Search Results (214)

Moldy pear core constitutes a severe internal defect that compromises fruit quality. This study proposes a nondestructive detection method for Korla pear moldy core using Vis/NIR spectral signals, aimed at supporting post-harvest quality control and automated industrial sorting. We collected spectral signals from pears and quantified the moldy pear core area to classify samples into healthy (S = 0%), slightly moldy (0 < S ≤ 10%), and severely moldy (S > 10%) categories. We constructed a three-tier comparative framework to evaluate the progression from conventional machine learning to advanced deep learning: traditional methods using univariate selection (US) and random forest (RF) for feature extraction followed by support vector machine (SVM) classification; 1D-ResNet for direct processing of spectral signals; and two-dimensional approaches transforming signals into improved gramian angular field (IGAF) or Laplacian pyramid Markov transition field (LPMTF) images processed through deep belief network (DBN), MobileNetv3, and Vision Transformer (ViT). The LPMTF-ViT combination delivered the best performance with 98.98% test accuracy and 94.44% external validation accuracy, significantly exceeding traditional approaches and 1D-ResNet. This innovative approach delivers effective technical support for early-stage, nondestructive detection of internal fruit defects. It also establishes a scalable foundation for automated industrial inspection systems, potentially reducing post-harvest losses while ensuring premium quality control in modern fruit supply chains. Full article

This paper introduces a rigorous class of two-dimensional Markov-switching autoregressive moving-average (2D MS-ARMA) models for spatial lattice data exhibiting regime-dependent dynamics. The switching mechanism is governed by a latent causal Markov random field that drives spatial transitions between regime-specific autoregressive and moving-average structures. We provide sufficient conditions for the existence of a strictly stationary solution through the top Lyapunov exponent associated with a sequence of random matrices obtained from a state-space representation constructed along the lexicographic order. For the first-order bidirectional specification, we derive explicit spectral conditions linking stationarity to the regime-dependent spectral radii. Sufficient conditions ensuring the existence of finite second-order moments are also provided. Parameter estimation is carried out using a variational expectation–maximization (VEM) algorithm based on a mean-field approximation of the posterior distribution of the hidden regimes. The E-step yields closed-form coordinate ascent updates, while the M-step relies on gradient-based numerical optimization with derivatives computed via recursive differentiation. Under increasing-domain asymptotics, we discuss the consistency and asymptotic behavior of the variational estimator. The proposed framework fills a methodological gap between classical one-dimensional Markov-switching ARMA models and spatial autoregressive structures by extending regime-switching theory to multi-indexed processes with rigorous probabilistic foundations. It provides a comprehensive basis for statistical inference, model diagnostics, and prediction in spatially heterogeneous environments. Full article

Several well-known models in present-day computer vision take the form of Markov random fields. Any model of this kind amounts to a network of soft constraints, which are called potentials. These are the subject of this study. First, three kinds of information that are involved in any computer vision inference task are identified, namely, evidence, target, and principled information, and the concept of a variable as applied in this context is discussed. The general meaning of a potential is then described, which is a local soft constraint that aims to promote a corresponding desired condition. Following this, the formal structure of a potential is highlighted, which includes a set of parameters and an analytic frame, with this being a hierarchy of operations by which the value of the potential can be computed. The possible presence of a core in the analytic frame is considered, and two salient kinds of cores are distinguished and illustrated using examples from the literature: one involving a distance function and the other given by a probabilistic conditional. In summary, this contribution highlights substantial aspects of the semantics and syntax of potentials in Markov field models of computer vision, and constructs a framework within which these aspects may be consistently arranged and explained. Full article

Learning dependence graphs from multivariate continuous data is challenging when marginal distributions are heterogeneous, since likelihood-based nonparametric scores can be sensitive to smoothing choices and can confound marginal irregularities, including non-identifiability, with dependence. This work studies structure learning in the class of decomposable (chordal) Markov random fields, where junction tree factorizations enable tractable inference and local score updates. Our first contribution is a theoretical result showing that, under decomposability, mutual information can be expressed as a difference of clique/separator copula entropies, yielding a dependence-only decomposition aligned with the clique/separator structure. Building on this identity, we define an information-theoretic objective for decomposable graphs with a complexity penalty that preserves clique/separator additivity, and we derive closed-form local score differences for chordality-preserving single-edge insertions and deletions. To make the score computable from data, we instantiate clique/separator copula entropies using pseudo-observations and a probit-transformed kernel density estimator with predictive log score evaluation to mitigate boundary effects on the unit hypercube. The resulting nonparametric greedy procedure improves edge recovery accuracy on synthetic chordal benchmarks compared with a likelihood-driven nonparametric baseline, and it produces interpretable dependence summaries on an airway epithelial gene expression dataset. Concretely, this paper contributes (1) a decomposable mutual information identity via clique/separator copula entropies, (2) a copula information score with an additive complexity penalty for decomposable graphs, (3) a closed-form local score, enabling greedy chordal add or delete search, (4) a practical nonparametric copula entropy estimation pipeline, and (5) empirical gains on synthetic and real data. Full article

The integration of distributed data storage, P2P networks, consensus mechanisms, cryptography and other technologies, the application of blockchain technology has expanded from the initial financial field to many other areas, such as logistics and auditing. The consensus mechanism is the soul of blockchain technology, and it is of great significance to conduct a rigorous mathematical analysis. As far as we know, the Proof of Stake (PoS) consensus mechanism is only a qualitative description of the rich and the poor, the rich are richer, the poor are poorer, and there is no quantitative mathematical analysis. This paper presents a novel quantitative framework to quantitatively analyze the PoS consensus mechanism. Under the premise of not carrying out the attack, we use the expected reward and the reward ratio as the evaluation indicators, quantitatively analyze the optimal fund allocation strategy of the two parties game under the PoS consensus mechanism from the perspective of rich miners, and construct the reward function as the objective function. The inequality constrains the optimization problem and solves it using the Karush-Kuhn-Tucker condition. We consider the two schemes of assignment strategy and random strategy, and get the optimal fund allocation strategy. At the same time, it is compared with the general strategy to obtain the optimization effect of the optimal strategy. After that, we compare the situation in which both sides of the game use the optimal strategy. We found that for assignment strategy, the mining activity will not indicate that the rich are richer and the poor are poorer. However, for the random strategy, this will not happen. The random strategy is also the most common strategy in practice. We also use Markov decision process (MDP) to give the optimal strategy calculation method under the rational miner game, which is also applicable to the n-parties game. The work of this paper helps the blockchain developers to analyze the PoS consensus mechanism, and the adoption strategy of the assignment strategy and the random strategy can be used as the future research direction. Full article

Some open problems regarding fractional powers of the negative generator of a discrete-time random walk and a Markov process are discussed. The suggested approach combines analytic and probabilistic ideas and may be useful for developing fractional operators with multidimensional and/or abstract discrete arguments. Full article

Rapid land use and land cover (LULC) changes in densely populated watersheds pose serious challenges to the sustainability of ecosystem services (ES), yet their spatially explicit economic consequences remain insufficiently understood. This study analyzes the spatio-temporal dynamics of LULC and ecosystem service values (ESVs) in the Citarum Watershed, Indonesia, one of the country’s most critical and intensively transformed watersheds. Multi-temporal Landsat imagery from 2003, 2013, and 2023 was classified using a Random Forest algorithm, while future LULC conditions for 2043 were projected using a Multi-layer Perceptron–Markov Chain (MLP–MC) model under three scenarios: Business-as-Usual (BAU), Protecting Paddy Field (PPF), and Protecting Forest Area (PFA). ESVs were quantified at multiple spatial scales (county, 250 m grids, and 100 m grids) using both the Traditional Benefit Transfer (TBT) method and a Spatial Benefit Transfer (SBT) approach that integrates biophysical indicators with socio-economic variables. The contribution of LULC transitions to ESV dynamics was further assessed using the Ecosystem Service Change Intensity (ESCI) index. The results reveal substantial historical forest and shrubland losses, alongside rapid expansion of settlements and dryland agriculture, indicating intensifying anthropogenic pressure on watershed functions. Scenario analysis shows continued degradation under BAU, limited mitigation under PPF, and improved forest retention under PFA; although settlement expansion persists across all scenarios. Total ESV declined from USD 2641.33 million in 2003 to USD 1585.01 million in 2023, representing a cumulative loss of 46.13%. Projections indicate severe ESV losses under BAU and PPF by 2043, while PFA substantially reduces, but does not eliminate economic degradation. ESCI results identify forest and shrubland conversion to settlements and dryland agriculture as the dominant drivers of ESV decline. These findings demonstrate that integrating multi-scenario LULC modeling with spatially explicit ESV assessment provides a more robust basis for ecosystem-based spatial planning and supports sustainable watershed management under increasing development pressure. Full article

Fine segmentation of point clouds in hull structure junction regions is a key technology for achieving high-precision digital inspection. Conventional hard-segmentation methods frequently yield over- or under-segmentation in junction regions such as welds, compromising the reliability of subsequent inspections. This study presents a computational framework that combines the Gaussian-Uniform Mixture Model (GUMM) with the Hidden Markov Random Field (HMRF) and follows a “coarse segmentation–model construction–fine segmentation” pipeline. The framework jointly optimizes the sampling model, the probabilistic model, and the expectation–maximization (EM) inference procedure. By leveraging model simplification and dimensionality reduction, the algorithm simultaneously addresses initial value estimation, spatial distribution characterization, and continuity constraints. Experiments on representative structures, including wall corner, T-joint weld, groove, and flange, show that the proposed framework outperforms the conventional GMM-EM method by approximately 2.5% in precision and 1.5% in both accuracy and F1 score. In local segmentation tasks of complex hull structures, the method achieves a deviation of less than 0.2 mm relative to manual measurements, validating its practical utility in engineering contexts. Full article

High-fidelity 3D face reconstruction from a single image is challenging, owing to the inherently ambiguous depth cues and the strong entanglement of multi-scale facial textures. In this regard, we propose a hierarchical multi-resolution self-supervised framework (HMR-Framework), which reconstructs coarse-, medium-, and fine-scale facial geometry progressively through a unified pipeline. A coarse geometric prior is first estimated via 3D morphable model regression, followed by medium-scale refinement using a vertex deformation map constrained by a global–local Markov random field loss to preserve structural coherence. In order to improve fine-scale fidelity, a learnable Gabor-aware texture enhancement module has been proposed to decouple spatial–frequency information and thus improve sensitivity for high-frequency facial attributes. Additionally, we employ a wavelet-based detail perception loss to preserve the edge-aware texture features while mitigating noise commonly observed in in-the-wild images. Extensive qualitative and quantitative evaluation of benchmark datasets indicate that the proposed framework provides better fine-detail reconstruction than existing state-of-the-art methods, while maintaining robustness over pose variations. Notably, the hierarchical design increases semantic consistency across multiple geometric scales, providing a functional solution for high-fidelity 3D face reconstruction from monocular images. Full article

Accurate evaluation of demand response (DR) potential at the individual user level is critical for the effective implementation and optimization of demand response programs. However, existing data-driven methods often suffer from insufficient feature representation, limited characterization of load profile dynamics, and ineffective fusion of heterogeneous features, leading to suboptimal evaluation performance. To address these challenges, this paper proposes a novel demand response potential evaluation method based on multivariate heterogeneous features and a Stacking-based ensemble mechanism. First, multidimensional indicator features are extracted from historical electricity consumption data and external factors (e.g., weather, time-of-use pricing), capturing load shape, variability, and correlation characteristics. Second, to enrich the information space and preserve temporal dynamics, typical daily load profiles are transformed into two-dimensional image features using the Gramian Angular Difference Field (GADF), the Markov Transition Field (MTF), and an Improved Recurrence Plot (IRP), which are then fused into a single RGB image. Third, a differentiated modeling strategy is adopted: scalar indicator features are processed by classical machine learning models (Support Vector Machine, Random Forest, XGBoost), while image features are fed into a deep convolutional neural network (SE-ResNet-20). Finally, a Stacking ensemble learning framework is employed to intelligently integrate the outputs of base learners, with a Decision Tree as the meta-learner, thereby enhancing overall evaluation accuracy and robustness. Experimental results on a real-world dataset demonstrate that the proposed method achieves superior performance compared to individual models and conventional fusion approaches, effectively leveraging both structured indicators and unstructured image representations for high-precision demand response potential evaluation. Full article

We discuss Markov edge processes $\{Y_e;e\in E\}$ defined on edges of a directed acyclic graph $(V,E)$ with the consistency property ${\mathrm{P}}_{E^{\prime }}(Y_e;e\in E^{\prime })={\mathrm{P}}_E(Y_e;e\in E^{\prime })$ for a large class of subgraphs $(V^{\prime },E^{\prime })$ of $(V,E)$ obtained through a mesh dismantling algorithm. The probability distribution ${\mathrm{P}}_E$ of such edge process is a discrete version of consistent polygonal Markov graphs. The class of Markov edge processes is related to the class of Bayesian networks and may be of interest to causal inference and decision theory. On regular $\nu$-dimensional lattices, consistent Markov edge processes have similar properties to Pickard random fields on ${\mathbb{Z}}^2$, representing a far-reaching extension of the latter class. A particular case of binary consistent edge process on ${\mathbb{Z}}^3$ was disclosed by Arak in a private communication. We prove that the symmetric binary Pickard model generates the Arak model on ${\mathbb{Z}}^2$ as a contour model. Full article

With the advancement of battery technology and the promotion of the “dual carbon” policy, electric vehicles (EVs) have been widely used in industrial, commercial, and civil fields, and the charging infrastructure of highway service areas across the country has also shown a rapid development trend. However, the charging load of electric vehicles in highway scenarios exhibits strong randomness and uncertainty. It is affected by multiple factors such as traffic flow, state of charge (SOC), and user charging behavior, and it is difficult to accurately model it through traditional mathematical models. This paper proposes a hierarchical Markov chain Monte Carlo (HMMC) simulation method to construct a charging load prediction model with spatiotemporal coupling characteristics. The model hierarchically models features such as traffic flow, SOC, and charging behavior through a hierarchical structure to reduce interference between dimensions; by constructing a Markov chain that converges to the target distribution and an inter-layer transfer mechanism, the load change process is deduced layer by layer, thereby achieving a more accurate charging load prediction. Comparative experiments with mainstream methods such as ARIMA, BP neural networks, random forests, and LSTM show that the HMMC model has higher prediction accuracy in highway scenarios, significantly reduces prediction errors, and improves model stability and interpretability. Full article

The paper presents a novel probability-informed approach to improving the accuracy of small object semantic segmentation in high-resolution imagery datasets with imbalanced classes and a limited volume of samples. Small objects imply having a small pixel footprint on the input image, for example, ships in the ocean. Informing in this context means using mathematical models to represent data in the layers of deep neural networks. Thus, the ensemble Quadtree-informed Graph Self-Attention Networks (QiGSANs) are proposed. New architectural blocks, informed by types of Markov random fields such as quadtrees, have been introduced to capture the interconnections between features in images at different spatial resolutions during the graph convolution of superpixel subregions. It has been analytically proven that quadtree-informed graph convolutional neural networks, a part of QiGSAN, tend to achieve faster loss reduction compared to convolutional architectures. This justifies the effectiveness of probability-informed modifications based on quadtrees. To empirically demonstrate the processing of real small data with imbalanced object classes using QiGSAN, two open datasets of synthetic aperture radar (SAR) imagery (up to $0.5$ m per pixel) are used: the High Resolution SAR Images Dataset (HRSID) and the SAR Ship Detection Dataset (SSDD). The results of QiGSAN are compared to those of the transformers SegFormer and LWGANet, which constitute a new state-of-the-art model for UAV (Unmanned Aerial Vehicles) and SAR image processing. They are also compared to convolutional neural networks and several ensemble implementations using other graph neural networks. QiGSAN significantly increases the $F_1$-score values by up to $63.93\%$, $48.57\%$, and $9.84\%$ compared to transformers, convolutional neural networks, and other ensemble architectures, respectively. QiGSAN outperformed the base segmentors with the mIOU (mean intersection-over-union) metric too: the highest increase was $35.79\%$. Therefore, our approach to knowledge extraction using mathematical models allows us to significantly improve modern computer vision techniques for imbalanced data. Full article

Traditional Underwater Acoustic Communication (UAC) typically assumes static or slowly varying channels over short observation periods and models multipath amplitude fluctuations with single-state statistical distributions. However, field measurements in shallow-water high-speed mobile scenarios reveal that the combined effects of rapid platform motion and dynamic environments induce multi-scale time-varying amplitude characteristics. These include distance-dependent attenuation, fluctuations in average energy, and rapid random variations. This observation directly challenges traditional single-state models and wide-sense stationary assumptions. To address this, we propose a multi-scale time-varying multipath amplitude model. Using singular spectrum analysis, we decompose amplitude sequences into hierarchical components: large-scale components modeled via acoustic propagation physics; medium-scale components characterized by Hidden Markov Models; and small-scale components described by zero-mean Gaussian distributions. Building on this model, we further develop a time-varying impulse response simulation framework validated with experimental data. The results demonstrate superior performance over conventional single-state distribution and autoregressive models in statistical distribution matching, temporal dynamics representation, and communication performance testing. The model effectively characterizes non-stationary time-varying channels, supporting high-precision modeling and simulation for mobile UAC systems. Full article

The loss of localization in robots navigating GNSS-denied environments poses a critical challenge that can compromise mission success and safe operation. This article presents a method that fuses visual odometry outputs from both direct and feature-based (indirect) methods using Iterated Conditional Modes (ICMs), an efficient iterative optimization algorithm that maximizes the posterior probability in Markov random fields, combined with uncertainty-aware gain adjustment to perform pose estimation and mapping. The proposed method enhances the performance of visual localization and mapping algorithms in low-texture or visually degraded scenarios. The method was validated using the TUM RGB-D benchmark dataset and through real-world tests in both indoor and outdoor environments. Outdoor experiments were conducted on an electric vehicle, where the method maintained stable tracking. These initial results suggest that the technique could be transferable to electric vehicle platforms and applicable in a variety of real-world conditions. Full article