Search Results (451)

We examine the estimation of the Kullback–Leibler (KL) divergence and the use of the goodness-of-fit test for multivariate normality. Our starting point is the maximum entropy principle for Shannon entropy: among all distributions with a fixed mean vector and covariance matrix, the multivariate Gaussian distributions uniquely maximize entropy. As a result, the KL divergence from a moment-matched Gaussian distribution to an unknown density can then be written as the entropy difference, which is a suitable information-theoretic measure of divergence from the Gaussian distribution. To estimate, we use k-nearest neighbor (kNN) estimators based on Shannon entropy and KL divergence derived from the Kozachenko–Leonenko approach and subsequent improvements, along with the consistency and $L^2$-convergence results established for these estimators. Motivated by previous entropy-based goodness-of-fit ideas developed for Rényi-type functionals for generalized Gaussian and Student-type models, we describe a KL-based test statistic as being the difference between the entropy of a Gaussian model fitted to the sample mean and covariance and the KL divergence between the unknown entropy and the kNN estimate. The statistic converges to zero for multivariate normality and converges to a strictly positive bound with non-Gaussian alternatives. The results of Monte Carlo simulations conducted across various dimensions and sample sizes indicate that the proposed method provides accurate Type I error control among the alternatives considered and demonstrates promising empirical power. Full article

Strict minimum message length (SMML) is an information-theoretic coding principle that represents a continuous statistical model by a finite set of assertions and a partition of the sample space. We show that the SMML objective decomposes into assertion entropy and conditional cross-entropy, balancing the cost of identifying an assertion against the cost of encoding data under the assigned model. For any fixed partition, the optimal codepoint for each cell is the model distribution that minimises Kullback–Leibler (KL) divergence from the data distribution restricted to that cell. Using the local Fisher–Rao geometry of regular parametric models, we show that, under a high-resolution LAN-scale regime, SMML partitions are asymptotically the pullback, through the maximum-likelihood estimator, of weighted Fisher–Rao Voronoi tessellations in parameter space, with assertion probabilities appearing as additive weights. For regular canonical exponential families, SMML codepoints satisfy a moment-matching condition and admit an interpretation as KL/Bregman centroids, while exact SMML cells are pullbacks of convex polyhedra in sufficient-statistic space. Together, these results show that SMML induces a natural information-geometric quantisation linking entropy-based coding, KL projection, and divergence-based Voronoi geometry. Full article

Scheduling in multi-layer industrial networks must remain stable even when the feedback mechanism of the environment changes inside a single production episode. The system can switch between a step-continuous regime with dense process feedback and a task-driven regime with sparse milestone feedback, so that the same state requires different behaviour before and after the switch. A regime-oblivious policy may therefore optimise the wrong action preference after a switch. We formulate this setting as a mode-switched multi-industrial-chain Markov decision process (MS-MIC-MDP) and prove that a single fixed action preference is necessarily suboptimal in at least one regime. We then propose BHERA, a belief-guided homeostatic estimation framework for regime adaptation. BHERA builds cross-layer representations, performs structured variational inference of slow and fast latent beliefs, estimates the posterior probability of the task-driven regime, and uses that posterior to regulate sample weights, entropy strength, return-prediction emphasis, and latent information capacity. A homeostatic feedback rule on the Kullback–Leibler (KL) divergence keeps the latent representation informative without allowing uncontrolled information growth, and we analyse it as a two-timescale stochastic approximation with an associated convergence argument and a per-iteration complexity bound. Experiments in a multi-layer industrial scheduling simulator show that BHERA achieves higher return, lower cost, and higher utility than CReSCENT, HiTAC-MuSE, Informed Switching, and WToE across all tested perturbations, with paired statistical tests confirming significance. Expanded ablations and parameter-sensitivity studies confirm the importance of regime belief, regime-balanced weighting, bootstrap prediction, homeostatic capacity control, and the dual-timescale latent split. Full article

Background: Systemic risk in heterogeneous multi-subsystem settings has been addressed by composite stress indices, spectral entropy of correlation matrices, and regime-switching copula models; none directly measures structural divergence between regime-conditional coupling matrices under an explicit hidden-regime model. Methods: We embed whitened subsystem indicators in a two-regime Gaussian-copula hidden Markov process and define the coupling divergence as the matrix relative entropy between regime-conditional correlation matrices. We establish non-negativity, reduction to scalar Kullback–Leibler divergence between sorted eigenvalue distributions under commutativity, orthogonal invariance, and vanishing under the no-regime-switching null. Results: On stylized simulation, the framework separates regime-switching from single-regime null cases at an operating window T ∈ [250, 1000]; it isolates eigenbasis-rotation signals invisible to any sorted-eigenvalue method, with 99.9% of the divergence in the rotation regime residing in the non-commutative component; it tolerates Gaussian-copula misspecification under heavy-tailed processes with a quantifiable upward bias; and expectation–maximization convergence behavior serves as an auxiliary null-identification diagnostic. Conclusions: The framework composes existing primitives into a regime-to-regime structural divergence and isolates a compositional mode of regime change beyond scalar methods. Results are internal-validity claims on synthetic data; external validation on real multi-subsystem data is an open question. Full article

We reconsider information-theoretic principles, such as the maximum entropy principle/minimum Massieu potential principle, from the perspective of the dual probability distribution. This is introduced through Sanov’s Lemma for the multinomial distribution. The dual correspondence becomes asymptotically manifest. The Massieu potential is rewritten as the Kullback–Leibler divergence between the dual probability distribution and the dual reference distribution. Similarly, the dual potential is rewritten as the cumulant generating function with respect to the dual reference distribution. This perspective gives us new insight into information-theoretic principles. As the dual probability distribution naturally arises in data sampling, we anticipate that this new perspective will play a significant role in data analysis. Full article

To address the poor detection performance in low-light underground coal mine belt conveyors caused by information entropy degradation and high background noise, as well as the difficulty in multi-scale target extraction due to uneven entropy distribution, this paper proposes an efficient foreign object detection model named SIRI-YOLO based on an improved YOLOv11n architecture. First, a Self-Calibrating Illumination Network (SCINet) is introduced to restore image information entropy and enhance low-light adaptability. Second, the C2PSA module is enhanced to C2PSA-IRMB by incorporating an Inverted Residual Mobile Block (IRMB), improving multi-scale feature utilization and reducing ineffective entropy increase. Third, an improved Reparameterized Generalized Feature Pyramid Network (RepGFPN) is adopted to strengthen the fusion of high-level semantics and low-level spatial features, reducing information entropy loss during feature pyramid transfer. Finally, the Inner-MPDIoU loss function is introduced to replace CIoU, achieving more accurate entropy minimization from a KL divergence perspective. Experimental results on a dataset containing large coal chunks and anchor rods show that SIRI-YOLO achieves 92.8% mAP@50, 59.4% mAP@50:95, 89.5% precision, and 87.2% recall, with only 2.92M parameters and 70.01 FPS, outperforming mainstream YOLO models. Furthermore, on the public ExDark low-light dataset, SIRI-YOLO improves mAP@50 by 4.2% over YOLOv11n, demonstrating strong generalization across different low-light and complex scenarios. The proposed method effectively handles uneven illumination, scale variation, and complex backgrounds, offering a practical solution for coal mine safety through system entropy reduction. Full article

Promoting the high-quality development of farmers’ specialized cooperatives and narrowing regional development gaps is critical for advancing China’s rural revitalization strategy. Based on provincial panel data covering 30 Chinese regions from 2015 to 2023, this paper constructs a five-dimensional evaluation index system including standardized operation, operational performance, service scope, driving effect, and industrial upgrading, and adopts the entropy weight method to quantify the comprehensive development level of cooperatives. By combining spatial autocorrelation, kernel density estimation, the Dagum Gini coefficient and the Geodetector model, this paper explores the spatio-temporal evolution, regional disparities and multi-factor coupled driving mechanism of cooperative development. The main findings are as follows: (1) While the total quantity of cooperatives keeps expanding nationwide, their overall development level presents an evolutionary feature of declining first and then rising; industrial upgrading gradually becomes a new growth engine, whereas operational performance and driving effect slip downward. (2) The spatial layout of cooperatives maintains a typical pyramid structure; high-value agglomeration shifts from the Yangtze River Delta to southeast coastal regions, and low-value clusters are persistently concentrated in Northeast China. (3) The overall Dagum Gini coefficient reflects widening-then-shrinking regional gaps, and intra-eastern provincial differences constitute the primary source of nationwide spatial divergence. (4) Household consumption and rural labor force stock serve as core driving factors; regional economic development, agricultural production efficiency, rural human capital and land resource allocation form a coupled driving system, and all explanatory variables show mutual enhancement effects without offsetting interactions. Targeted policy suggestions are put forward to realize balanced and high-quality development of farmers’ specialized cooperatives across China. Full article

Amid accelerating global environmental change, assessing ecological vulnerability is critical for sustainability science. Focusing on the Yellow River Source Region (YRSR)—a key water source and ecological shield in China—this study develops an integrated assessment system based on the “Pressure–State–Response” (PSR) framework, incorporating 29 indicators. A combined weighting approach integrating analytic hierarchy process (AHP) with entropy-based objective weighting characterizes the spatiotemporal patterns, drivers, and future trajectories of ecological vulnerability. Key findings reveal: (1) heterogeneous warming–wetting trends with stronger humidification in the south and relative stability in the north drive divergent hydrological responses, highlighting the limitations of single-climate metrics in explaining vulnerability dynamics; (2) vulnerability patterns are primarily shaped by climatic factors—especially temperature and potential evapotranspiration—with anthropogenic pressures serving as secondary modulators, reinforcing the foundational role of thermal and moisture regimes in alpine ecosystem resilience; and (3) scenario projections consistently identify the northeast as a persistently high-vulnerability zone, yet show that balanced socioeconomic development can reconcile ecological protection with development needs. Based on these insights, a four-tier ecological zoning scheme and a governance framework comprising three strategies—strict conservation, adaptive regulation, and sustainable utilization—are proposed. This work offers actionable scientific guidance for tailored ecological conservation in the YRSR and contributes methodological advancements for vulnerability assessment and adaptive management of high-elevation ecosystems globally. Full article

From an information geometric perspective, this study considers a natural foliation of dualistic structures associated with escort distributions of exponential families. We propose an extended divergence on this foliation by continuous-type escort distributions. Specifically, we investigate the foliation formed by escort distributions to analyze the transition of q-parameters, rather than relying on a fixed parameter. Within this foliation, distinct q-parameters and their corresponding dualistic $\alpha$-parameters were defined on each leaf. Finally, we present a decomposition of the extended divergence on this foliation, providing an analog to the method previously established for discrete escort distributions. Full article

Tsagris and Alzeley proposed the generalized circular projected Cauchy (GCPC) distribution, whose special case is the wrapped Cauchy distribution. In this paper we first derive the relationship with the wrapped Cauchy distribution, and then we attempt to characterize the distribution. We establish the conditions under which the distribution exhibits unimodality. We provide non-closed-form expressions for the mean resultant length and the Kullback–Leibler divergence and analytical forms for the cumulative probability function and the entropy of the GCPC distribution. We propose log-likelihood ratio tests for one- and two-location parameters without assuming the equality of the concentration parameters. We revisit maximum likelihood estimation with and without predictors. In the regression setting we briefly discuss the addition of circular and simplicial predictors. Simulation studies illustrate (a) the performance of the log-likelihood ratio test when one falsely assumes that the true distribution is the wrapped Cauchy distribution, and (b) the empirical rate of convergence of the regression coefficients. Using a real data example, we show how to avoid the log-likelihood being trapped in a local maximum, and we correct a mistake in the regression setting. Full article

The rapid advancement of Generative Artificial Intelligence (Gen-AI) is fundamentally reshaping labor markets, creating an urgent need for higher education institutions to adapt their program capacities and curricula. This paper proposes a data-driven Robust Multi-Objective Planning (RMOP) framework to translate heterogeneous Gen-AI labor shocks into actionable, program-level decisions regarding enrollment scaling and curriculum design. Grounded in O*NET micro-task structures, we model occupational evolution as a dynamic system of substitution, augmentation, and insulation driven by logistic technology diffusion. Our simulations across STEM, trade, and arts occupations reveal sharply divergent trajectories: Information Security Engineers face a 62% total impact dominated by substitution, whereas Electricians retain over 80% insulation, and Musicians experience high exposure but low substitution. To bridge these macro-level forecasts with immediate institutional maneuvers, the framework couples an AI-adjusted Grey Model (GM(1,1)) demand model with a Program Effectiveness Index (PEI) to yield discrete enrollment policy levers (Expand, Contract, and Adjust). For curriculum optimization, we employ Ridge regression to rank employability-related curriculum drivers and NSGA-II to generate Pareto portfolios under competing institutional objectives, including employability, instructional cost, ethics, and environmental impact. Final implementable recommendations are selected through entropy-weighted TOPSIS, where student well-being and education equity are treated as supplementary decision criteria rather than direct prediction targets. In addition, an Automation Risk Score (ARS) and a K-means TC clustering module are used to illustrate potential transfer paths across broader institutional settings. Internal scenario checks show that the AI-adjusted GM(1,1) reduces average hold-out MAPE from 7.0% to 5.8% relative to the baseline GM(1,1), and that NSGA-II achieves slightly stronger Pareto coverage than MOPSO and MODE under the same curriculum-portfolio setting. These checks are interpreted as preliminary decision-support evidence rather than external predictive validation. Overall, RMOP is presented as a scenario-based decision-support framework that links Gen-AI occupational exposure, enrollment adjustment, and curriculum portfolio design. Full article

Background: Perception-based evaluation using Likert-scale survey data is widely applied in tourism and transport research, yet conventional point-valued encoding imposes artificial precision and overlooks ambiguity between adjacent ordinal categories. This limitation is particularly relevant in experiential contexts, where subjective judgments often involve transitional evaluations. Methods: This study develops a parameterized fuzzy–entropy exploratory factor analysis (FE-EFA) framework for uncertainty-aware analysis of ordinal perception data. The approach transforms ordinal responses into parameterized fuzzy membership distributions governed by a single effective uncertainty ratio, constructs a correlation structure in the five-dimensional membership space, and incorporates Shannon entropy and Jensen–Shannon divergence to characterize distributional dispersion and representation differences. The framework is applied to survey data from Chengdu Tramway Line 2 (N = 1242; 32 indicators). Results: Under the Kaiser criterion (eigenvalues > 1), conventional EFA yields a seven-factor structure, whereas FE-EFA identifies an additional eighth factor located near the retention boundary. Under a unified factor specification, both approaches preserve a consistent high-level structure, while FE-EFA shows fewer cross-loadings and a more differentiated loading pattern in this empirical case under the adopted exploratory specification. From an information-theoretic perspective, FE-EFA produces higher entropy (average = 0.8688) and low Jensen–Shannon divergence (average = 0.0133), suggesting a limited redistribution of ordinal information without substantially altering the overall distributional structure. Entropy-adjusted weighting further reveals systematic shifts in indicator importance across key dimensions. Conclusions: The FE-EFA framework extends conventional Likert-scale analysis by introducing an uncertainty-aware representation layer prior to factor extraction. It preserves overall structural stability while suggesting a more differentiated organization of latent constructs and indicator-level representations in this empirical context. The proposed approach provides an exploratory representation-level extension for perception-based evaluation and decision support in tramway cultural tourism development and related contexts. Full article

To address the challenges of time-dependent error divergence in Strapdown Inertial Navigation Systems (SINS) and the insufficient accuracy of traditional terrain matching algorithms in feature-sparse flat terrain environments, this paper proposes an intelligent terrain-aided navigation method integrating an Improved Osprey Optimization Algorithm (IOOA), Distribution Estimation, and Q-learning. Utilizing terrain information entropy as a robust matching metric, the algorithm establishes a two-phase evolutionary framework comprising Lévy flight-based random search (exploration phase) and elite-guided Gaussian Estimation of Distribution (exploitation phase). By introducing a Q-learning mechanism to adaptively regulate exploration parameters, an intelligent balance between population diversity and convergence speed is achieved. Under a unified computational benchmark, systematic multi-scenario simulations were conducted using datasets from simulated moderately undulating foothill terrain, the Libyan Sahara, and the real Digital Elevation Model (DEM) of the Junggar Basin in Xinjiang, China. Experimental results demonstrate that, compared to traditional TERCOM and mainstream swarm intelligence algorithms, the proposed algorithm drastically reduces positioning errors in the aforementioned complex terrains and significantly enhances matching accuracy. Robustness and real-time performance tests indicate that the algorithm achieves an average single-match processing time of only 0.08 s and maintains error variability as low as ±0.83 m under random perturbations. Furthermore, an ablation study confirms the necessity of the multi-strategy fusion mechanism in suppressing local optima entrapment and non-convergent oscillations. This study validates the engineering feasibility of the algorithm under conditions of low computational dependency, providing an effective technical approach for high-precision autonomous navigation in GPS-denied environments. Full article

With the advancement of carbon peaking and carbon neutrality goals, the increasing penetration of renewable energy sources such as wind and photovoltaic power poses severe challenges to the power supply reliability of AC/DC hybrid distribution networks due to their fluctuating, intermittent, and stochastic outputs. This paper proposes a reliability assessment method for AC/DC hybrid distribution networks under large-scale renewable energy integration based on clustering of typical operating scenarios. The net load duration curve is adopted as the feature variable to characterize typical operating scenarios. An improved t-distributed Stochastic Neighbor Embedding (t-SNE) nonlinear dimensionality reduction method with Kullback–Leibler (KL) divergence elbow correction is proposed for effective reduction of high-dimensional time-series data. An adaptive Density-Based Spatial Clustering of Applications with Noise (DBSCAN) parameter optimization method based on the k-nearest-neighbor curve and a secondary K-means clustering method based on entropy-weighted multi-objective optimization are further developed, forming a hybrid t-SNE-DBSCAN–K-means clustering algorithm. The power supply reliability is then assessed based on the clustered typical operating scenarios. A typical AC/DC hybrid distribution network is used as the test system. Results show that the DB index of the proposed clustering method improves by at least 22% compared with conventional methods, the maximum relative error between the typical-day-based and full time-series simulation results is less than 6%, and the computational efficiency improves by about 8.8 times, achieving a good balance between accuracy and efficiency. Full article

We investigate the finite-temperature Casimir interaction between two delta-function potentials in a $(1+1)$-dimensional scalar field model using Lifshitz theory, canonical quantization, and the Green’s function method. The Casimir force computed from all three approaches is in complete agreement. The Casimir entropy is also broadly consistent across the three methods, with subtle differences that can be traced to the infrared logarithmic divergence in the free energy. This divergence originates from the zero-frequency term and affects the entropy but not the force. In the Lifshitz approach, regularization requires an external infrared cutoff; in canonical quantization and the Green’s function method, the cutoff is naturally related to the finite size of the physical system. Full article