To address the low reduction efficiency and limited classification performance of traditional dominance-based rough sets when the attribute scale expands, this paper introduces a generalized decision combination entropy derived generalized decision classes by integrating attribute dependency and information entropy. This measure reflects attribute importance from multiple perspectives. Based on this measure, attributes are ranked by importance, and a machine learning classifier is used to select an attribute subset with high classification accuracy. Comparative experiments validate the effectiveness of the proposed method.

Firstly, aiming at the problem of  estimation of  causal effects in interval Ⅰtype censored data with unmeasured confounding and treatment noncompliance, we  combined instrumental variables with the generalized exponential proportional hazards model and used the maximum likelihood method to estimate the causal treatment effect among compliers. Secondly, the simulation experiment results verified the effectiveness of the proposed method. Finally, the  proposed method was applied to clinical trial data of the HIP breast cancer screening to verify its effectiveness.

Within the framework of sublinear expectations, for linear processes constructed by m-asymptotically almost negatively associated (m-AANA) random variable sequences as innovations, combined with probabilistic inequalities in sublinear expectation space, the Toeplitz theorem and the Borel-Cantelli lemma, and under the assumptions that the coefficient sequence of the linear process is absolutely summable and that the innovations satisfy a uniform moment condition, we give the strong law of large numbers for this linear process.

In this paper, the artificial boundary method and the optimal control theory are adopted to investigate the forward problem of the semi-infinite degenerate parabolic equation and the inverse problem of determining the source term under additional conditions. First, for the forward problem, the artificial boundary method is used to transform the problem defined on a semi-infinite domain into an equivalent problem on a bounded domain, and  exact boundary conditions at the right boundary are established. Then, the existence and uniqueness of the weak solution are demonstrated through  energy estimates. Second, based on the optimal control theory, the original inverse problem is transformed into an optimal control problem, and the existence of an optimal solution and the necessary conditions it satisfies are proved. Finally, the stability of the optimal solution is proven by using the necessary conditions. This work provides both theoretical analysis and numerical solution support for the forward and inverse problems of such equations.

By using the priori estimates, Lipschitz continuity and squeezing estimates of the high frequency of the solutions, we studied the problems of stability and finiteness of fractal dimension of solutions to the  stochastic convection Brinkman-Forchheimer (CBF) equations driven by colored noise, and obtained the existence of random exponential attractors for these equations.

The structure of Lie higher derivable mappings at the zero point on generalized matrix algebras is investigated. Firstly, using the method of algebraic decomposition, the author proves that every Lie higher derivable mapping at the zero point can be expressed as the sum of a higher derivation and a center-valued mapping. Secondly, as an application, the explicit form of Lie higher derivable mappings at the zero point on triangular algebras is obtained.

A power-type iterative algorithm is proposed for computing the H-spectral radius of nonnegative tensors. By utilizing the directed graph associated with the tensor, the R-linear convergence of the algorithm is established, and sufficient conditions for linear convergence are further derived. The proposed algorithm is applicable to all weakly irreducible nonnegative tensors. Compared with the NQZ algorithm, which is designed for weakly primitive tensors, the proposed method has a broader range of applicability.

Using the weight coefficient method and real analysis techniques, the author considers the  constructing semi-discrete Hilbert-type reverse inequality with  non-homogeneous kernel. It provides sufficient necessary conditions for constructing such inequality and calculation formulas for the best constant factor. Finally, the operator expression for the inequalities and some special cases are presented.

Let F be a functor from the category of finitely presented right R-modules to the category of Abelian groups. If there exists a strongly
 FP-injective left R-module M , then F is called a strongly SFP-injective functor. This paper adopts methods from homological algebra to study and characterize the homological properties of strongly SFP-injective functors. We prove that the class of strongly SFP-injective functors is closed under extensions and direct products, and the class consisting of strongly SFP-injective functors is an injective resolving class.

Let T be a formal triangular matrix ring. First, this paper investigates clean-projective modules over T, and proves that if a left T-module (X,Y)_φ is clean-projective, then X/(Im φ) is a clean-projective left R-module and Y is a clean-projective left S-module. Second, the recollements for clean-derived categories and clean-singularity categories over T are constructed separately.

Firstly,  we  define and study n-torsion pairs in Abelian categories, and let (A,B,C) be a recollement of Abelian categories. Secondly, by using methods such as higher extensions, pushout, and pullback, we prove that an n-torsion pair in A and C can induce an n-torsion pair in B. Conversely, an n-torsion pair in B can also induce an n-torsion pair in A and C.

Using the weight transfer method, we studied the vertex-partition problem for planar graphs without 4,6-cycles, and obtained that the vertex set of a graph G without adjacent 5-cycles could be partitioned into two subsets, so that the derived subgraph of each subset was a forest with maximum degree at most 3. This  improved the conclusion about the existence of  (F₅,F₅)-partition of planar graphs without 4,6-cycles.

Aiming at the problems that the traditional low-rank matrix factorization methods commonly suffered from low computational efficiency, excessive memory consumption, and insufficient decomposition accuracy when handling large-scale data, based on the core theory of CUR decomposition, combined with random sampling and optimization strategies, we proposed two new random low-rank matrix factorization methods: column random factorization and column-row random factorization. By optimizing the algorithmic randomness design, we introduced dedicated iterative optimization strategies, effectively improving the operational deficiencies of traditional algorithms. The comparative experimental results show that, compared with traditional decomposition methods, the two proposed methods have superior computational efficiency, faster convergence speed, and significantly enhanced noise robustness. They effectively refine the technical framework of low-rank decomposition for large-scale data, provide efficient and stable new solution for massive data processing, as well as reliable technical support for engineering applications in related fields such as machine learning and data mining.

Monte Carlo-based ray tracing has been widely adopted in photorealistic rendering due to its physical accuracy, flexibility, and universa
lity. However, existing hardware limitations restrict real-time implementations to low sample-per-pixel rates, where Monte Carlo integration exhibits significant noise under sparse sampling conditions. This paper employs neural network techniques to address the trade-off between quality and performance, effectively resolving noise issues in Monte Carlo ray tracing with low sample counts. The proposed framework incorporates three core innovations: a multi-scale dilated convolution module that  enhances denoising quality by fusing local feature details with global contextual information with minimal parameter overhead; a temporal cross-attention mechanism that improves temporal coherence by adaptively reusing denoised historical frames; and a composite loss function combining reconstruction and temporal consistency terms to strengthen detail preservation and stability. Evaluated on the BMFR benchmark dataset, our method achieved an average 3.7% improvement in peak signal-to-noise ratio (PSNR) and a 23.5% reduction in root mean squared error (RMSE) compared to state-of-the-art approaches while maintaining comparable structure similarity index measure (SSIM) performance. The inference time meets real-time requirements.

Aiming at the prediction challenges caused by the inherent nonlinearity and low signal-to-noise ratio of financial volatility series, we proposed an adaptive gated hybrid model  SCLA-GARCH that fused structural priors with deep learning. The model utilized the generalized autoregressive conditional heteroskedasticity (GARCH)  to capture linear structures, and constructed a parallel CNN-LSTM-Attention network to learn nonlinear patterns in its residuals, which were dynamically fused by an adaptive gating mechanism. Empirical analysis results show  that the prediction error of this model is significantly lower than that of multiple benchmark models, with a maximum reduction of 59% in mean squared error.

Aiming at the problems of target omission in dense scenes and insufficient generalization ability in complex backgrounds for the detection transformer (DETR) series models, we proposed an attention-enhanced Salience DETR model. By embedding a foreground attention mechanism as well as spatial and channel joint attention mechanisms into the Salience DETR model, the model’s ability to extract features of small targets and recognize multiple targets in complex environments was improved. The experimental results on the Common Objects in Context dataset, Vision Meets Drone dataset, and Insects dataset show that the mean average precision of this model is improved  by 1.0 percentage point, 1.2 percentage points, and 2.2 percentage points respectively compared to the Salience Detection Transformer model. The experimental results on a self-collected corn borer dataset show that the model improves  the evaluation metrics for small target recognition  by 2.0 percentage points, verifying the model’s generalization capability. Therefore,  this model enhances detection performance in complex environments and provides a feasible technical solution for small target recognition and specific domain applications.

Aiming at  the problems of high computational complexity, large parameter size, and limited deployability of existing models in the  image recognition tasks of pepper diseases and pests,  we  proposed a lightweight  disease and pest recognition method based on an improved ResNet34. Firstly,  depthwise separable convolution structures were introduced to replace conventional standard convolutions, which significantly reduced model parameter count and computational cost while maintaining feature extraction capability. Secondly, a convolutional block attention mechanism was integrated to enhance the model’s ability to focus on critical region features of lesions from both channel and spatial dimensions, and  improve the discriminative power of feature representations. In order to verify the effectiveness of the proposed method, systematic experiments were conducted on a pepper  disease  and pest dataset as well as the public PlantVillage tomato disease dataset. Experimental results show that the improved model achieves significant improvements in  multiple evaluation metrics, with a recognition accuracy of 98.36%, which is  5.64% higher than  the original ResNet34. In comparative experiments with models such as MobileNetV2, GoogLeNet, AlexNet, VGG16, and ResNet18, the proposed method performs better  in accuracy, precision, recall, and F₁ values. Furthermore, the parameter count of proposed model is  only 2.73 M, and the  model volume is  10.62 MiB, which has good  lightweight characteristics and deployment applicability  while maintaining high recognition accuracy.

Aiming at the problems that portable ultrasound devices suffered from low imaging quality due to hardware constraints, high- and low-quality ultrasound images were difficult to pair, and traditional enhancement methods failed to sufficiently preserve fine details, we proposed a registration-free generative adversarial network for the stable enhancement of unpaired medical ultrasound images. The network was based on the cycle-consistent generative adversarial network, we  designed a maximum  perception  feature extraction  enhancement module to extract  global and local features of images while preserving their spatial structures. 
We constructed  a clustering feature enhancement learning network to strengthen the ability of extracting complex details from the image. Meanwhile, the loss function was optimized by integrating pseudo-label classification loss and multilayer perceptron feature loss. Experimental results on the USenhance 2023 ultrasound image enhancement challenge dataset show that the three core evaluation metrics of the proposed network are significantly superior to those of mainstream and state-of-the-art ultrasound image enhancement methods. The enhanced images exhibit lower noise, with clearer structural, textural, and contour details of organs.

Aiming at the problem that in industrial defect detection, the collection of point cloud was incomplete due to factors such as component damage and environmental interference, structural discrepancies between incomplete and standard point clouds caused outlier correspondences during registration, resulting in a decrease in registration accuracy, we proposed an improved partial point cloud registration network based on point pyramid and maximal cliques. Firstly, we designed incomplete completion module to generate virtual points, the module extracted local and global  features of point cloud through  multi-resolution dynamic graph convolution, and added a point pyramid fractal prediction network to complete missing regions of the point cloud and compensated for the missing  feature information. Secondly, the maximal cliques algorithm was integrated into the registration module to filter incompatible matching pairs, optimizing the matching matrix and pose estimation strategy. The results of  unknown category partial point cloud registration  on the ModelNet40 dataset show that the average absolute errors of rotation and translation of the proposed network are reduced to  0.650 7 and 0.005 9, respectively, effectively improving registration accuracy and robustness of outlier correspondences. The experiment on the ESB dataset further show that the proposed network provides a reliable partial point cloud registration scheme for industrial defect detection.

Addressing the challenge that privacy protection and recognition accuracy are difficult to balance in distributed environments for network intrusion detection, this paper proposes a hybrid neural network model integrating a federated learning architecture. By integrating residual structures, gated recurrent units, and the squeeze-and-excitation channel attention mechanism, the model addresses the problems of insufficient temporal feature mining and lack of weight perception in network traffic. Meanwhile, the synthetic minority over-sampling technique and the label smoothing cross-entropy loss algorithm are utilized to effectively overcome the problem of model performance degradation caused by heterogeneous data distribution across nodes. Experimental results on the CICIDS2017 dataset demonstrate that the model achieves 99.80% in key metrics such as accuracy, precision, and recall, significantly outperforming existing federated learning and classical detection algorithms. These results validate the feasibility of achieving ultra-high precision collaborative defense without sharing raw sensitive data, which not only effectively alleviates the data island dilemma in the field of network security but also provides a reliable technical basis for constructing privacy-preserving intelligent defense systems.

To address the unreliable explicit relationships and consistency deviations among non-missing data objects in incomplete multi-view clustering, we propose a shared latent subspace-guided graph completion and clustering algorithm. Secondly, the learning of each view’s adjacency graph is guided by the subspace self-representation matrix to preserve latent consistency. Then, graph Laplacian regularization is applied to ensure that the view manifold is followed by the completed graph, by which multi-view data complementarity is maintained. Finally, consistency representation and missing data completion are integrated into a unified framework, enabling mutual enhancement between completion and clustering. Experimental results on five commonly used public datasets demonstrate the effectiveness of the proposed algorithm for incomplete multi-view clustering.

Aiming at the problems of noise interference in multi-source interaction data, semantic inconsistencies between auxiliary behaviors and target behaviors, and the difficulty of statically allocating multi-task loss weights to adapt to users’ personalized preferences in multi-behavior recommendation scenarios, this paper proposes a multi-behavior denoising-aware recommendation model based on graph meta-networks. First, a multi-behavior-aware encoder is developed to extract high-order features from multi-type interaction data using graph convolution. Second, a selective cross-behavior contrastive learning method is designed to filter false negative samples using user node similarity, thereby achieving denoising optimization at the user representation level. Third, a hard negative sample sampling strategy based on item similarity is proposed to improve the quality of item representations. Finally, a meta-learning-based dynamic weight adjustment mechanism is implemented to adaptively adjust the multi-task loss weights. Extensive experiments and ablation studies conducted on three real-world datasets demonstrate that the proposed model outperforms various state-of-the-art recommendation methods, fully validating the effectiveness of our approach.

To address the issuse of the insufficient collaborative modeling of semantic and structural information and the inadequate utilization of multilayer features in knowledge graph node classification with limited labels, a semi-supervised graph convolutional and attention-based jump network is proposed in this paper. The model employs a graph convolutional network to extract structural features, a graph attention network to adaptively aggregate neighborhood information, and a long short-term memory network combined with an attention mechanism to fuse node representations from different layers. Experimental results on the computer science paper citation network dataset in the open graph benchmark demonstrate that the model achieves an accuracy of 75.96%, a precision of 73.52%, a recall of 72.34%, and a harmonic mean of precision and recall of 72.93%, which outperforms several mainstream graph neural network models. The results demonstrate that the proposed model effectively integrates node semantics, graph structures, and cross-layer features, thereby improving the performance of node classification  under limited supervision.

Aiming at the problems of high communication complexity, poor scalability and unbalanced primary node load in the traditional practical Byzantine fault tolerance consensus algorithm in large-scale distributed networks. This paper proposes an improved practical Byzantine fault tolerance consensus algorithm based on balanced iterative reducing and clustering using hierarchies and hash ring data structure. The algorithm achieves dynamic clustering sub-organization division of network nodes through distributed optimization of the balanced iterative reducing and clustering using hierarchies algorithm. Meanwhile, combined with the virtual node hash ring mechanism, the problems of load balancing and uneven task assignment within sub-organizations are resolved, and a global committee mechanism is also introduced to significantly reduce the communication complexity of the entire network. Experimental results demonstrate that when the network node scale reaches 256, the system delay of the proposed algorithm is only 713.4 ms, which is 62.4% lower than the 1 895.4 ms of the traditional practical Byzantine fault tolerance algorithm, and its delay growth curve slope is significantly smaller than those of two other mainstream improved consensus algorithms. The proposed algorithm also exhibits significant advantages in terms of throughput, communication overhead, and resource consumption, demonstrating good scalability and stability in large-scale distributed networks. This research significantly improves the consensus efficiency in distributed networks, effectively meets the requirements of complex business scenarios in the Internet industry for high-performance consensus algorithms, and provides important theoretical basis and technical support for the architecture optimization of large-scale blockchain systems.

To address the task offloading decision problem in a dynamic Internet of Vehicles (IoV) network environment, a three-tier task offloading network architecture consisting of vehicles, multiple edge servers, and cloud servers is  proposed. Secondly, the task offloading decisions problem with the aim of minimizing latency, energy consumption, and enhancing service quality (TOD-LEQ) in this network is defined.  Thirdly, the TOD-LEQ is modeled as a Markov decision process (MDP) model. Finally, in order to cope with the impact of dynamically changing environments on task offloading in telematics, a meta learning-based distributed reinforcement learning task offloading (ME-DRO) algorithm is proposed, which can be executed in multiple threads to seek the optimal task offloading decision. Simulation results show that the ME-DRO algorithm significantly outperforms other baseline algorithms in terms of latency, quality of service and convergence speed.

Due to the dynamic properties of transmission channels and transmission queue tasks, it is difficult to achieve high-level stable output of network uplink hybrid retransmission transmission rate using a fixed resource allocation scheme is challenging. Therefore, research on wireless multimedia network uplink hybrid retransmission resource allocation algorithm has been carried out. Combining Shannon’s formula to calculate the peak rate of network enhanced mobile bandwidth for uplink hybrid retransmission, using binary variables to determine the expected channel resource allocation at the peak rate, and constructing a network uplink hybrid retransmission resource allocation objective function with transmission rate as a parameter, so that the objective function includes channel dynamic properties; when solving the objective function, an iterative mechanism is introduced to use the resource allocation parameters that constrain Lyapunov drift as the allocation result of the current task in the transmission queue, and update the allocation scheme recursively based on the transmission queue task. The test results demonstrate that the application design algorithm achieves high fairness in allocating network uplink hybrid retransmission resources, and the transmission rate remains stable at a high level while delivering high throughput.

We studied adaptive sliding mode synchronization of variable fractional-order Sprott-R chaotic system. Based on variable fractional-order Lyapunov stability theory, we applied finite-time synchronization related conclusions and designed a variable fractional-order finite-time adaptive sliding mode controller to obtain the synchronization conditions of variable fractional-order Sprott-R chaotic system under certain assumptions. We then used MATLAB for number simulation to verify the conclusion.

We used multi-scale computational simulations to study the modulation mechanisms by which lattice strain regulated magnetic stability of monolayer NiBr₂, and analyzed the physical origins of its electronic structure and electrical transport anisotropy. We combined density functional theory (DFT)+U with Perdew-Burke-Ernzerhof (PBE) functional based PBE0 hybrid functional to accurately modify the electronic structure, determined the stable magnetic structure by using energy calcuations of PBE, and simulated the electrical conductivity (σ) and the Seebeck coefficient (S) at 300—900 K using AMSET to analyze the correlation between carrier concentration and transport behavior. The results show that when a lattice constant is 0.369 nm, the energy of the cycloidal spiral magnetic order is the lowest, which is consistent with the non-collinear magnetic order observed in the experiment. The band gap value of PBE0-calculated (3.60 eV) is same as the experimental value ((3.4±0.2)eV). σ exhibits extreme anisotropy, σ_a/σ_c≈125 at room temperature, σ_a/σ_c≈480 at 900 K, this is due to the extremely high vacuum potential barrier suppression along the c-axis. S exhibits a critical carrier concentration threshold in p-type doping, which reverses after exceeding the threshold (S_c>S_a). This is due to the saturation of the density-of-states gradient along the a-axis at high carrier densities and the enhanced contribution from dispersionless bands along the c-axis. These results reveal the anisotropy of electrical transport properties of monolayer NiBr₂, providing a theoretical foundation for the experimental exploration of low-dimensional magnetic semiconductor devices. 

Aiming at the problem of significant energy consumption constraints when unmanned aerial vehicle (UAV) assisted mobile edge computing (MEC) systems performed computing tasks, we constructed a system model of UAV that combined computing units and relay nodes, and used non-orthogonal multiple access (NOMA) technology to improve spectral efficiency. By meeting the task requirements of ground users, the energy efficiency of the entire system was maximized by optimizing user communication scheduling, task computation offloading, transmit power, and UAV flight trajectory. We decomposed a non-convex mixed-integer nonlinear fractional programming (MINLFP) problem that could not be directly solved into easily solvable subproblems and iteratively solved them. The fractional form of the objective function was solved by using the Dinkelbach method, which utilized successive convex approximation (SCA) to transform the original subproblems of the fractional problem into convex form. The simulation results show that the proposed method can improve the energy efficiency of the system.

Here it is reported that Na-A zeolite can be synthesized by a clear solution. This synthesis method is based on the fact that the condensation reaction of [SiO₂(OH)₂]^2- and [Al(OH)₄]^- occurs readily, however, the condensation reaction of [Al(OH)₄]^- and [Al(OH)₄]^- does not occur. A solution can be prepared in which [SiO₂(OH)₂]^2- ions are surrounded by a large number of [Al(OH)₄]^- ions, so that the condensation reactions of [SiO₂(OH)₂]^2- and [Al(OH)₄]^- produce a large number of [Si(O—Al—(OH)₃)₄]^4- ions, but these [Si(O—Al—(OH)₃)₄]^4- ions are not condensed ulteriorly, so no sediment is formed. In this way, a clear solution is obtained for the synthesis of Na-A zeolite. A high-quality film of Na-A zeolite on the glass or on the porous alumina ceramic tube can be prepared by using this clear solution. 

We used density functional theory (DFT) to investigate the reaction mechanisms of the sodium ion valine chelates (Val→Na⁺) with hydroxyl radicals (·OH) in aqueous liquid environment at 310.15 K. We explored the potential energy surfaces of the hydrogen abstraction and addition reactions of Val→Na⁺ and ·OH, and the free energy barriers and free energy changes of the single-electron transfer reactions between them. The calculation results show that thermodynamics allows for the hydrogen abstraction reactions with a reaction energy barrier of 23.3—75.6 kJ/mol for implicit water solvent effects, and 33.8—81.2 kJ/mol for explicit water solvent effects. Most hydrogen abstraction energy barries increase slightly. Thermodynamics and kinetics do not allow for electron transfer under both implicit and explicit solvent effects. It can be seen that Val→Na⁺ can rapidly scavenge ·OH through hydrogen abstraction reaction in aqueous liquid phase, and sodium valine chelate can be used as ·OH scavenger.

We prepared and obtained dimercaptomethyl trisulfide containing two structural isomers  5，7-d-imercaptomethyl-1,11-dimercapto-3,6,9-trisulfide and 4,8-dimercaptomethyl-1,11-dimercapto-3,6,9-trisulfide through three steps:  nucleophilic substitution,  chain extension reaction,  and thioetherification and chain extension.  As the core monomer for modifying polyurethane optical materials,  polymeric optical materials could be prepared by synthesizing polythiol composition compounded with polyisocyanate and bisphenol A epoxy resin using this monomer. The experimental results show that the optical material has high transmittance,  high refractive index,  and excellent mechanical properties.

Aiming at the characteristics of perfluorinated chemicals (PFCs), including refractory nature, widespread occurrence in aquatic environments and aquatic organisms, as well as their adverse impacts on ecological environment and human health, paper spray ionization mass spectrometry (PS-MS) was employed to establish a non-invasive direct detection method for endogenous metabolites in tilapia epidermal mucus. Differential metabolites were screened by multivariate statistical analysis, and the mechanism of metabolic disorders was elucidated through database matching and pathway enrichment analysis. The optimized PS-MS method allowed direct and rapid detection of mucus samples, with an analysis time of ≤1 min per sample. A total of 44 differential metabolites were screened in positive ion mode and 40 in negative ion mode. These differential metabolites were mainly enriched in 15 metabolic pathways, covering amino acid metabolism, energy metabolism, lipid metabolism, and carbohydrate metabolism, confirming the metabolic disturbance by perfluorooctanoic acid in fish. This study verified that the PS-MS method can rapidly obtain the metabolic fingerprints of tilapia epidermal mucus under laboratory conditions, providing an effective approach for the non-invasive exploration of the biological metabolic effects of emerging pollutants.