniform hypergraphs, grounded in hypergraph theory, set theory, and statistical mechanics. This approach aims to uncover the complex group organization of the corresponding systems, significantly preserving linear operations, and thereby mitigating the complexity commonly associated with tensor-based hypergraph computations. The refined concepts and analytical tools we have developed are crucial for assessing the distribution and importance of groups of varying sizes. For each of these two practical challenges, we have conducted experiments using two different real-world datasets. Our research findings have substantially advanced hypergraph theory, while also providing valuable insights for analyzing group characteristics in higher-order networks based on hypergraphs, thereby expanding the application scope of network science.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130512"},"PeriodicalIF":2.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628738","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}

{"title":"Information index augmented eRG to model vaccination behaviour: A case study of COVID-19 in the US","authors":"Bruno Buonomo ,&nbsp;Alessandra D’Alise ,&nbsp;Rossella Della Marca ,&nbsp;Francesco Sannino","doi":"10.1016/j.physa.2025.130429","DOIUrl":"10.1016/j.physa.2025.130429","url":null,"abstract":"<div><div>Recent pandemics triggered the development of a number of mathematical models and computational tools apt at curbing the socio-economic impact of these and future pandemics. The need to acquire solid estimates from the data led to the introduction of effective approaches such as the <em>epidemiological Renormalization Group</em> (eRG). A recognized relevant factor impacting the evolution of pandemics is the feedback stemming from individuals’ choices. The latter can be taken into account via the <em>information index</em> which accommodates the information–induced perception regarding the status of the disease and the memory of past spread. Therefore, we show how to augment the eRG through the information index. We first develop the <em>behavioural</em> version of the eRG (BeRG) and then test it against the US vaccination campaign for COVID-19. We find that the BeRG improves the description of the pandemic dynamics of the US divisions for which the epidemic peak occurs after the start of the vaccination campaign. Additionally, we observe, via the BeRG model, a behavioural impact on the increase in the number of vaccinated individuals for all US divisions when compared to the original eRG model. The BeRG reasonably captures the COVID-19 vaccination behaviour which has not undergone stressful periods as the nearly linear growth of the vaccinated individuals suggests. Our results strengthen the relevance of taking into account the human behaviour component when modelling pandemic evolution. To inform public health policies, the model can be readily employed to investigate the socio-epidemiological dynamics, including vaccination campaigns, for other world regions.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"667 ","pages":"Article 130429"},"PeriodicalIF":2.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759103","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}

{"title":"Deterministic risk modelling: Newtonian dynamics in capital flow","authors":"Anna Szczypińska,&nbsp;Edward W. Piotrowski,&nbsp;Marcin Makowski","doi":"10.1016/j.physa.2025.130499","DOIUrl":"10.1016/j.physa.2025.130499","url":null,"abstract":"<div><div>Risk is a universal concept that is applied in many scientific disciplines. We demonstrate the relationship between the risk associated with the dynamics of capital flows and a specific class of problems from classical mechanics, which rely solely on the deterministic nature of the constructed models. This approach differs from the currently dominant one, where risk is mainly associated with probabilistic methods of modelling Brownian motion. We point out the safest form of loan repayment while considering profit maximization. We derive formulas that allow us to calculate the value of capital at any discrete moments in time, given lower and upper interest rate bounds. We use matrix rates and Newton’s principles to analyse capital dynamics in both continuous and discrete systems. We illustrate the proposed theory with a practical example: a measure of the efficiency of buying and selling transactions.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"665 ","pages":"Article 130499"},"PeriodicalIF":2.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143601163","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}

{"title":"Unified CNNs and transformers underlying learning mechanism reveals multi-head attention modus vivendi","authors":"Ella Koresh ,&nbsp;Ronit D. Gross ,&nbsp;Yuval Meir ,&nbsp;Yarden Tzach ,&nbsp;Tal Halevi ,&nbsp;Ido Kanter","doi":"10.1016/j.physa.2025.130529","DOIUrl":"10.1016/j.physa.2025.130529","url":null,"abstract":"<div><div>Convolutional neural networks (CNNs) evaluate short-range correlations in input images which progress along the layers, whereas vision transformer (ViT) architectures evaluate long-range correlations, using repeated transformer encoders composed of fully connected layers. Both are designed to solve complex classification tasks but from different perspectives. This study demonstrates that CNNs and ViT architectures stem from a unified underlying learning mechanism, which quantitatively measures the single-nodal performance (SNP) of each node in feedforward (FF) and multi-head attention (MHA) sub-blocks. Each node identifies small clusters of possible output labels, with additional noise represented as labels outside these clusters. These features are progressively sharpened along the transformer encoders, enhancing the signal-to-noise ratio. This unified underlying learning mechanism leads to two main findings. First, it enables an efficient applied nodal diagonal connection (ANDC) pruning technique without affecting the accuracy. Second, based on the SNP, spontaneous symmetry breaking occurs among the MHA heads, such that each head focuses its attention on a subset of labels through cooperation among its SNPs. Consequently, each head becomes an expert in recognizing its designated labels, representing a quantitative MHA modus vivendi mechanism. This statistical mechanics inspired viewpoint enables to reveal macroscopic behavior of the entire network from the microscopic performance of each node. These results are based on a compact convolutional transformer architecture trained on the CIFAR-100 and Flowers-102 datasets and call for their extension to other architectures and applications, such as natural language processing.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130529"},"PeriodicalIF":2.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143636973","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}

{"title":"Microcanonical Monte Carlo simulation of opinion dynamics under the influence of mass media","authors":"Yasmín Navarrete ,&nbsp;Carlos Femenías ,&nbsp;Sergio Davis ,&nbsp;Claudia Loyola","doi":"10.1016/j.physa.2025.130516","DOIUrl":"10.1016/j.physa.2025.130516","url":null,"abstract":"<div><div>The formation of large social groups having uniform opinions influenced by mass media is currently an important topic in the social sciences. In this work, we explore and extend an off-lattice, two-dimensional Potts model (Eur. Phys. J. B <strong>87</strong>, 78 [2014]) that describes the formation and dynamics of opinions in social groups according to individual consequence and agreement between neighbors. This model was originally obtained by the application of the maximum entropy principle, a general method in statistical inference, and using the same methodology we have now included the influence of mass media as a constant external field. By means of microcanonical Monte Carlo Metropolis simulations on a setup with two regions with opposing external influences, we have shown the presence of metastable states associated to the formation of clusters aligned with the locally imposed opinion. Our results suggest that, for some values of the total energy of the system, only a single cluster with a uniform opinion survives, thus the presence of two large, opposing groups is not a thermodynamically stable configuration.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"666 ","pages":"Article 130516"},"PeriodicalIF":2.8,"publicationDate":"2025-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637078","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}