Focusing on delayed inertial bidirectional associative memory (BAM) neural networks, this paper addressed their exponential input-to-state stability (EIS). Rather than relying on conventional reduced-order methods and Lyapunov-Krasovskii functionals (LKFs), we established EIS via the characteristics method by introducing three sufficient conditions cast as linear scalar inequalities. Three illustrative numerical examples, backed by simulation results, confirmed the theoretical conclusions.

Real-time multi-person pose estimation suffers from inter-instance occlusion and severe scale variations. To resolve these bottlenecks, we present focal-dynamic context (FDC)-pose, an efficient single-stage architecture tailored for crowded scenes. The framework incorporates three sequential innovations: 1) a cascaded pyramid network-focal omni-dimensional dynamic convolution (CPN-FocalOD) backbone combining context modulation with omni-dimensional dynamic filtering to disentangle overlapping silhouettes; 2) a cross-scale fusion network featuring content-aware upsampling (DySample) to suppress quantization errors and preserve distal joint details; and 3) a minimum point distance intersection over union (MPDIoU) regression loss enforcing point-level geometric constraints to eliminate occlusion-induced localization jitter. Evaluations on the common objects in context (COCO) 2017 dataset demonstrate that FDC-pose yields absolute gains of 3.4% in AP, 3.0% in AP₅₀, and 4.2% in the strict AP₇₅ metric relative to the baseline. Parallel evaluations on the CrowdPose dataset show that our framework presents a prominent robustness gain, yielding an absolute improvement of 4.5% in AP.

We propose a lowest equal-order stabilized mixed finite element method for an elliptic optimal control problem with box control constraints. First, optimality conditions are derived based on the variational principle, transforming the original problem into a coupled system consisting of the state equation, the costate equation, and a variational inequality. The state and costate variables are approximated using the lowest equal-order mixed finite element pair, and the control variable is approximated by piecewise constant functions. A stabilization term for velocity projection based on the difference between two local Gauss integrations is introduced to circumvent the Ladyzhenskaya– Babuška–Brezzi (LBB) condition. Subsequently, a priori error estimates for the state, costate, and control variables are derived. Finally, 2D and 3D numerical experiments are performed to validate the theoretical analysis and the efficiency of the method.

Chu and Zhang (2014) found several remarkable transformations for well-poised hypergeometric series. One of them is employed in this paper to investigate infinite series of convergence rate “−1/4” involving generalized harmonic numbers. Numerous closed-form formulae are established that explicitly express a large class of series in terms of π, ln 2, and the Hurwitz zeta function. Thirteen transformations are derived from harmonic series into nine seemingly simpler multifold k-sums, whose exact values are still not determined.

In this paper, we investigated the formation and optimal control of spatial patterns in a plankton ecosystem. Based on a reaction-diffusion model with time delay and cross-diffusion, linear stability analysis revealed the conditions for Turing instability and Hopf oscillations, providing a dynamical explanation for plankton patchiness and periodic red tide outbreaks. A networked reaction- diffusion model was further constructed to account for ecological connectivity. Through global sensitivity analysis, the most influential parameters were identified, and node-dependent control as well as time-dependent optimal control was implemented. Extensive numerical simulations verified that when the network topology and average connectivity varied separately or simultaneously, the proposed control strategy could effectively steer the system toward the target spatial pattern, maintaining the average relative error below 8%. Moreover, the control method could significantly reduce system deviations in the short term, thereby effectively mitigating the adverse effects of time delay. This work provides a quantitative framework for understanding and regulating spatial heterogeneity in plankton ecosystems, with potential implications for red tide management.

This study focused on the modified F-expansion method and the $\frac{G^{\prime}}{b G^{\prime}+G+a}$-expansion method to find exact solutions to the (1 + 1)−dimensional Kaup–Kupershmidt (KK) equation, an important nonlinear model that incorporates both dispersive effects and higher-order nonlinearity. By applying these analytical techniques, several classes of exact solutions, including periodic, bright, and singular soliton solutions, were successfully obtained. The graphical representation of these solutions was evaluated by creating two-dimensional, three-dimensional, and contour plots for each solution type to explore the wide range of dynamic behaviors associated with these solutions. Additionally, modulation instability for the equation was determined with linear stability analysis. Observing the outcomes, it is clearly evident that the suggested methods are significant mathematical tools to solve nonlinear partial differential equations arising in various areas of applied mathematics and physics. The novelty of the work lies in the combined application of the $\frac{G^{\prime}}{b G^{\prime}+G+a}$-expansion and modified F-expansion methods to the KK equation, providing broader classes of exact solutions and deeper insight into the equation’s nonlinear dynamics beyond earlier studies in the literature.

The Sombor index (SO) and harmonic-arithmetic index (HA) stand as two well-established topological indices constructed based on vertex degrees. The difference between the SO index and HA index of a graph G is introduced as

where d(u) stands for the degree of vertex u ∈ V(G). In the present work, we determined the trees, unicyclic graphs, and bicyclic graphs that achieved extremal SO − HA values, characterized the chemical graphs with extremal SO−HA values, and obtained the trees with fixed maximum degree minimizing the SO − HA index. Furthermore, by performing QSPR analysis on octane isomers, we observed that the SO − HA index possessed favorable physicochemical predictability.

This paper focused on the coefficients of prescriptiveness in the field of contextual optimization, which measure the efficacy of a prescriptive analytics method in leveraging contextual information for prescribing data-driven decisions. We identified two key deficiencies of the original coefficient of prescriptiveness proposed in the literature. First, this coefficient is problem-dependent, i.e., it lacks a universal scale: its asymptotic upper bound (less than or equal to 1) varies across problems, making cross-problem comparisons infeasible. Second, this coefficient is data-dependent, i.e., its calculation is contingent on specific training and test datasets, limiting its generalizability. To address the two deficiencies, we proposed two novel coefficients of prescriptiveness in this paper: (i) the adjusted coefficient of prescriptiveness, which replaces the deterministic perfect-foresight benchmark in the original coefficient with the full-information optimum; and (ii) the expected coefficient of prescriptiveness, derived by taking the expectation over the sampling distribution of the training dataset. Meanwhile, we developed their empirical estimators for practical applications. Moreover, rigorous theoretical analysis established two fundamental properties of these coefficients of prescriptiveness. Through extensive numerical experiments based on the newsvendor problem, we validated the effectiveness of our proposed coefficients of prescriptiveness in addressing the identified deficiencies. By refining the evaluation framework for prescriptive analytics, this work advances the generalizability and applicability of the coefficients of prescriptiveness.

Modern computational intelligence and data science applications frequently operate on complex, non-Euclidean domains. Applying differential privacy (DP) to these structures requires mechanisms that respect their underlying geometry. Instance-adaptive mechanisms in DP improve utility over global worst-case bounds but often require heavy-tailed noise, leading to numerical instability and unbounded variance. We introduced a geometric framework that lifted sensitivity analysis to the tangent bundle of a Riemannian manifold. The proposed directional local sensitivity operator captured maximal directional derivatives along minimizing geodesics, enabling our operator normed adaptive Laplace mechanism (ON–ALM). By enforcing a β-log-Lipschitz stability condition on the regularized sensitivity, noise was precisely calibrated via directional operator norms. Under (ε, δ)-DP, extracting a typical set allowed the use of light-tailed Laplace noise, achieving strictly bounded variance, improved numerical stability, and high utility for geometric and directional queries.

Rolling bearing fault diagnosis under practical compute constraints and long time series remains challenging in industrial settings. This study presented a compact same-source multi-view framework that combines a multi-scale gated Mamba sequence branch, a residual network with a convolutional block attention module (ResNet-CBAM) image branch, and lightweight low-rank cross-view fusion. Continuous wavelet transform (CWT) images were used as the default image view in the main experiments because they provide the most suitably maintained same-condition representation among the evaluated image views. Under a unified three-seed protocol, the proposed model reached 99.20% on Case Western Reserve University (CWRU) and 99.61% on Southeast University (SEU) in same-condition diagnosis, and attained the strongest cross-condition results within the internal comparison, with 27.39% on CWRU and 30.43% on SEU. The model used about 5.46×10⁵ parameters and 5.64 × 10⁸ multiply–accumulate operations (MACs). These results indicate a balanced trade-off between relative cross-condition generalization and computational cost, while also showing that broader operating-condition diversity, industrial validation, and deployment-oriented central processing unit (CPU) or edge profiling remain necessary.

The aim of this paper was to discuss the boundedness of commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand Herz-Morrey spaces with two variable exponents η(·), q(·). We proved that the fractional Hardy and Hardy-Littlewood-Pólya operators are bounded on grand variable Herz-Morrey spaces, where the symbols of the commutators belong to Lipschitz spaces.

Underwater image quality is inevitably degraded by the selective absorption and scattering of light, which introduce severe blurring and abrupt high-frequency noise. These interferences obscure latent structural information and make robust restoration a significant challenge. To address this, we present MWGANet, a multi-stage dynamic wavelet-gated aggregation network designed to decouple complex underwater noise distributions caused by environmental disturbances. The core of our architecture was a parallel strategy with three pathways tailored for feature extraction across domains. Specifically, the Gated Wavelet Transform Branch (GWTB) isolated noise spikes in the frequency domain to effectively safeguard critical structural textures from corruption. Our adaptive reuse branch (ARB) incorporated a dynamic aggregation block at multiple scales to facilitate feature flow across layers while adaptively filtering redundant information through learnable gating mechanisms. Furthermore, the dilated context branch (DCB) expanded the model’s receptive field via graduated dilation rates to enhance the perception of diverse object priors. Extensive evaluations confirmed that MWGANet achieves a superior balance between denoising fidelity and computational efficiency. In particular, the model maintained a high-fidelity output on the EUVP dataset, achieving a PSNR of 31.06 dB even under severe synthetic additive white Gaussian noise (AWGN) (σ = 50). Such robustness and efficiency indicated that MWGANet has the potential to serve as a practical real-time solution for resource-constrained autonomous underwater vehicle (AUV) platforms.

We study existence and nonexistence of positive solutions for nonlinear fractional boundary value problems of order $\alpha+3$, where $\alpha \in(m-1, m]$ with $m \geq 3$, governed by the Riemann-Liouville (RL) operator $D_{0+}^{\alpha+3}$. The Green’s function is constructed by pairing the RL semigroup property $D^{3}\left(D_{0+}^{\alpha} u\right)=D_{0+}^{\alpha+3} u$ with a convolution of the RL core $G_{\alpha}$ and a third-order integer bridge, which takes one of two boundary-adapted forms: left-clamped $G_{LC}$ or right-clamped $G_{RC}$. A key structural finding is that left and right convolutions produce fundamentally different boundary condition types, providing selectivity in the Green’s function construction. An explicit closed-form formula for $\mathcal{G}_{L C}=G_{\alpha} * G_{L C}$ is derived via Beta function reduction; $\mathcal{G}_{R C}=G_{\alpha} * G_{R C}$ is evaluated numerically as it consists of incomplete Beta functions. Positivity, monotonicity, and cone estimates for both kernels are established to utilize the Guo-Krasnosel’skii fixed-point theorem to identify parameter intervals for existence and nonexistence. Hybrid pairings and their structural implications are discussed; a worked example illustrates the results.

Infrared small target detection faces numerous challenges due to weak target features and complex backgrounds. Existing methods have drawbacks such as mixed background and target signals, imbalanced local and global feature modeling, and insufficient learning of direction-specific context. To address these issues, this paper proposes a dual-branch network based on background-suppression sparse graph-enhanced Mamba (BSG-Mamba). We build this network on a U-shaped encoder-decoder architecture. We design a background-suppression branch to initially separate the target from the background and combine it with a target-enhancing gating (TEG) mechanism to enhance target features. On this basis, we effectively capture non-local feature correlations in small targets by embedding a sparse graph encoder (SG-encoder), compensating for the shortcomings of traditional convolutional segmentation. At the deep encoder position, it constructs a Mamba module with multi-state space model (SSM) decoupling and adaptive fusion. We configure independent SSM parameters for four-direction scanning and introduce learnable fusion weights to achieve unified modeling of long-range dependencies and direction-specific features. Experimental results on the NUAA-SIRST and NUDT-SIRST datasets show that the core detection metrics of the model outperform existing state-of-the-art (SOTA) methods, achieving detection rates of 97.74% and 98.90%, respectively, on the two datasets, while maintaining a lightweight network parameter count and balancing detection accuracy and computational efficiency.

This paper studies a stage-structured two-species amensalism model incorporating fear effects on the inhibited species. Extending the framework of Lei, we introduce a single fear parameter f that simultaneously suppresses adult reproduction and amplifies adult mortality via a saturating Holling-Type II response, ensuring that the total adult mortality rate under fear remains biologically bounded by 2δ₂. We establish a threshold-based dynamic classification in the biologically feasible region governed by a net reproduction number N₀ and a critical threshold f_crit. When N₀ > 1 and 0 ≤ f < f_crit, the coexistence equilibrium is globally asymptotically stable, which can be proved via a Volterra-type logarithmic Lyapunov function; when f ≥ f_crit, the extinction equilibrium is globally asymptotically stable, which can be proved via a linear Lyapunov function. When f_crit > 0, the system undergoes a transcritical bifurcation at f =f_crit, verified by Sotomayor’s theorem. Hopf bifurcation is ruled out by the decoupled structure of the system, which forces the relevant Jacobian trace to remain strictly negative. Ecologically, reproductive suppression and mortality amplification act as amplifying interactions: the combined extinction threshold is strictly lower than the birth-only threshold, while mortality associated with fear alone may lack a finite threshold entirely owing to the saturation of the Holling-Type II response. This dual-pathway interaction is quantified analytically and confirmed by model-variant numerical comparison. All analytical results are corroborated by numerical simulations.

In this paper, a comprehensive coupled dynamic model was developed for a double-cable mine hoisting system to investigate nonstationary vibration responses induced by rigid-guide imperfections. The spatial motions of the cables in the longitudinal, transverse, and lateral directions were described by nonlinear partial differential equations (PDEs), whereas the cage dynamics and guide-roller interactions were formulated as coupled ordinary differential equations (ODEs). By incorporating time-varying cable lengths and rigid guide-roller contact excitation, the governing equations were transformed into a finite-dimensional ODE system using a normalized spatial coordinate and Galerkin projection. The numerical implementation was verified through modal, time-step, and no-guide-deviation benchmark analyses. Numerical simulations were then conducted to characterize the nonstationary dynamic behavior of the system under guide curvature and verticality deviations, with particular emphasis on tension inconsistency between the suspension strings. The model-based reference deviation amplitudes were further identified, providing a theoretical basis for assessing the influence of guide-structure geometric deviations on hoisting-operation safety.

Pediatric biomarker reference intervals (RIs) are crucial for clinical diagnosis and health assessment, but the establishment of RIs is often limited by issues such as scarce labeled data and the inadaptability of traditional methods to implicit hierarchical data distributions. To overcome these challenges, we proposed a semi-supervised model integrating partial supervised information guidance and hyperbolic space representation for efficient prediction of pediatric biomarker reference intervals. By introducing hyperbolic space exponential mapping, we mapped the preprocessed high- dimensional features from Euclidean space to the hyperbolic space of the Poincaré ball. Leveraging the negative curvature property of hyperbolic space, the model more accurately characterizes the hierarchical distribution patterns of biomarkers. The partially labeled samples guide hyperbolic representation learning through a supervised loss, and the structural information of unlabeled samples guide the reconstruction of unsupervised loss. This enables the collaborative use of a small number of labeled samples and a large number of unlabeled samples, balancing model performance and data collection cost. Analytical and comparative experiments were conducted on pediatric datasets using two biomarkers, validating the proposed method as a proof of concept.

Most existing fuzzy integral transforms rely on non-additive measures and absolute integrability, making them invalid for discontinuous fuzzy signals. In this paper, we developed a unified frequency-domain analysis framework via fuzzy Henstock-Kurzweil (FHK) integrals without measure restrictions. We formulated the bilateral FHK Laplace transform (bi-FHKLT) and elaborated its inherent linkage with the fuzzy Henstock-Kurzweil Fourier transform (FHKFT) over complex domains. Under the FHK integral framework, the fuzzy Dirac delta distribution was constructed to derive the inversion formula of the FHKFT. Rigorous time/frequency domain convolution theorems are established for general discontinuous fuzzy functions. Numerical comparisons on rationally defined and countably discontinuous fuzzy signals demonstrated that the proposed transforms produce well-defined bounded magnitude outputs, whereas classical fuzzy Riemann transforms collapse completely. The constructed system offers an effective frequency analysis tool for fuzzy signals beyond the scope of traditional fuzzy Riemann integral methods.

In this paper, we investigated the energy conservation for the incompressible homogeneous and inhomogeneous Euler equations on a periodic domain of dimensions n = 2,3, enabling for the presence of a vacuum. We established sufficient conditions based on the integrability of the vorticity: If the vorticity belongs to space $L^{p}\left(0, T ; L^{q}\left(\mathbb{T}^{n}\right)\right)$ with the exponents p,q satisfying:

and the density satisfies suitable conditions, then the energy equality holds for almost every t ∈ [0,T]. Our result extended several existing vorticity-based energy conservation criteria by providing a weaker integrability condition on $\nabla \sqrt{\rho} $.

Half-ℓ-sequences as an extension of ℓ-sequences generated by feedback with carry shift registers (FCSRs) possess desirable pseudorandom properties. In this work, we focus on the arithmetic autocorrelation of binary half-ℓ-sequences with connection integers of the form $q=p_{1}^{r} p_{2}^{s}$. For this family of sequences, we establish a tight upper bound on the arithmetic autocorrelation and determine all possible values it can attain, which generalizes earlier results when the connection integer is a prime power. Our statements indicate that such sequences exhibit large arithmetic autocorrelation values yet can also demonstrate almost ideal arithmetic correlations for certain special forms of q. We reveal a profound connection between these values and the class numbers of imaginary quadratic fields. Numerical experiments further validate the theoretical findings.

In this paper, we examine the asymptotic properties of solutions to first-order linear non- homogeneous differential equations with variable delays and variable coefficients. Initially, a unique global solution to the relevant characteristic equation is obtained. Subsequently, the asymptotic prop- erties of the solutions to the delay equation are demonstrated through the utilization of the solution of the characteristic equation. Finally, upon examination of specific cases pertaining to the variable coef- ficients of the delay differential equation, three discrete results are obtained. The findings are expressed as the solution of the characteristic equation. In addition, seven examples are given to demonstrate the hypothesis of the main theorem.

This paper studies a host–commensal model with a multiplicative Allee effect on the host and nonselective harvesting on both species. Exploiting the upper-triangular structure, equilibrium and stability analyses reduce to one-dimensional problems. Three harvesting thresholds corresponding to a fold and two transcritical bifurcations yield a complete classification of at most six equilibria. Global dynamics is determined via asymptotically autonomous systems: The separatrix y =y₁ divides coexistence and extinction basins at low harvesting, and the system collapses to monostability beyond the fold. Numerical simulations verify the three qualitatively distinct dynamical regimes.

This paper focused on the direct data-driven set-point tracking control problem of linear discrete-time systems with input time-delay. First, a tracking error was introduced by constructing an extended state vector through state reconstruction to generate a data-driven model. Second, a data-based tracking controller was designed with the objective of minimizing the L₂ gain from disturbances to the performance output through H_∞ control, thereby reducing the impact of input delay and disturbance and ensuring asymptotic tracking stability. Finally, to validate the effectiveness and practicality of the proposed method, this paper took an autonomous direct current (DC) micro-grid with two distributed generation units as the research object. Through simulation results, the effectiveness of the data-driven method in addressing set-point tracking control issues for time-delay systems was demonstrated.

We introduce a new epidemic framework to model the adoption and abandonment dynamics of users on an online social network (OSN), with special emphasis on the novel compartment pauci-engaged. Pauci-engaged individuals have been exposed to an invitation to an OSN, but remain undecided about joining, thus reflecting real-world hesitation and trial behaviors. Building on the infectious–recovery dynamics studied by Chen, Kong, and Wang, we derive the basic reproduction number R₀ and establish threshold conditions for the stability of both the user-free equilibrium and the user-prevailing equilibrium. Local stability analysis using the Jacobian matrix, together with global stability results based on Lyapunov functions, shows that when the basic reproduction number R₀ < 1, the OSN cannot sustain an engaged user base, while when R₀ > 1, a persistent engagement state emerges. Our findings highlight the pivotal role of the decision-making phase in the growth of the digital platform and offer actionable insights to optimize user recruitment and retention strategies in OSNs.

Language phrases are effective tools for depicting uncertain information and are highly consistent with the cognitive habits and expression needs of decision-makers when they evaluate things using natural language. During the decision-making process, decision-makers can compare the alternative options in pairs to obtain a linguistic judgment matrix. First, the comparative preference relationship among schemes is regarded as a binary relation on the set of decision schemes. The preference relation matrix derived from the linguistic judgment matrix is, in essence, the matrix-based expression of this set relation. From the perspective of relational transitivity, if the transitive closure of this set relation coincides with the preference relation matrix, meaning the relation possesses complete transitivity, the linguistic judgment matrix can be determined to meet the requirement of satisfactory consistency. Second, if decision-makers have logical conflicts in pairwise comparisons, the corresponding linguistic judgment matrix will inevitably fail to satisfy the satisfactory consistency condition. For the precise identification of such logical contradictions, the second-order submatrix derived from the preference relation matrix within the linguistic judgment matrix is amenable to application. This submatrix can represent illogical preference judgments formed by 3 or 4 decision schemes. Therefore, by examining whether there exists an illogical preference structure in the second-order submatrix, we could inversely infer whether the original linguistic judgment matrix possesses satisfactory consistency. We conducted analysis combined with decision cases, confirming the feasibility and application value of this theoretical framework from the perspective of case application.

We study a class of one-dimensional thermoelastic models combining second-gradient effects, both in the mechanical displacement and the thermal component, as dissipation mechanisms. While second-gradient elasticity is always assumed in the mechanical part, three alternative thermal models are considered, involving different combinations of thermal displacement and temperature gradients. For each system, we establish existence and uniqueness of solutions using semigroup theory and analyze their long-time behavior. We show that exponential stability generally fails in most of the cases and that all solutions exhibit polynomial decay toward equilibrium, with rate of order t^−1/2. The decay analysis relies on resolvent-based semigroup techniques and, in a degenerate case, on energy methods. In addition, numerical approximations are investigated for two of the models. A priori error estimates for a fully discrete scheme are derived, and numerical experiments are presented to illustrate the accuracy of the method and to confirm the theoretical decay rates.

Identifying influential nodes in hypergraphs is essential for applications in social network analysis and bioinformatics. Conventional centrality metrics, designed for pairwise interactions, fail to capture the higher-order dependencies inherent to hypergraphs. To address this, we have proposed the HDCN (hypergraph dual-branch convolutional network), a dual-branch convolutional network that fuses local and global higher-order signals. The HDCN adopts two existing centrality measures as complementary feature channels, namely, multi-scale hyper-degree centrality (HD) for local topology and hypergraph distance-based fuzzy centrality (HDF) for higher-order neighborhood aggregation, and proposes a dual-branch convolutional architecture with a fully τ-aligned pairwise ranking objective to fuse them effectively. The two branches are separately encoded by convolutional layers and subsequently fused to yield robust node influence estimates. The task was formulated as a pairwise learning-to-rank problem optimized directly for Kendall’s τ, with ground-truth rankings derived from Monte Carlo susceptible infected recovered (SIR) simulations. Experiments on five real-world hypergraph datasets showed that the HDCN outperforms traditional centrality baselines, ranking first on four of five datasets. On the structurally complex Geometry dataset, the HDCN achieves τ = 0.5253, a 56% relative gain over the strongest traditional baseline (EHDF, τ = 0.3368). the HDCN also surpasses learning-based methods including the hypergraph neural network (HGNN) on all five datasets, confirming the effectiveness of our dual-branch higher-order fusion strategy.

By combining the telescoping method with an algebraic relation, four classes of binomial moments are examined:

Several explicit summation formulae are established with most of them having not appeared previously in the literature except for the first class corresponding to the “+” sign.

The notion of a nonlinear mixed skew Jordan-Lie-type higher derivation on unital *-algebras is introduced, which combines the skew Jordan product with skew Lie-type higher derivations. Under conditions satisfied by prime *-algebras, factor von Neumann algebras, and standard operator algebras, it is proved that every nonlinear mixed skew Jordan-Lie-type higher derivation on a unital *-algebra is an additive higher *-derivation.

This paper proposes a parametric mixture cure model within the accelerated failure time (AFT) framework for interval-censored data with competing risks. The model integrates multinomial logistic regression for the incidence of various event types (including cure) and AFT models for the latency among susceptible individuals. We consider three lifetime distributions (Weibull, lognormal, loglogistic) and develop an expectation-maximization (EM) algorithm for estimation. The large-sample properties of the proposed estimators are established and validated through comprehensive simulations, which show minimal bias, well-aligned standard errors, and coverage probabilities reaching the nominal level. In an empirical application to Lending Club personal loan data, our model, which accounts for default and prepayment as competing risks, reveals distinct covariate mechanisms overlooked by models ignoring competition: Annual income symmetrically “delays default while accelerating prepayment”, while loan amount consistently accelerates only prepayment. Model comparison based on Akaike information criterion (AIC) selects the Weibull distribution as optimal.

In this paper, we define fuzzy dual number matrix equations and investigate the Moore-penrose weak core inverse (MPWC inverse) to solve fuzzy dual number matrix equations. First, we define fuzzy dual number matrix equations based on the properties of fuzzy dual number. Second, we obtain the block structure of the MPWC inverse corresponding to the coefficient matrix of fuzzy dual number matrix equations by characterizing some properties of the MPWC inverse and use it to obtain a strong fuzzy solution of a fuzzy dual number matrix equation. Third, we propose two methods to derive the general strong fuzzy solution of fuzzy dual number matrix equations: one with an algorithm starting from a representation matrix obtained via the MPWC inverse, and the other starting from a representation matrix corresponding to a strong fuzzy solution. Lastly, some numerical examples are presented to illustrate the main results.

This work investigated a Caputo ϑ-fractional iterative integro-differential equation (Caputo ϑ-FIIDE). First, the existence of solutions was established by means of Schauder’s fixed point theorem, and uniqueness was obtained under suitable sufficient conditions. The continuous dependence of solutions on the given data was then analyzed. Furthermore, the Ulam-Hyers stability (the U-H stability) and the Ulam-Hyers-Rassias stability (the U-H-R stability) of the proposed problem were examined. A new illustrative example was presented to demonstrate the applicability of the theoretical results and to validate the developed analysis. Thus, this paper presents novel theoretical results, supported by an illustrative example that highlights the applicability of the proposed approach and contributes to the existing literature. Since the stability analysis of fractional iterative integro-differential equations plays a significant role in both theory and applications, the results obtained here provide a useful framework for future research and stimulate further advances in this area.

Colorectal cancer is one of the leading causes of cancer-related mortality, and both early detection and the removal of adenomatous polyps are effective treatment measures. However, identifying adenomatous polyps remains challenging due to the diverse polyps, boundaries, and intestinal mucosal background. Therefore, we have proposed a boundary-enhanced adenomatous polyp segmentation network with Kalman-mamba (BKMNet), which integrates visual state space mechanisms and Kalman filtering for precise segmentation and identification of adenomatous polyps. Specifically, we adopted a multi-frequency combined attention block to enhance feature representation by focusing on varying channel frequency components. A fast visual state space module extracts multi-level feature maps, the partial channel transformation aggregates the surrounding contextual information, and the structure-aware local-enhanced residual state space module enhances structure awareness. A Kalman-mamba layer aims for long-range dependency modeling. The decoder has a dual attention module with multi-level features, and a refined differential and boundary-enhanced module performs edge detection and global edge feature learning. Results demonstrated that BKMNet outperforms state-of-the-art methods in terms of segmentation accuracy and clinical applicability. This study provides a reliable auxiliary diagnostic tool for supporting clinicians in improving diagnostic efficiency and reducing misdiagnosis rates.

In this paper, we investigated the sensitivity and second-order perturbation expansions for simple generalized eigenvalues of a parameter-dependent analytic complex matrix pair. Our findings extended the perturbation analysis established by Sun (1985), which originally focused on simple eigenvalues. These results provided a theoretical foundation for applying Newton-type methods to generalized inverse eigenvalue problems.

Integrated learning and optimization (ILO), an emerging paradigm for contextual optimization also known as “smart predict-then-optimize” or “end-to-end optimization”, typically presents major challenges for practical applications in the community of operations research and management science (OR/MS). This study developed a general evaluation framework that systematically assesses the difficulty of implementing ILO for contextual optimization problems. It distinguishes between computationally tractable and challenging problems, offering the corresponding exact and approximate solution strategies to obtain the final prescriptions, respectively. Our main contributions are threefold. First, we identified conceptual ambiguities in traditional definitions of parameters and hyperparameters in machine learning (ML) models, proposing new complexity- based definitions that strengthen the theoretical foundations. Second, building on this, we developed optimization frameworks to identify the optimal ML models and prescriptions under sequential learning and optimization (SLO) and ILO, respectively. The ILO evaluation framework was then established, which is structured around several key questions regarding the specific characteristics of the ML model and the downstream optimization problem. Third, we illustrated the applicability of the proposed evaluation framework through a numerical case study on a stochastic binary decision- making problem and provided a cautious discussion of the observed numerical comparison. Moreover, we analyzed and compared the efficacy and efficiency of SLO and ILO. This study provides valuable insights and practical guidance for implementing ILO in solving real-world problems in OR/MS. Furthermore, it enriches the literature on the comparative effectiveness of SLO and ILO.

This study proposes a delay-aware predictive maintenance control framework for multiequipment systems operating under dynamic and uncertain industrial environments. The proposed framework integrates a multilayer neural reliability prediction model, an approximate Bayesian reliability updating mechanism, and a rolling-horizon maintenance optimization model to support maintenance decision-making under delayed and asynchronous industrial information. Unlike conventional predictive maintenance approaches that rely primarily on instantaneous observations or static reliability estimation, the proposed framework explicitly models time-varying communication delays, degradation evolution, imperfect maintenance effects, and dynamic state propagation within a closed-loop maintenance control architecture. The proposed methodology first estimates machine failure probabilities using a multilayer neural network trained on heterogeneous operational and degradation-related variables. The predicted reliability is subsequently refined through approximate Bayesian filtering by integrating historical posterior information and delayed observations. Based on the updated reliability trajectories, a rolling-horizon genetic algorithm determines preventive maintenance schedules while considering maintenance capacity, workforce availability, and operational constraints. The optimization objective minimizes the total expected maintenance cost, including preventive maintenance, corrective maintenance, downtime, and reliability penalty costs. Experimental results demonstrate that the proposed framework provides competitive probability prediction performance while achieving superior maintenance cost reduction and improvements in reliability under delayed operating conditions.

This paper addresses the null-controllability of a non-autonomous degenerate parabolic equation in divergence form, considering a diffusion coefficient a that degenerates in space and varies arbitrarily in time, thus generalizing the previously studied separable case in [1, 2]. Boundary conditions of Dirichlet or Robin type are imposed at the degeneracy point, while the control acts in the interior of the domain. After establishing well-posedness, we prove null-controllability by deriving new Carleman estimates for the associated non-homogeneous adjoint problem.

In this work, we were interested in approximating the solutions of nonlinear systems with singular Jacobian matrices. It is well known that the Newton iterative method loses its quadratic convergence when the Jacobian matrix of the nonlinear operator is singular in a neighborhood of the solution. We introduced a semilocal convergence analysis for a modification of this iterative method that overcomes this drawback. We performed several dynamical experiments to illustrate the effects of singular Jacobian matrices and solved different nonlinear systems, thereby corroborating the theoretical results obtained.

This paper proposes a new multi-term normalized time-fractional diffusion equation. The proposed model extends the normalized time-fractional derivative to include several fractional orders. It keeps the normalization property and uses weighting coefficients to control short- and long-term memory effects. An implicit finite difference method is developed, and the tridiagonal linear system is solved by the Thomas algorithm. The proposed algorithm is unconditionally stable and converges with a temporal accuracy of 2 − α_max and second-order spatial accuracy. Numerical convergence tests agree with the theoretical results. Numerical examples show that the fractional orders and weighting coefficients control the diffusion rate, memory strength, and frequency-dependent decrease. Additionally, the computational results show that the proposed model is more flexible than the single-term normalized equation for describing anomalous diffusion with multiple memory scales. Finally, a simple two-dimensional extension of the proposed model is presented. MATLAB codes for both the single-term and multi-term normalized time-fractional diffusion models are provided in the Appendix.

Defect detection in photovoltaic (PV) modules is crucial for long-term reliable operation of solar plants, reducing levelized cost of energy, and preventing safety incidents. Electroluminescence (EL) images suffer from low contrast, complex background noise, and frequent overlapping defects, hindering the balance between detection accuracy and real-time processing speed for current algorithms. To address this, a novel real-time object detector is proposed. First, a convolutional additive self-attention block (CAS-Block) reconstructs the backbone by replacing dot-product with additive similarity, enhancing the response sensitivity to weak defect features in low-contrast images while maintaining linear computational complexity. Second, an efficient dynami-scale intra-feature interaction (EDII) module based on frequency-domain learning employs adaptive spectral filtering to suppress environmental noise interference, such as illumination variations. Finally, a gated cross-scale feature fusion (GCFF) module built on gated linear unit (GLU) uses a dynamic gating mechanism to precisely disentangle feature confusion arising from overlapping defects. Experimental results show that the proposed model achieves a mean average precision (mAP)@0.5 of 93.2% and a detection speed of 104.2 frames per second (FPS), outperforming the state-of-the-art (SOTA) YOLOv12-L and EER- DETR. The method achieves an optimal accuracy–speed trade-off, offering an efficient, cost-effective solution for intelligent inspection of large-scale PV plants.

This paper studies an optimal reinsurance, investment, and prevention problem for an insurer under common shock dependence. The aggregate loss consists of two claim streams with independent claim sizes and dependent claim arrivals driven by a common shock component. The insurer chooses reinsurance, investment, and prevention to maximize the expected utility of terminal wealth, where prevention lowers the arrival intensities at a convex cost. Reinsurance is modeled in a general admissible framework without imposing a specific contract form. Under exponential utility, we derive the Hamilton-Jacobi-Bellman equation and establish a verification theorem. The optimal investment strategy is explicit, the optimal reinsurance policy is shown to be of the excess-of-loss type, and the optimal prevention strategy can be expressed using the inverse marginal cost function. Numerical results further demonstrate the value of prevention and show how prevention effectiveness, prevention cost, and risk aversion affect the optimal strategies.

This paper investigates a predator–prey model incorporating both the fear effect and a Holling type IV functional response with group defense. In this model, the fear effect characterizes the suppression of prey reproduction caused by predator presence, whereas the Holling type IV functional response describes the enhanced group defense of prey at high densities. First, for the non-impulsive system, we analyze the positivity and boundedness of solutions, as well as the existence and local stability of equilibria. Second, when the equilibrium of the uncontrolled system fails to meet ecological management requirements, we introduce unilateral and bilateral state-feedback impulsive control strategies. The existence of order-one periodic solutions is established by the successor function method, and criteria for orbital asymptotic stability are derived using impulsive Floquet theory. Finally, numerical simulations validate the theoretical results, which provide a theoretical basis for designing ecologically balanced impulsive management strategies that suppress pest outbreaks while maintaining predator and prey populations within acceptable ranges.

Accurate skin lesion segmentation remains challenging due to vague boundaries and heavy artifact interference in complex backgrounds. To address these issues, we introduce WMSM-Net, a frequency-space collaborative network built upon the visual state space (Mamba) architecture. WMSM-Net proposes a Wavelet-enhanced Visual State Space Block (W-VSSB) to extract high-frequency boundary details and mitigate edge loss. Concurrently, a Bidirectional Mutual-Feedback Spatial-Channel Attention Bridge (MF-SCAB) was constructed to deliver two-way guidance across spatial and channel dimensions, enhancing the perception of subtle lesions. Feature transitions were further optimized via dynamic gated fusion to suppress background noise. Extensive experiments demonstrated that WMSM-Net achieves state-of-the-art performance, yielding Dice coefficients of 91.01%, 91.08%, and 94.06% for the ISIC 2017, ISIC 2018, and PH2 datasets, respectively. The code is publicly available at https://github.com/fuxinrong2024/WMSM-Net.

Overdispersed count data are common in many applications, where the variance exceeds the mean, and the Poisson model is inadequate. The two-parameter negative binomial (NB2) model addresses this limitation through a dispersion parameter and provides a standard framework for modeling overdispersed counts. In this paper, we evaluated Bayesian credible intervals for the NB2 mean and Bayesian posterior predictive intervals for a single future count and for the mean of a future sample in a controlled one-sample, intercept-only setting. Posterior inference was obtained using weakly informative priors and Hamiltonian Monte Carlo with the No-U-Turn Sampler. The Bayesian intervals were assessed through simulation using operational coverage probability and expected width, and were compared with Wald, MLE-based normal, and parametric bootstrap confidence and prediction intervals. Prior-family sensitivity was examined using calibrated lognormal, Gamma, and log-Student-t priors. Robustness was also evaluated under zero-inflated NB2, structured-zero, and Poisson-lognormal data-generating mechanisms while fitting the NB2 model. Two real-data examples, involving Quine school-absence counts and epilepsy baseline seizure counts, illustrated the practical implementation of the methods.

Different from the classical triangular-structure hyperjerk forms, this work constructed a new five-dimensional (5D) hyperjerk system from a novel perspective and analyzed its dissipativity as well as the stability of the equilibrium point. By employing methods such as Lyapunov exponents, bifurcation diagrams, the 0-1 test, and Poincaré sections, the existence of a hyperchaotic attractor and the rich dynamical behaviors of the system were revealed. Based on normal form theory and symbolic computations, the existence of Hopf bifurcations and the stability of the bifurcation solutions were further investigated, and numerical examples were provided to validate the theoretical findings. By incorporating Lyapunov functions, we designed a suitable nonlinear controller that achieves global asymptotic synchronization of the hyperchaotic system. Simulation results demonstrated that the drive-response system achieves synchronization rapidly. In addition, an electronic circuit design scheme for the 5D hyperchaotic system was presented. The circuit simulation results were in good agreement with the numerical simulations, thereby verifying the physical realizability of the system. Finally, the practical application of the proposed hyperchaotic system in information encryption and decryption was explored. Based on this 5D hyperchaotic hyperjerk system, we developed encryption and decryption algorithms. From the analysis results of multiple metrics, including the correlation coefficient, information entropy, key space, number of pixel change rate, and unified average changing intensity, the proposed algorithm demonstrated favorable confidentiality and robust security performance.