High-dimensional change point detection is a fundamental problem in modern statistical learning, particularly when distributional changes are driven by a small and unknown subset of variables. In heterogeneous settings, uniform aggregation across coordinates may suffer from signal dilution, because stable or noisy variables can mask the evidence carried by structurally unstable coordinates. Moreover, many existing procedures primarily focus on temporal localization and provide limited information about the variables responsible for a detected structural break. To address these challenges, we propose WAVE, a weighted adaptive variable selection procedure for interpretable change point detection. WAVE constructs variance-standardized global CUSUM evidence and locally standardized exponentially weighted evidence for each coordinate and then adaptively maps intervalwise coordinate evidence into a continuous weight vector. The learned weights strengthen coordinates with persistent or local evidence of change while downweighting nuisance coordinates with weak evidence. The resulting weighted scan statistic is calibrated by a residual moving block bootstrap that preserves temporal and cross-sectional dependence and re-applies the weighting rule within bootstrap samples to account for data-adaptive aggregation. Detected change points are further equipped with coordinate-level attribution through a multi-criteria fusion rule combining adaptive weights, local standardized effect sizes, and marginal testing evidence. Simulation studies show that WAVE achieves accurate localization and reliable support recovery in both single and multiple change point settings, particularly under sparse and heterogeneous alternatives. An empirical analysis of S&P 100 stock returns in 2020 further demonstrates that WAVE identifies economically meaningful market regime shifts with interpretable coordinate-level attribution.
In this paper, we consider the extremal trace problem for the coupled Laplacian on the sets homeomorphic to the Stiefel manifold defined on the complex Euclidean space. The study is implemented via various mathematical methods, including topological and probabilistic approaches. A detailed, comprehensive classification of the stationary points is given, which itself deserves to be considered as a general method in the framework of the optimization theory. Finally, an application to biologically meaningful integration of heterogeneous datasets, in which the structure of molecular interactions serves as a significant constraint for the mathematical model, is proposed. The main advantage of the elaborated method in comparison with the previously used ones is the absence of any conditions on the structure of the initial heterogeneous datasets. This paper is a continuation of a series of papers by our research group devoted to the development of new mathematical methods for integrating multi-omics data.
Generalizable deepfake detection is essential for trustworthy visual understanding in real-world computer vision applications. This paper presents a dynamic spatial-temporal inconsistency learning algorithm designed to achieve high generalization in deepfake video detection. Current video-based detection approaches tend to either isolate spatial artifacts or merely exploit coarse temporal inconsistencies when identifying deepfake videos, which impedes the acquisition of fine-grained spatial-temporal clues and consequently limits their generalization capability. To this end, we propose the dynamic spatial-temporal network (DST-Net), a deep architecture that systematically mines comprehensive inconsistency cues through three synergistic modules. The short-term temporal modality extraction (STME) module captures temporal dynamics from adjacent frames. The short-term spatial-temporal inconsistency extraction (SSTIE) module with pixel-wise supervision learns semantically meaningful inconsistency features resistant to perturbations. The dynamic-term spatial-temporal inconsistency extraction (DSTIE) module adaptively aggregates these features across timescales, building robust multi-scale representations. This design ensures that the learned representations capture intrinsic forgery patterns, enhancing generalization and robustness. Comprehensive evaluations conducted on five widely adopted benchmark datasets reveal that our method surpasses nine representative competitors, with superior robustness to common image perturbations. This work advances the application of deep learning algorithms to reliable visual understanding in multimedia forensics.
Oil price volatility forecasting remains a central challenge in financial risk management and macroeconomic policy, particularly when market uncertainty stems from expert judgment, geopolitical assessments, or imprecisely quantified fundamentals rather than statistical frequencies. We propose a bivariate uncertain vector autoregressive (UVAR) model to jointly forecast crude oil realized volatility (RV) and the Overall Equity Market Volatility (EMV) tracker within the framework of uncertainty theory, using 204 monthly observations from January 2008 to December 2024. Three cross-validation schemes consistently identify UVAR(1) as optimal, and least-squares estimation reveals an asymmetric bidirectional relationship between the two variables. Residual analysis and uncertain hypothesis testing confirm the adequacy of the fitted model at both alpha=0.05 and alpha=0.10, the conventional significance levels reported in the empirical literature. Relative to a univariate UAR benchmark, UVAR(1) yields lower residual variance and, on average, narrower 95% confidence intervals for both variables and remedies the hypothesis-test failure of UAR(1) for realized volatility; while its fixed-origin ATE is marginally higher on the EMV tracker, this is more than offset by substantial gains on realized volatility, the primary economic variable of interest. Against a probabilistic VAR(1) benchmark, UVAR(1) attains marginally lower out-of-sample sum of squared mean errors while uniquely supporting principled uncertain-statistical inference under non-frequentist data-generating mechanisms. These results provide principled inputs for value-at-risk assessment and portfolio hedging in oil-dependent economies.
In this paper, we investigate fundamental properties of (m,p)-isometric tuples ((m,p)-I.T.) in normed spaces. We first establish conditions under which the product of two (m,p)-I.T. remains in the same class, providing a framework for composing such tuples. Next, we derive necessary conditions for an (m,p)-I.T. to become a (2,p)-I.T., characterizing when higher-order isometric behavior can change under parameter adjustments. We also show that any (m,p)-I.T. that is power-bounded reduces to a (1,p)-I.T., revealing a structural collapse from higher-order to first-order isometries under boundedness constraints. Furthermore, we prove that if a tuple (N1,& mldr;,Nd) is simultaneously an (m,p)-I.T. and an (m,infinity)-isometry, then (N1m,& mldr;,Ndm) is a (1,p)-I.T., providing a link between different isometric classes. These results provide a systematic understanding of the stability, transformation behavior, and interrelations of (m,p)-I.T., extending classical operator-theoretic concepts to tuples of commuting linear or nonlinear transformations in normed and Banach spaces.
Triangular mesh is one of the most widely used representations for 3D surfaces. However, high-resolution mesh models often contain a large number of triangles, leading to significant burdens in storage, transmission, and real-time rendering. Mesh simplification aims to reduce model complexity while preserving geometric fidelity and structural features. Classical methods, such as quadric error metrics (QEM), rely solely on local geometric errors, making them difficult to distinguish between redundant regions and structurally important features, often resulting in feature loss and topological degradation. To address these limitations, this study proposes a structure-aware triangular mesh simplification framework based on graph neural networks (GNNs)-guided QEM. GNNs are employed as a structural importance estimator to predict geometric saliencies of mesh edges. The predicted importances are incorporated into the classical QEM edge collapse cost through a soft modulation mechanism. Furthermore, a geometry-saliency-driven dynamic cost modulation strategy is designed, enabling the simplification process to prioritize critical features in early stages and gradually transition to global error minimization in later stages, without compromising the geometric optimality of QEM. In terms of model design, hybrid structural representation GNNs are constructed by integrating spectral geometry and a dual-branch architecture. Laplacian positional encoding is introduced to capture global topological information, while 1-hop and 2-hop message passing branches enable multi-scale representation of complex geometric structures. In addition, a staged inference strategy is adopted to dynamically update graph structural features during simplification, effectively mitigating topological drift. Experimental results on the TOSCA dataset demonstrate that the proposed method achieves stable performance across various simplification ratios. It consistently outperforms FQMS and QEM in terms of geometric error (PCD) and normal consistency (PNE). For structural preservation (PLE), the method shows advantages, with win-rates generally exceeding 90%. Moreover, it significantly improves the preservation of local geometric details at low to moderate simplification ratios. In summary, the proposed method effectively enhances local structural preservation while maintaining global geometric topology, providing an interpretable and practical solution for integrating learning-based structural awareness with classical geometric optimization in mesh simplification.
In response to the bottleneck issue of natural rubber selection in aircraft tire formulation design, this study proposes a data-driven screening methodology that integrates a simulated performance database with grey system theory. A multidimensional performance simulation database was constructed, encompassing representative NR brands from six major global producing regions: Malaysia, Indonesia, Thailand, Vietnam, Hainan (China), and Yunnan (China). This repository encompasses critical metrics, including raw rubber constitution, molecular characteristics, and the static/dynamic mechanical behaviors of vulcanizates. Utilizing this foundation, a novel material selection protocol was formulated, grounded in a multi-objective weighted intelligent grey target decision framework. The Analytic Hierarchy Process (AHP) was applied to ascertain differentiated performance criteria and assign corresponding weights, specifically tailored to the functional necessities of distinct aircraft tire sections. To substantiate the model’s efficacy, the primary tire of the ubiquitous Boeing 737-800 served as a validation case. The optimal Natural Rubber (NR) grade identified by the algorithm was cross-referenced with the empirical expertise and engineering practices of premier global tire manufacturers, thereby confirming the framework’s robustness and predictive accuracy. Consequently, this investigation establishes a comprehensive intelligent decision-making architecture, spanning data construction to engineering deployment, offering a quantitative and referential pathway for NR material screening in aviation applications.
Characterizing specific types of units in group rings in terms of the Jacobson radical constitutes a frequently investigated problem in the theory of group rings. In this study, since R is a commutative ring with unity and G is a finite Abelian group, Uft(RG) as the set of feckly trivial units in the group ring RG, consisting of units that are congruent modulo J(RG) to some g is an element of G, where J(RG) denotes the Jacobson radical of RG, is defined. Secondly, some necessary and sufficient conditions are given for the group U(RG) of units of the group ring RG to be feckly trivial under the assumption that supp(G)boolean AND jp(R)=& empty; where P is the set of all prime integers, supp(G)={p is an element of P:Gp not equal eG}, jp(R)={p is an element of P:there exists r is an element of R\{0R},pr is an element of J(R)} and Gp is the p-primary component in G. Finally, two open problems related to this notion are introduced.
Linear and weakly nonlinear instabilities in thermosolutal rotating convection of a Casson fluid, incorporating the effects of helical forcing, are investigated. The governing equations, expressed in non-dimensional form, are solved by employing the normal mode method. We have shown the effect of various key parameters on convective regions and presented them graphically. The parameter regimes corresponding to the onset of stationary and oscillatory instabilities are systematically delineated. The effect of different key parameters on linear theory is obtained. The Taylor number, helical force parameter, and solute Rayleigh number have a stabilizing effect, whereas the Lewis number and Casson parameter have a destabilizing effect on the system. Within the framework of weakly nonlinear analysis, an amplitude equation is derived using the method of multiple scales. The amplitude equation is solved numerically to calculate the convective amplitude. Using the Nusselt and Sherwood numbers, the heat and mass transfer are analyzed.
We construct three new families of asymmetric quantum MDS codes from nested Hermitian self-orthogonal generalized Reed-Solomon and extended generalized Reed-Solomon codes over Fq2. The construction is developed in three settings: affine partitions of Fq2, projective norm partitions of Fq2*, and extended affine configurations obtained by adjoining the point at infinity. In each case, the Hermitian orthogonality conditions are reduced to explicit linear systems over Fq, whose solvability follows from structured moment identities and Vandermonde-type arguments. This yields nested classical MDS codes satisfying the Hermitian dual-containment condition required in the Hermitian construction of asymmetric quantum codes. As a consequence, we obtain three explicit families of asymmetric quantum MDS codes with fully determined lengths, dimensions, and asymmetric distances dz and dx. Our results show that affine and projective partition techniques provide a natural and effective framework for constructing optimal asymmetric quantum codes with flexible parameters.
Understanding the coupled dynamics of groundwater flow and salinity transport is essential for the sustainable management of aquifer systems, particularly in irrigated and semi-arid regions where evaporation, recharge variability, and groundwater abstraction strongly influence hydrogeological regimes. In multilayer porous media, groundwater-level fluctuations and salt migration processes are closely interconnected, since hydraulic gradients control solute transport while salinity variations may affect flow behaviour through density-related mechanisms. In this study, a nonlinear mathematical model is developed to describe groundwater-level evolution and salt transport within a two-layer porous medium consisting of a phreatic layer and an underlying confined aquifer. The model accounts for filtration processes, interlayer hydraulic exchange, density-dependent effects, and external forcing factors including surface recharge, evaporation, and pumping. For numerical implementation, the governing equations are discretized using a finite-difference scheme with central spatial approximations and an implicit Crank-Nicolson-type temporal formulation. A hybrid second-order time approximation is introduced for the main-layer equation to improve numerical smoothness and stability. The resulting tridiagonal algebraic systems are solved using the Thomas algorithm within an iterative quasi-linearization framework, ensuring both computational efficiency and numerical robustness. Simulation results reveal a clear difference in the dynamical behaviour of the two layers. The phreatic aquifer exhibits rapid and high-amplitude responses to external forcing, whereas the confined aquifer demonstrates slower and smoother hydraulic and geochemical adjustments. Sensitivity analysis further identifies the filtration coefficient, transmissivity, porosity, density-related parameters, surface flux, and pumping intensity as the dominant factors governing groundwater dynamics and salinity redistribution. The proposed modelling framework provides a reliable tool for analysing coupled groundwater-salinity processes and offers a scientifically grounded basis for groundwater monitoring, salinization risk assessment, and sustainable aquifer management.
Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang-Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang-Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results.
This paper investigates the optimal dynamic policies of time-inhomogeneous unreliable multi-server queueing systems with multiple customer sources and differentiated maintenance speeds. Under the criterion of global revenue optimality, we first elaborate the existence of bias-optimal policies and rigorously prove the existence of optimal time-inhomogeneous multi-threshold policies. We further derive two sufficient conditions to solve the monotonicity problem of the optimal time-inhomogeneous multi-threshold policies. Finally, to reduce the computational complexity of deriving optimal policies under the global optimization objective, we propose a heuristic algorithm based on the above theoretical results. The numerical examples not only demonstrate the strong performance of the proposed algorithm, but also indicate that the assumption of the monotonicity of production loss cost with respect to service states is no longer valid when the preset thresholds are differentiated by customer types.
Consider a unital & lowast;-algebra A defined over the complex field C. In this work, we establish that a mapping, referred to as a nonlinear mixed left bi-skew Jordan and right Jordan n-derivation, reduces to an additive & lowast;-derivation under certain conditions. As applications, we further investigate special classes of unital & lowast;-algebras, namely, prime & lowast;-algebras and factor von Neumann algebras using our main result.
This paper focuses on constructing four novel multiquadric (MQ) quasi-interpolation operators. We conduct a comprehensive analysis of the essential properties of the proposed operators and further derive rigorous optimal upper and lower bounds for the approximation error. Numerical experiments are performed to verify the theoretical results, and the numerical outcomes are in excellent agreement with our theoretical analysis.
This paper investigates the problem of stability analysis for Takagi-Sugeno fuzzy systems with time-varying delays. By integrating an augmented delay-dependent Lyapunov-Krasovskii functional (LKF) structure, a refined LKF based on auxiliary function-based integral inequalities, and utilizing a linear switching method, this paper proposes less conservative stability criteria that effectively enhance fuzzy membership characteristics. The proposed stability criteria are formulated in the framework of linear matrix inequalities. Through three numerical examples, the effectiveness and superiority of the proposed approach are demonstrated by achieving significantly improved maximum delay bounds compared to the existing literature.
We propose various hybrid predictive systems to forecast the Bitcoin next-day price. In particular, we combine the decomposition methods based on signal processing techniques including maximum overlap discrete wavelet transform (MODWT), empirical wavelet transform (EWT), empirical mode decomposition (EMD), and variational mode decomposition (VMD) for feature extraction from original price series. Then, the extracted features are fed to the machine learning models for training and forecasting. We implemented five machine learning models, including regression Gaussian process (RGP), support vector regression (SVR), k-nearest neighbors algorithm (kNN), regression trees (RT), and feedforward neural networks (FFNN). The grey wolf optimization (GWO) algorithm is employed for hyperparameter optimization of the machine learning models. The root mean squared error (RMSE) is used for the evaluation and comparison of 20 hybrid predictive systems. The simulation results show that the RGP-GWO-VMD hybrid predictive system achieved the lowest forecasting error. In addition, RGP-GWO yielded on average the lowest forecasting error across all of the machine learning systems. Furthermore, among signal decomposition methods, the lowest forecasting error is generally achieved under the EWT. Hence, we presented the best results in forecasting Bitcoin prices from 20 hybrid prediction systems to serve as the baseline for future work and to guide traders, investors, and portfolio managers.
