This work established synchronization criteria for master-slave inertial neural networks with leakage time-varying delays and proportional delays, The solution employed a direct analysis method based on parameterized system solutions. The derived synchronization conditions consisted of only a few simple inequalities, which were easy to solve.Based on the adopted approach, a novel class of synchronization controllers was designed for proportional delays without constructing any complex functionals. Using the proposed method, leakage delays could be transformed into their maximum absolute values, enabling the derivation of delay-dependent conditions without any intricate treatment of leakage delays. Furthermore, it was noteworthy that this paper presented the first investigation into this problem using the proposed method, and the technique employed was novel. Finally, numerical simulations were provided to verify the effectiveness of the proposed method.

Alzheimer’s disease (AD) is a progressive neurodegenerative disorder that imposes a substantial burden on families and healthcare systems. Mild cognitive impairment (MCI), as an intermediate stage between normal aging and AD, can be further divided into progressive MCI (pMCI) and stable MCI (sMCI) based on follow-up outcomes. Unlike the marked differences observed between cognitively normal (CN) individuals and AD patients, sMCI and pMCI share highly similar characteristics, making early identification of pMCI extremely challenging. Although deep learning methods based on structural magnetic resonance imaging (sMRI) have advanced AD classification, research on predicting MCI progression remains limited due to the high similarity between sMCI and pMCI as well as the substantial cost of prospectively collecting longitudinal data. Accurate early identification of pMCI is essential for timely intervention, slowing disease progression, and reducing healthcare costs. Therefore, this study focused on the early identification of progressive MCI. To address this, we proposed a novel vision Transformer framework, the multi-scale multi-domain frequency-aware vision Transformer (MMF-ViT), which employs a multi-scale cross-domain fusion (MSCDF) module to enable deep interaction between spatial and frequency domain features, thereby enhancing the modeling of fine-grained brain structural variations. The multi-scale frequency encoder (MSFE) and multi-scale context encoder (MSCE) were designed to extract and fuse frequency and spatial information, effectively improving classification performance. Experimental results on the ADNI dataset demonstrate that MMF-ViT achieves an accuracy of 72.84% and an AUC of 72.99% for sMCI versus pMCI classification, significantly outperforming mainstream 2D and 3D models. In AD vs. CN classification, MMF-ViT also achieves an accuracy of 85.59%, highlighting its strong feature representation capability and practical potential.

This paper examines the controllability of the second-order evolution problems in Banach spaces in the presence of a nonlinear term depending on both the solution and its first derivative, and of a time-dependent linear term. The first goal of the paper is to introduce a definition of controllability for such problems that considers not only the solution but also its derivative at the final point using the same control function. Subsequently, the paper addresses the second goal: Finding conditions that guarantee the solvability of the controllability problem. The main statements of the paper are proved by the combination of Schauder fixed point theorem, approximate solvability, and weak topology. Using the method of approximate solvability allows us to avoid any compactness restrictions, and the results are therefore proved under non restrictive conditions imposed on the fundamental operator as well as on the right-hand side.

Overlapping and non-overlapping domain decomposition methods are proposed for the physics and equality constrained neural networks (PECANN) to solve the Helmholtz equation. A coarse component is introduced using a small neural network defined on the whole domain with carefully designed loss functions. This coarse component supplies both function values and normal derivatives on the subdomain interfaces to the local solvers, ensuring the scalability of the algorithms; the number of outer iterations remains nearly constant as the number of subdomains increases. Numerical experiments conducted with a wide range of wavenumbers over both standard and enlarged domains demonstrate the efficiency and scalability of the proposed algorithms.

In this paper, we employed the Bernstein method to prove some Liouville-type theorems of the equation $\Delta_{p_{1}, \cdots, p_{r}} v+f(v)=0 \text {. Here, } \Delta_{p_{1}, \cdots, p_{r}} v:=\operatorname{div}\left(\sum_{i=1}^{r}|\nabla v|^{p_{i}-2} \nabla v\right)$. This could be regarded as a natural generalization of the p-Laplacian and the (p,q)-Laplacian. As applications, we derived Liouville-type theorems of positive solutions to some generalized static Fisher-KPP equation, Allen- Cahn equation, static Newell-Whitehead equation, and Lichnerowicz equation.

The main aims of this study are the introduction of Pell coefficient polynomials and their numerical treatment of the first-order hyperbolic partial differential equations. Our suggested numerical algorithm will be derived from the utilization of some novel formulas of the Pell coefficient polynomials, along with the application of the spectral tau method. For the proposed expansion, we investigate the convergence and error estimations in detail. The presented numerical results indicate that the suggested numerical method is accurate, converges exponentially, and is computationally efficient.

This paper presents a classification of real matrix representations of Rota-Baxter operators on the real Lie algebra so(3). We obtained all non-isomorphic classical Rota-Baxter operators of weight 0 up to orthogonal similarity, as well as special Rota-Baxter operators (multiplicative and pseudo-Rota-Baxter operators) of weights 0 and 1. For weight 0, we found three canonical symmetric matrix forms that solve the classical Yang-Baxter equation and used them to construct explicit left-symmetric algebra structures. Interestingly, no non-trivial multiplicative Rota–Baxter operators exist on so(3) for weights 0 or 1. Pseudo-Rota-Baxter operators exhibit a rich structure: for weight 1, we found two families of symmetric matrices, while for weight 0, there were five families parameterized by continuous parameters g₁₁ ∈ [0, 1] and g₂₂ ∈ [¹/₂, 1]. These findings contribute to the theoretical exploration of Rota-Baxter operators on real orthogonal Lie algebras by presenting explicit 3×3 matrix solutions, which offer valuable tools for their practical implementation in robotic mechanisms.

D. Suyama and H. Terao established an exact basis construction for the derivation modules of the cone over the Shi arrangements utilizing Bernoulli polynomials. In this paper, building on the above basis, we introduce an explicit basis construction for a class of Free arrangements that lie between the cone of Linial arrangements and Shi arrangements.

Pathological β-band oscillations (13–35 Hz) in the basal ganglia (BG) are strongly associated with Parkinson’s disease (PD). Recent evidence shows that subpopulations of external globus pallidus (GPe) neurons exhibit distinct responses to pathological conditions, and that their inhibitory feedback to the striatum strongly shape BG dynamics, features often overlooked in conventional models. To address this, we developed an extended BG network using a modified Hodgkin–Huxley framework, incorporating two GPe subclasses, arkypallidal (TA) and prototypical (TI), along with striatal medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs). Simulations revealed that mutual inhibition within the GPe drives TI neurons from tonic firing into β-bursting, retrogradely suppressing striatal activity through the GPe–FSI–MSN loop and disrupting direct/indirect pathway balance. We further show that GPe-TA projections exert strong inhibitory control over striatal populations, and that reducing MSN M-current reproduces β oscillations that propagate downstream. Blocking D2 MSN → GPe-TI and GPe-TI → GPe-TA synapses restores normal TI firing. Our results emphasize the role of GPe heterogeneity in pathological oscillations and suggest circuit-level therapeutic strategies for PD.

In the paper, autonomous and nonautonomous predator-prey models with nonlinear harvesting and Beddington-DeAngelis functional response were proposed. The mathematical goal was to explore the evolution process of specific bifurcation dynamics, the existence, and attractiveness of positive periodic solutions. The ecological objective was to ascertain the population growth coexistence modes and their underlying driving mechanisms from a specific perspective of dynamic evolution. Regarding the autonomous predator-prey model, mathematical theoretical work has investigated the existence and local stability of all equilibrium points, as well as the occurrence of specific bifurcation dynamics. Regarding the nonautonomous predator-prey model, the boundedness of all solutions, the possibility and global attractiveness of a positive periodic solution were theoretically derived in detail. The numerical simulation work not only verified the feasibility of the theoretical derivation work, but also dynamically showed that the autonomous model had transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation, while the nonautonomous model had attractive periodic solutions. It was worth emphasizing that predator and prey had steady state constant growth coexistence mode and steady state periodic oscillation growth coexistence mode. It must also be pointed out that their intrinsic driving mechanisms were mainly the specific bifurcation dynamics evolution mechanism in autonomous model and seasonal disturbance of key ecological environment parameters in the nonautonomous model. In summary, it was expected that these research results would contribute to the rapid development of nonlinear dynamics in predator-prey models.

Flow polytopes are fundamental objects in algebraic combinatorics. In this paper, we study the enumeration of lattice points in flow polytopes associated with (a₁,a₂)-caracol graphs on n + 2 vertices. Our main result establishes a closed-form expression for the number of lattice points by constructing an explicit combinatorial bijection between Dyck paths and the integer lattice points of the two-parameter family of polytopes (a1,a2)-$\mathrm{Car}_{n+1}$, using pseudo-ladder diagrams together with vector partition techniques. When a₂ = 1, the lattice point sequence of caracol polytopes coincides with the OEIS sequence A126216 (The On-Line Encyclopedia of Integer Sequences), which enumerates Schröder paths of semilength n with exactly k peaks. Furthermore, we establish a bijection between Schröder paths and the integer lattice points of the two-parameter family of polytopes (a1,a2)-$\mathrm{Car}_{n+1}$. All bijections are implemented as explicit algorithms in Python, with the complete source code provided in the appendix to ensure reproducibility.

This article aims to study the fixed/predefined-time control problem of a social network- based delayed interconnected system with a discontinuous interconnection. First, unlike the fractional power function, hyperbolic tangent function and logistic function, a particular exponential function with an indefinite coefficient is utilized to establish fixed/predefined-time stability criteria for discontinuous delayed differential equations based on delayed differential inclusion. The settling time of fixed-time stability is estimated, and the estimation formula is independent of the system’s initial states. The Lyapunov energy function method in this article extends the existing fixed/predefined time stability to the case of indefinite derivatives. Second, taking time-varying coefficients, discontinuity, and the time-delay effect, a social network-based interconnected model is established. With the help of the established fixed/predefined-time theorems and the design of the state feedback control schemes, the fixed/predefined-time stabilization is implemented on the social network-based delayed interconnected system with discontinuity. Finally, a numerical example is given to verify the effectiveness of the fixed/predefined-time control. Numerical simulation shows that, under the state feedback control scheme, the social network-based delayed interconnected system with two subsystems is stabilized in a fixed time at zero within 0.69 seconds. Under the predefined time control scheme, the stabilization at zero for the predefined time can be ensured within any set predefined time T_p = 0.25. It is of practical significance to study the social network-based delayed interconnected system and its fixed/predefined-time control for the rapid formation of stable relationships and the implementation of accurate social governance.

It is proved in this paper that if G is a $\mathcal{G}$-topological group and {K_i : i ∈ ω} is a family of generalized open subsets containing the identity element e in G satisfying K²_i+1 ⊂ K_i and K^-1_i = K_i for every i ∈ ω, then G/H is metrizable where H = ∩_i∈ω K_i. Let (G, τ) be a G-topological group satisfying for every e ∈ U ∈ τ that there is e ∈ O ∈ τ such that O² ⊂ U. Then, we obtain that 1) if H is generalized κ-narrow and cl_G H = G, then G is also generalized κ-narrow; 2) AB is generalized κ-narrow in G provided that A and B are generalized κ-narrow in G. Finally, we consider coset spaces. It is shown that 3) for a subgroup H of G, if H and the generalized quotient space G/H have countable generalized pseudocharacter, then G also has countable generalized pseudocharacter; 4) for a subgroup H, if H is the generalized connected component containing e in G, G/H is generalized totally disconnected; 5) if H is a generalized closed subgroup and generalized totally disconnected, then G is also generalized totally disconnected when G/H is generalized totally disconnected.

For $\alpha>-\frac{1}{2}$, the Laguerre differential operator is defined as

For sufficiently good function f, the maximal functions associated with heat and Poisson semigroups are defined by where $\left\{T_{t}\right\}_{t>0}$ is the heat semigroup {e^{−tL_α}}_{t>0} or Poisson semigroup $\left\{e^{-t L_{\alpha}}\right\}_{t>0}$ related to the Laguerre differential operator L_α. In this paper, we first established a T1 criterion for the boundedness of the γ-Laguerre-Calderón-Zygmund operator on $B M O_{L_{\alpha}}^{\beta}((0, \infty))(0 \leq \beta \leq 1)$ spaces related to the Laguerre differential operator L_α. As applications, using this T1 criterion, we proved the boundedness on $B M O_{L_{\alpha}}^{\beta}((0, \infty))(0 \leq \beta \leq 1)$ of the maximal operators for semigroups related to the Laguerre differential operator L_α.

The fractional diffusion equation involving the fractional Laplacian is used to govern fractional random walk dynamics on network, which allowing long-range displacements. This paper develops a high accuracy numerical method for the computation of nonlinear fractional diffusion equation. The main idea is to approximate the spatial domain with a spectral Galerkin method based on Fourier-like basis functions, and then to discretize time by the general linear methods which contains Runge-Kutta methods, multistep methods, and many new classes of methods. For (k,l)-algebraically stable general linear methods with general stage order p, the nonlinear term satisfies the locally Lipschitz condition, and the proposed method is proved to be well-posed, stable, and convergent with order p in time. Moreover, an optimal spatial error estimate is established, whose convergence rate is independent of the fractional parameter α. Finally, several numerical experiments are presented to verify and support the theoretical results.

The spread of infectious diseases is profoundly influenced by spatial heterogeneity and the availability of medical resources. While reaction-diffusion epidemic models have been extensively studied, there has been little research on SIR models that incorporate a spatially heterogeneous standard incidence rate and a saturated treatment function, which is crucial for modeling the limited capacity of health care systems. To address this, we proposed a novel diffusive SIR epidemic model in a heterogeneous environment. Methodologically, we defined the basic reproduction number R₀ and employed Lyapunov functions, the theory of monotone dynamical systems, and asymptotic analysis to investigate the dynamics. Our key results showed that if R₀ < 1, the disease-free equilibrium is globally asymptotically stable, implying epidemic extinction. If R₀ > 1, the disease becomes uniformly persistent, and an endemic equilibrium exists. Furthermore, we derived the asymptotic profiles of the endemic equilibrium as the diffusion rates of susceptible or infected populations approached zero. Numerical simulations not only validated our theoretical findings but also demonstrated that increasing medical resources or reducing spatial heterogeneity can effectively lower the infection peak and help control the disease. These results provide theoretical guidance for designing effective public health policies.

The Cahn-Hilliard equation plays a central role in modeling phase separation processes in complex systems, including alloys, polymers, and biological materials. Numerical schemes for this equation must balance efficiency, stability, and accuracy in order to capture the rich dynamics of interfacial evolution. In this work, we developed a new second-order predictor–corrector scheme within the scalar auxiliary variable (SAV) framework, combined with Crank–Nicolson (CN) time discretization. The proposed method is linear, uniquely solvable, and unconditionally energy stable, while also providing rigorous error estimates. Computational experiments demonstrated that the new scheme not only maintains second-order temporal accuracy for relatively large time steps, but also yields smaller numerical errors compared to standard SAV-CN methods. These results highlight both the theoretical advantages and practical potential of the predictor–corrector SAV approach for advancing accurate and efficient simulations of phase-field models in science and engineering.

In the hot-rolled strip steel production process, the finishing entry temperature (FET) is directly related to the mechanical properties, microstructural uniformity, and surface quality of the steel, while also having a significant impact on energy consumption and carbon emissions. Traditional temperature measurement and prediction methods each have their limitations, such as large measurement errors, high computational complexity, or overfitting issues. To address these challenges, this paper proposes a finishing entry temperature-physics-informed neural network (FET-PINN) method that integrates rough delivery temperature (RDT) data with thermodynamic equations. First, by leveraging the advantage that the temperature in the RDT region more closely approximates the true billet temperature, an initial prediction of the FET was obtained via a FET-PINN model in conjunction with thermodynamic equations. Subsequently, to account for model errors, the fusion weight was calculated using a nonlinear least squares method, and a weighted averaging approach was employed to fuse this predicted value with the temperature computed from instrumentation measurements, thereby achieving a more accurate temperature estimation. Finally, considering the effect of FET on the subsequent rolling force, the paper evaluated the model comprehensively by comparing the predicted rolling force with the actual rolling force using the coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as evaluation metrics. Experimental results demonstrated that the proposed method enhances the accuracy of temperature prediction and provides effective technical support for temperature control in hot rolling processes.

We utilize a fluid kinetic hybrid approach to analyze dust acoustic wave propagation in collisionless, unmagnetized dusty plasmas, specifically investigating how linear Landau damping effects in the ion population affect weakly nonlinear and weakly dispersive wave behavior. An electron-depleted plasma is considered, consisting of a cold fluid of negatively charged dust particles and two types of ions at different temperatures, modelled by a kappa-type distribution. Anticipating nonlinear solitary waves, a reductive perturbation technique is employed, leading to a nonlinear partial differential equation for the electrostatic potential in the form of a modified Korteweg–de Vries (mKdV) equation, featuring an additional term to account for linear Landau damping of the ions. The solitary wave’s amplitude is found to decay with time. A parametric analysis is carried out of the impact of the plasma configuration on the Landau damping rate under the influence of this latter (Landau damping-related) term. The results of this work are highlighted in space plasma, such as that around Enceladus and Saturn’s E ring, where the occurrence of Landau damping in combination with a nonthermal ion distribution may affect wave propagation significantly.

This paper presents a numerically stable, time-accurate algorithm for simulating the gradient flow associated with the Modica–Mortola functional with a uniformly spaced multi-well potential. The scheme uses operator splitting; the nonlinear component is updated analytically, while the linear part is advanced by a Fourier spectral discretization. The method is unconditionally stable, preserves pointwise boundedness independently of the time step size, and attains spectral accuracy in space and first-order accuracy in time. We provide a theoretical analysis establishing unconditional stability and boundedness, and present comprehensive numerical experiments that demonstrate the accuracy and robustness of the proposed approach.

Remote sensing images exhibit significant spatial geometric characteristics for ground objects such as buildings and roads, while targets within scenes show enormous scale variations, posing challenges to semantic segmentation algorithms’ spatial structure modeling capabilities and cross-scale information processing abilities. Traditional methods lack specialized modeling mechanisms for spatial geometric features and suffer from information loss in multi-scale feature fusion. This paper proposes the SC-Net network, addressing these issues through three key technological innovations. First, we designed a feature attention layer where the spatial attention module captures spatial geometric patterns through directional feature decomposition, and the multi-scale attention module preserves feature information at different scales through adaptive pooling strategies. Second, we constructed a three-branch fusion transformer that employs cross-window attention and nine-group feature key-value pair interactions to achieve collaborative modeling of spatial, multi-scale, and global features. Finally, the multi- branch cascaded decoder enhances segmentation boundary accuracy through hierarchical feature fusion strategies. Comprehensive experiments on three standard remote sensing datasets validated the method’s superiority. SC-Net achieved 63.04% mean intersection over union (MIOU) on Wuhan dense labeling dataset (WHDLD), 71.57% on Potsdam dataset, and 81.57% on Vaihingen dataset, outperforming state- of-the-art methods such as AerialFormer and SERNet by 0.67–2.12% MIOU. The method particularly demonstrated outstanding performance in scenarios with complex spatial structures and dense multi-scale targets, providing an effective solution for precise remote sensing image interpretation.

An absence seizure is a common neurological disorder primarily associated with abnormal interactions between the corticothalamic network and the basal ganglia. In order to better understand how the basal ganglia contributes to absence seizure regulation, we use an improved mean field model of the basal ganglia-corticothalamo (BGCT) by introducing a direct projection from the glutamatergic mediated subthalamic nucleus to the striatum (STN-D). The results indicate that enhancing the excitatory coupling strength of the STN-D pathway significantly suppresses spike-wave discharges (SWDs) by increasing striatal activation levels, which promotes the transition from the pathological state to either simple oscillations or low firing state. We propose a new stimulation paradigm, namely a four-phase pulse stimulation (FPS), which sequentially delivers four pulses to the striatum (D), thus targeting the cortical excitatory neurons (EPN), specific relay nuclei (SRN), STN, and D. The results indicate that FPS can successfully replace the original inputs to the D and effectively control absence seizures by adjusting the anodal pulse amplitudes (A₁,A₂, and A₃), which correspond to the excitatory inputs to the D from SRN-D, EPN-D, and SRN-D. These findings offer new insights into understanding the pathophysiology of an absence seizure and its precise therapeutic interventions.

This paper studies the optimal portfolio decisions of participants in defined contribution (DC) pension plans who are able to invest their wealth in transnational securities. More specifically, pension participants can allocate their investments across cash, bonds, domestic stocks, foreign stocks, inflation-indexed instruments, and exchange rate futures. Furthermore, we assume that pension managers face ambiguity regarding the distribution of foreign asset prices. In this context, by employing dynamic programming and the “relative entropy penalty” method, the paper derives robust optimal portfolio strategies for DC pension plan participants, accompanied by a verification theorem. Additionally, we explore two specific scenarios: the optimal investment strategy for pension managers under ambiguity neutrality, and the utility loss incurred by ambiguity-averse fund managers who misapply the optimal investment strategy. Our analysis is illustrated through numerical examples.

The ability to discriminate highly similar memories depends critically on pattern separation mediated by the dentate gyrus (DG). Although intrinsic neural mechanisms have been extensively studied, the influence of external input patterns on this process is often overlooked. Here, we established a biologically plausible DG model, subjected it to input pattern pairs with varying degrees of overlap, and examined the firing properties of granule cells (GCs) as output patterns. Based on the analysis of population coding, we observed that as the overlap between input pairs decreased, both the separation distance and orthogonalization level increased, indicating enhanced separation performance. Subsequently, from the perspective of rate coding, we computed the mean firing rate of individual GC to paired inputs and statistically analyzed the distributions of mean firing rates and their pairwise differences across GCs. Our results showed that these firing rate metrics unaffected by variations in input overlap. However, the Pearson correlation coefficient and mutual information between GC ensembles were significantly influenced, with both measures decreasing as input overlap is reduced. We also found that high-overlap inputs (> 70%) induced substantial firing rate variability in individual GC, which predominantly manifested as rate remapping. Furthermore, clustering analysis based on time-windowed firing rates demonstrated that pattern separation does not alter the structural characteristics of GCs, with similar cluster configurations emerging across different input overlap conditions. Together, these findings provided a detailed characterization of GC firing properties during pattern separation.

Riemannian cubics are critical points of the total squared norm of the accelerations of the curves on Riemannian manifolds with given end-points and end-velocities. Riemannian cubic splines are C² track sums of Riemannian cubics. Determining Riemannian cubics with given boundary data is equivalent to solving fourth-order ordinary differential equations with boundary conditions, while finding Riemannian cubic splines is tantamount to solving boundary and interior value problems, which are both hard in practice. The present paper proposes Riemannian gradient-based methods to tackle the former problem by taking advantage of the variational principle and the shooting method. The core idea is to add a number of junctions and associated velocities between given boundary points and to adjust such junctions and associated velocities according to a variational principle. Based on the obtained Riemannian cubics, Riemannian cubic splines are determined by constructing piecewise Riemannian cubics of class C² at interior points. The effectiveness of the proposed method is assessed by numerical experiments on a unit sphere.

This article discusses the issue of delay-dependent stability in generalized neural networks (GNNs). First, a suitable Lyapunov-Krasovskii functional (LKF), including more state information on time delays, was constructed, effectively reducing the system’s conservatism. Second, a novel stability condition was established by utilizing the suitable LKF and the matrix-valued cubic polynomials to determine the negative definite conditions. Finally, the experimental simulation results were validated using three typical numerical examples. The experimental results demonstrated the efficiency and merits of our proposed approach compared with the existing methods.

This paper focuses on the robust data-driven load frequency control (LFC) of an interconnected power system involving Markovian jump parameters from damaged data by unknown noise. Firstly, due to the changes in system structure, the LFC model for an interconnected power system involving Markovian jump parameters is described. The vehicle-to-grid technique is also applied to regulate the power system frequency by employing the electric vehicles as a new frequency regulation loop in this model. Secondly, a data-driven control method is used to stabilize the Markovian jump power system (MJPS). Drawing on the damaged data corrupted by unknown noise, two robust stability conditions for the MJPS are formulated, corresponding to the energy-bound approach and the instantaneous-bound approach, respectively. Then, the control gains of the system are obtained by the data-based linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed methods is verified by applying them to a two-area interconnected power system with the participation of electric vehicles.

To address the slow convergence and sensitivity to initial values of the traditional Levenberg-Marquardt (LM) algorithm in 3D point cloud conical surface fitting-issues caused by ill- conditioned Hessian matrices-this paper developed a preconditioned Landweber iterative framework for nonlinear least-squares optimization. A residual model based on point-to-cone geometric distances was constructed, the analytical Jacobian was derived, and a spectral preconditioning strategy was introduced. Theoretical analysis showed that the preconditioner effectively reduced the condition number of the normal matrix, thereby improving numerical stability and accelerating practical convergence. A relaxation-factor rule was further derived to balance stability and efficiency. Experiments on synthetic and industrial datasets demonstrated that, compared with the Levenberg- Marquard(LM) algorithm, the proposed method reduced iteration counts by 51.9%, decreased root mean square error (RMSE) by 98%, and shortened computation time by 73%. It also maintained robust performance under high-noise and non-uniform sampling conditions, providing an efficient and reliable tool for accurate conical surface fitting in industrial inspection and reverse engineering.

Classification of imbalanced data streams in nonstationary environments poses a significant challenge in machine learning. Ensemble learning has demonstrated efficacy in managing imbalanced data streams and concept drift. However, most existing methods develop different strategies for each aspect, overlooking their relationships and interactions, which hinders the expected performance of these strategies. To address this issue, an adaptive dual dynamic ensemble selection (AD-DES) method was proposed for classifying imbalanced data streams with concept drift. First, an adaptive equalization resampling (AER) strategy was proposed to obtain balanced data chunks, which can help to reduce the risk of overfitting or insufficient sampling caused by excessive data imbalance. Following that, the data chunk obtained by the AER strategy was stored to balance the subsequent ones. Second, a dual dynamic ensemble selection (D-DES) strategy was introduced to perform two rounds of selection in the classifier pool to obtain the optimal ensemble model. Finally, an adaptive drift detector in AD-DES was integrated, which is beneficial for the model to adjust to newly emerging concepts in nonstationary environments. The research findings demonstrated that AD-DES outshines 9 comparison algorithms in terms of classification precision and robustness across 10 synthetic datasets and 5 real-world datasets featuring diverse forms of concept drift.

The purpose of this paper was to develop a unified combinatorial framework for fault localization in heterogeneous software systems, where parameters may have different numbers of levels. Specifically, we investigated mixed-level detecting arrays (MDAs) on graphs, extending the classical detecting array model to accommodate non-uniform factor structures. In this paper, we established an optimality criterion that minimizes the number of required test cases and analyzes the structural and combinatorial properties of optimal MDAs on graphs. Furthermore, several constructive methods were proposed to generate optimal arrays, and existence results were derived that achieve the theoretical lower bounds. The findings enhance the theoretical understanding of detecting arrays in graph-based settings and provide practical guidelines for designing cost-efficient and fault-sensitive test suites in complex, heterogeneous software systems.

With the widespread application of location-based services, how to effectively publish trajectories while preserving users’ privacy has become a critical challenge. Existing privacy-preserving trajectory publishing methods often face issues such as missing in synthetic trajectories, low data utility, and privacy leakage of users’ social relationships due to trajectory correlation. To address these issues, a differentially private trajectory publishing method based on feature extraction and trajectory correlation (DP-FETC) is proposed in this paper. The method is composed of two synergistic core algorithms. First, a trajectory synthesis algorithm (SynFE) employs adaptive grid discretization to extract key statistical features-including weighted location, origin-destination (OD), and length distributions-to generate high-fidelity synthetic trajectories that maintain high data utility. Second, to mitigate the risk of social relationship disclosure, an innovative correlated trajectory protection algorithm (PreOD) identifies highly correlated trajectories using a novel metric based on stay duration at points of interest. It then applies a targeted perturbation exclusively to the OD points of these high-risk trajectories. This strategy effectively obscures social links while minimizing the impact on overall data quality. Experimental results on two real-world datasets validate that the proposed method has good data utility while providing robust privacy guarantees.

Alzheimer’s disease (AD) is an age-related neurodegenerative disorder that is difficult to diagnose early. Traditional methods can only confirm the diagnosis when symptoms are evident, but by that time, brain damage is irreversible. Recent research has found that changes in brain activity patterns occur early in AD. Using brain imaging and computational modeling techniques, we can hopefully detect these changes before the onset of symptoms, enabling early intervention. In this paper, we constructed a neurovascular coupling (NVC) whole-brain dynamic model by integrating brain structural data with biophysical modeling methods, aiming to explore the association between dynamical parameters and biomarkers of AD and to reveal their relationship with the overall brain function and network dynamic changes. First, the model simulates properly the resting-state functional connectivity (FC) at various stages of AD development; second, the strength of circulatory connectivity and NVC parameters generated by the brain simulation may be some potential new indicators for the early diagnosis of AD; and finally, the predictive ability of the indicator is quantified using the area under the curve (AUC) values of the receiver operating characteristic (ROC) curves, which suggests a dual strategy for the early diagnosis of biomarkers. These new indicators not only deepen our understanding of the mechanisms of disease progression but also provide an important theoretical basis and technical support for the formulation of early intervention strategies and the development of novel therapeutic approaches.

As the cost of data labeling continues to escalate, research on feature selection for a partially labeled multiset-valued decision information system (p-MSVDIS) has emerged as a core challenge in the field of data mining. Information entropy, as an uncertainty measurement tool, can be used for feature selection via global equivalence relations. However, it fails to capture features within local data regions. Furthermore, in partially labeled scenarios, its limitations in dealing with missing labels cause poor accuracy in feature selection. In contrast, local conditional entropy can accurately characterize the discriminative ability of features in local regions by quantifying the information of the dataset. To address the problem of feature selection in a p-MSVDIS, this paper proposed two algorithms for feature selection in a p-MSVDIS. First, we utilized the Hellinger distance in a p-MSVDIS to define the tolerance classes of different attributes. Second, we introduced local conditional entropy and designed two feature selection algorithms for a p-MSVDIS with predicted labels. Finally, comparative experimental results demonstrated that the proposed algorithms significantly improved classification performance and reduced redundant features in partially labeled data scenarios.

This paper addresses the common challenges of multi-source nonlinear disturbances and parameter uncertainties in traditional electro-hydraulic servo systems by proposing an enhanced sliding mode control method based on a neural network adaptive observer. First, a nonlinear mathematical model of the electro-hydraulic system was established based on the structure and working principle of the valve-controlled hydraulic cylinder. Second, by leveraging the strong nonlinear approximation capability of radial basis function (RBF) neural networks, the nonlinear terms in the system were approximated online and compensated in real time. Next, an adaptive state observer utilizing RBF neural networks was developed to precisely estimate the difficult-to-measure states within the hydraulic system. The state estimates from the observer were integrated with sliding mode control to design the system control law. Additionally, a low-pass filter was introduced to smooth the control law, improving the smoothness of the controller’s output and the overall system stability. Finally, the bounded stability of the closed-loop system was proven by constructing a Lyapunov function. Simulation results demonstrate that under various reference signal inputs and parameter abrupt change scenarios, the designed controller exhibits faster convergence and superior robustness compared to traditional nonlinear controllers. Its average tracking error is reduced by 27.51%–90.2% relative to the intelligent PID controller and by 14.55%–68.82% relative to the adaptive sliding mode controller (ASMC). It exhibits notable improvements in control precision, dynamic response velocity, and disturbance rejection performance, thereby offering an efficient approach to addressing nonlinear control challenges in electro-hydraulic servo systems.

In this paper, we study parametric quasilinear elliptic equations driven by the double phase operator, where the right-hand side consists of a singular term and a sublinear term. By combining a new Hopf’s Lemma with truncation techniques and an abstract critical point theorem, we establish the existence of three bounded positive solutions and provide an explicit upper bound for the parameter.

The hippocampus in the brain encodes memorized information as long-term memory through the plasticity of the CA3–CA1 synaptic network, thereby forming stable engrams. Based on the hippocampal CA3–CA1 synaptic network model, memory engrams are encoded as trajectories within a stable heteroclinic network, where saddle points signify different information blocks. This stable heteroclinic network is further refined into a knowledge network that illustrates the relationships between information blocks, defining the retrieval efficiency, capability, and integration quality of the network among these blocks. In this paper, we examined the impact of the local and global topological properties of the knowledge network on retrieval efficiency, capability, and integration quality. Numerical results indicated that the retrieval efficiency between any two information blocks in the knowledge network decreased with the out-degree of the cue’s corresponding node, increased with the in-degree of the target’s corresponding node, and was negatively correlated with the distance between node pairs. The retrieval capability of any information block was determined by the out-degree centrality and out-closeness of the corresponding node, while the integration quality of the knowledge network was influenced by the information blocks corresponding to nodes with higher degree centrality or betweenness centrality, and was negatively correlated with the average path length of the network.

In this paper, we study a delayed almost periodic differential neoclassical growth model with nonlinear depreciation rate. Relying on the theory of almost periodic functions and by making use of the Lyapunov functional approach, some novel criteria for guaranteeing the existence and global exponential stability of positive almost periodic solutions of the studied model are established. Besides, the correctness of the theoretical results is validated by a numerical example. The established theoretical findings supplement and improve the conclusions in the literature.

In this paper, a novel type of 3-parameter generalized quaternions (3-PGQs) is introduced, constructed from higher order Leonardo numbers and referred to as the higher order Leonardo 3- parameter generalized quaternions (shortly, higher order Leonardo 3-PGQs). Several fundamental properties of these quaternions are examined, including their recurrence relations, a Binet-type formula, and both generating and exponential generating functions. In addition, the obtained identities show that the higher order Leonardo 3-PGQs can be expressed in closed form in terms of Fibonacci numbers, Fibonacci generalized quaternions, and higher order Leonardo numbers.

Algebraic graph theory explores the relationship between abstract algebra and graph theory. It uses algebraic concepts to define the structures of graphs and investigates how graph theory can characterize algebraic properties. There has been considerable scholarly interest in the connection between group-theoretic and graph-theoretic properties, especially concerning the role of symmetry in linking these two areas. This research contributes to the ongoing development of equitable graphs by introducing the concept of an equitable graph of Type II on finite groups which is defined on a group G, where two vertices x and y with different orders are adjacent if their orders are differ by at most the minimum of their orders (|o(x) − o(y)| ≤ min{o(x),o(y)}) or if one of them is the identity element. We investigate the properties of this graph for specific classes of groups, including cyclic, dihedral, and dicyclic groups. Furthermore, we derive general formulas for some degree-based indices of the equitable graph of Type II across various group families. Finally, we explore the relationship between the isomorphism of equitable graphs and the associated groups.

We considered a nonlinear elliptic boundary value problem driven by the variable (anisotropic) (p,q)-Laplacian with Robin boundary condition and a superlinear reaction which does not satisfy the Ambrosetti-Rabinowitz condition. Using critical point theory, truncation and comparison techniques and critical groups, we showed the existence of five nontrivial smooth solutions all with sign information and ordered.

In this paper, we define the B_σ-type grand Morrey spaces and establish the extrapolation theorem on the B_σ-type grand Morrey spaces. In the process of proving the theorem, we find that the predual spaces of these spaces are H_σ-block spaces and obtain the boundedness of the Hardy–Littlewood maximal operator on the predual spaces. By the extrapolation theory, the boundedness of the Calderón–Zygmund operator and commutators on the nonhomogeneous B_σ-type grand Morrey space is also obtained. In particular, the classical bounded mean oscillation (BMO) spaces are characterized by establishing the John–Nirenberg inequality on the nonhomogeneous B_σ type grand Morrey space.

In this paper, we propose a new formulation of the artificial-viscosity penalty finite element methods for solving the mathematical model of non-Newtonian blood flow, treating blood as a pseudo- plastic fluid obeying the power-law Navier-Stokes equations. The proposed schemes are based on the artificial-viscosity mixed finite element method in the spatial direction, combined with a backward-Euler scheme and penalty-projection scheme for temporal discretization. It is rigorously derived the stability and error estimates for the fully discrete schemes. Numerical examples are presented to validate the theoretical ideas and to demonstrate the effectiveness of our proposed strategies. The comparison shows that the artificial viscosity penalty-projection scheme demands less central processing unit time, as well as a slightly higher-order precision. Finally, the penalty-projection finite element scheme is successfully applied to study the influence of blood viscosity on hemodynamics in aortic aneurysms. Moreover, numerical investigations for flow patterns based on patient-specific geometric models of cerebral aneurysms through segmentation of magnetic resonance imaging have been performed. The present study clearly illustrates the importance of taking the non-Newtonian properties of blood flow within aneurysms into account when studying the risk of aneurysm rupture.

This study investigates the prespecified-/finite-time stability for a class of memristor-based BAM neural networks (MBAMNNs) with discontinuity. By C-regular Lyapunov approach stability theories, some criteria are established to ensure that the switched MBAMNNs can achieve prespecified- /finite-time stabilization, which are independent of the initial states. Finally, some numerical examples demonstrate the effectiveness of the proposed criteria. This work provides a theoretical foundation for precise temporal control in complex neural networks.

Goursat’s lemma gives a good method to describe subgroups of the direct product of two groups G₁,G₂, and to determine whether subgroups of G₁ ×G₂ are direct products. However, the usual symmetric version of Goursat’s lemma is difficult to describe subgroups of a direct product of a finite number of groups. Fortunately, the asymmetric version of Goursat’s lemma provide a new method to solve the difficulty. In this paper, we used additional conditions π_i(H) =G_i, the injectivity ρ_i, and H_i22 =H_i12 ∩ H_i21 for 1 ≤ i ≤ 3 to give some related results about groups (resp.R-modules,R-algebras (rings as corollary)), and then we gave the answer on whether a R-submodule M of M₁ × ...×M_n has the form $M=\widetilde{N} \times N_{n}$ and M =N₁ × ...×N_n. Further, we extended similar conclusions to R-algebras (rings as corollary).

The primary focus of this study was to analyze the convergence and superconvergence properties of an ultra-weak discontinuous Galerkin (UWDG) method for nonlinear second-order initial-value problems (IVPs) for ordinary differential equations (ODEs) of the form u^′′ + (g(x,u))^′ = f(x,u), x ∈ [a,b], subject to u(a) = α and u^′(a) = β. By carefully choosing suitable numerical fluxes and employing a special projection, we established optimal error estimates in the L²-norm. The order of convergence was proved to be p + 1, when utilizing piecewise polynomials of degree at most p. We further proved that the UWDG solution was superconvergent of order p + 2 for p ≥ 2 toward a special projection of the exact solution. Additionally, we proved that the p-degree UWDG solution and its derivative were O(h^2p) superconvergent at the end of each step. Our proofs were valid for arbitrary uniform or non-uniform partitions of the domain using piecewise polynomials with degree p ≥ 2. Finally, several numerical examples were provided to validate all theoretical results. It is worth noting that the proposed UWDG method offers a significant advantage for second-order differential equations, as it can be applied directly without introducing auxiliary variables or reformulating the equation as a first-order system. This advantage reduces memory and computational costs.

This research focused on solving fractional Sturm-Liouville equations subject to mixed boundary conditions and a combination of instantaneous and non-instantaneous impulses. Through the use of variational methods, the existence of both solutions and multiple solutions for the aforementioned problem was established under assumptions that were weaker than the classical superlinear Ambrosetti-Rabinowitz type growth requirement. Finally, the examples demonstrated the validity of the paper’s results.

In this paper, we investigated a class of nonlinear triply coupled systems of fractional Langevin equations subject to closed boundary conditions. The existence of solutions to the proposed boundary value problem was first established by applying Krasnoselskii’s fixed point theorem. Furthermore, the uniqueness of the solution was obtained via the Banach contraction mapping principle. To demonstrate the effectiveness of the theoretical results, illustrative examples are provided.

This manuscript researches the optimal portfolio of the defined contribution (DC) pension plan, comprising a stock index and cash within a dynamic model that incorporates uncertainty regarding climate change. The global temperature is supposed to have an impact on the stock index price, with the probability distribution of the global temperature considered uncertain. To address this uncertainty, we apply Girsanov’s theorem for measure transformation. The optimal investment strategy under climate uncertainty and stochastic interest rates is derived in closed form. We further demonstrate that climate uncertainty can result in specific losses in returns. We discover through numerical analysis that the investment in the stock index is especially sensitive to climate uncertainty.

In this article, we consider a class of critical Schrödinger-Poisson type systems on the first Heisenberg group. We demonstrate that the system admits a positive ground state solution by utilizing the concentration compactness principle and critical point theory. The system has double critical nonlinearity on the Heisenberg group, which is the novelty and peculiarity of this paper. To some extent, we extend some previous results.

The 2D/3D interaction systems consisting of the incompressible Navier-Stokes equations in a bounded domain and the classical full von Kármán shallow shell equation were investigated in this paper, where the fluid and the shell were coupled via both the transverse and longitudinal displacements. The global existence of weak solutions in 2D/3D was proved by using a special choice of basis functions for the related elliptic equations, which allows one to tackle the delicate estimates for the interaction between the fluid and the shell. Moreover, the uniqueness of the weak solution in 2D was also established via a localization technique.

In this study, we established several relations between generalized (weak) vector controlled inequalities of Minty and Stampacchia type and the associated multi-cost models. To this end, we introduced the updated concepts of preconvexity and (strictly) strong convexity for functionals governed by controlled simple integrals and a mean-value-type result. Also, we introduced the corresponding multiobjective extremization models. The theoretical notions and the main results were justified by suitable numerical examples that were non-trivial.

In this paper, we study the following quasilinear Schrödinger equation with a parameter: $-\varepsilon^{2} \Delta u+V(x) u-\varepsilon^{2} \kappa \beta \Delta\left(|u|^{2 \beta}\right)|u|^{2 \beta-2} u=|u|^{q-2} u+|u|^{(2 \beta) 2^{*}-2} u \text { in } \mathbb{R}^{N}$, where $N \geqslant 3, \beta>\frac{1}{2}, 4 \beta<q<(2 \beta) 2^{*}$, κ is a constant, and V : $\mathbb{R}^{N} \rightarrow \mathbb{R}$ satisfies the classical global assumption. By using a change of variable, we obtain the existence, multiplicity, and concentration behavior. We will see that the existence of solutions depends heavily on the parameter β.

This article investigates a type of hyperbolic equation of the fractional Kirchhoff with viscoelastic and logarithmic nonlinear terms subject to homogeneous Dirichlet-boundary: 

where $[u]_{s}$ is the Gagliardo semi-norm of u, $(-\Delta)^{s}$ is the fractional Laplacian with $s \in(0,1), 2<2 \gamma<h<2_{s}^{*}$ $u_{0}$ and $u_{1}$ are the initial functions, and $\Omega \subset \mathbb{R}^{N}$ is a bounded domain with a smooth boundary. First, the global existence of solutions is established by combining the Galerkin method with the potential well theory. Subsequently, the finite-time blow-up of solutions is derived via the concavity method and a series of peculiar inequalities.

The shape parameter is crucial for radial basis functions (RBF) interpolation accuracy. Fixed global parameters often fail with complex data, whereas variable shape parameters improve flexibility by adjusting each basis function dynamically. To address the issue that variable shape parameter selection in the inverse multiple quadratic radial basis function (IMQ-RBF) interpolation is influenced by multiple factors, we proposed a hybrid prediction model based on the sparrow search algorithm (SSA) combining a multilayer perceptron and random forest (SSA-MLP-RF), which maps local geometric features of data points to the corresponding shape parameters. First, a dataset was constructed from scattered points, including the shape parameter values and 17 local features, to accumulate influencing factors. Subsequently, outlier removal, variance inflation factor analysis, XGBoost feature average gain, and mutual information methods were applied to perform feature selection, identifying seven key features. Finally, SSA was employed to optimize the hyperparameters of the MLP and RF, and a weighted combination model was constructed to achieve adaptive selection of shape parameters. Based on the test set results, the ablation experiments verified that the proposed SSA-MLP-RF hybrid model achieved significant performance improvement. Compared with several classical metaheuristic algorithms (particle swarm optimizatio, genetic algorithm, whale optimization algorithm, and blood-sucking leech optimizer), the SSA-MLP-RF model demonstrated the best predictive accuracy for the deformation shape parameter, achieving an R² of 0.9203, with MAE, RMSE, MAPE, and NMSE values of 0.0391, 0.0499, 3.8201%, and 0.0797, respectively, and a Rényi entropy of 0.1200. The findings validated the effectiveness and rationality of the proposed model, providing a reliable approach for the adaptive selection of shape parameters in RBF interpolation.

The image encryption technology is an important means to ensure network digital data transmission security. To improve the security and encryption computational efficiency, we proposed a novel bit-level image encryption algorithm that integrates hyper-chaotic systems with DNA encoding operations. First, we generated high-quality pseudo-random sequences through K-means clustering, which were applied to hyper-chaotic sequences; second, we implemented multi-level scrambling at both bit-plane and bit-level; finally, we employed dynamic DNA encoding rules combined with bidirectional diffusion. Experimental results demonstrated that the proposed algorithm achieves a large key space (approximately²⁵⁶), high information entropy (close to 7.9899), and strong resistance to differential attacks (NPCR = 99.61%, UACI ≈ 33.46%). Our results also showed that the histograms of the encrypted images are even, and the correlation coefficients approach 0. Moreover, the proposed algorithm can effectively resist the chosen plaintext attack, brute force attack, clipping attack, salt and pepper noise attack, etc.

In this paper, we study the singular Hopf bifurcation in a class of singularly perturbed systems with delay. The key condition for the generation of a singular Hopf bifurcation involves the existence of eigenvalues of the singular pure imaginary part. The necessary and sufficient conditions for the generation of a singular Hopf bifurcation are discussed in a class of general nonlinear ( n, 1)- fast-slow systems with delay on slow variables (n ≥ 1).

This study investigated biodiversity changes in host-virus coevolution, focusing on a system incorporating a resistance-growth trade-off. We derived the basic reproduction number for the host system and identified conditions for host-virus coexistence. Numerical simulations revealed that the resistance-growth trade-off may influence diversity patterns, leading to both monotonic and unimodal dynamics. Additionally, the resistance-growth trade-off may drive transitions between stable equilibria and periodic solutions under specific mutation rates, cause shifts in dominant species in both algal and viral communities, and trigger a hydra effect under specific dilution rates. Our results offer insights into the mechanisms driving biodiversity fluctuations in host-virus coevolutionary dynamics.

This paper addressed the problem of highway traffic flow multivariate time series forecasting with the challenges of variate heterogeneity. To improve forecast performance without a heavy computational burden in large-scale networks, we innovatively introduced variational mode decomposition and established a decomposition-assisted multi-tasking deep learning forecasting architecture. To improve variate-specific pattern learning and mitigate pattern mixing, we proposed a novel temporal-frequency pure convolutional neural network incorporating discrete Fourier transform, deepwise convolution, and batchwise feedforward neural network. To verify the proposed model, we conducted a case study on a regional network located in Jiangsu, China. Results demonstrate strong forecast performance and efficient computation. The proposed model offers suitability toward highway operators for large-scale engineering deployment and better facilitates their managerial actions.