重庆师范大学

The graph-based clustering aims to utilize structural information from graphs to provide clustering solutions. However, many existing graph clustering methods separate graph construction from the learning of clustering results, and rely on the assumption of consistent feature importance, which often leads to suboptimal clustering outcomes. Anchor-based graph clustering offers an efficient and scalable solution for clustering tasks. Nevertheless, the need to manually specify the number of anchors limits its practicality. Motivated by these issues, this paper proposes a method called Multi-granularity Granular-ball Anchor Graph Clustering with self-weighting (MGAGC). The MGAGC utilizes granular-ball computing to adaptively generate granular-ball anchors based on the data distribution, where the number of granular-ball anchors is much smaller than the number of data samples. Then, by enabling interaction between fine-granularity sample points and coarse-granularity granular-ball anchors in a self-weighting feature space, the MGAGC integrates graph construction with the learning of clustering results. Extensive experiments are conducted on fourteen public datasets to compare the proposed MGAGC with nine classic or state-of-the-art baseline clustering methods. Experimental results show that MGAGC achieves an average ACC of 75.50% and an average NMI of 51.22%, outperforming other clustering methods by an average of 13.60% and 12.21%, respectively. Moreover, statistical test results indicate that its performance differences are statistically significant compared to most of the competing methods. Code is available at https://github.com/awaw-Liyely/2026-IPM-MGAGC.

In this paper, we consider the Cauchy problem for a highly nonlinear shallow water model arising from the full water waves with Coriolis effect. By the transport equation theory and the classical Friedrichs regularization method, the local well-posedness for this shallow water model in the critical Besov spaces B1+ 1p (p,1) is established, and the ill-posedness for this model in the critical Besov spaces B-s (p,infinity) with s > max {3/2 , 1 + 1/p} is also obtained. Moreover, the precise blow-up criteria for the strong solutions of this equation are determined in Besov spaces B-p,r(s). Finally, the Gevrey regularity and analyticity of the solution of this model are presented.

Deep hashing has potential application prospects in large-scale image retrieval due to its low-cost and efficient retrieval advantages. However, traditional instance-based hashing methods match images by directly comparing their hash codes, but this process is easily disturbed by appearance factors such as color, angle, and background, resulting in semantic mismatches. Approaches based on centroid/proxy representations have been proposed to alleviate the above problems. Existing centroid/proxy-based approaches are limited to training and do not optimize retrieval efficiency, which goes against the core benefits of hashing. In this paper, by using the mean centroid representation in both training and retrieval, a novel Mean Centroid Representation for Deep Hashing framework (MCRDH) is proposed to learn a highly discriminative embedding space, realizing intra-class aggregation and inter-class separation. Specifically, by calculating the mean centroid of each class of samples, a novel mean centroid triplet loss is designed to alleviate the negative impact of outliers, thereby generating compact and discriminative hash codes. In addition, since the samples of each class are represented by a mean centroid, the number of target vectors in the database set is significantly reduced, thereby greatly narrowing the search space, reducing retrieval time and storage requirements, which is suitable for production deployment. Comprehensive experiments conducted on three public datasets demonstrate that our proposed MCRDH framework surpasses various state-of-the-art methods. The source code of our proposed MCRDH framework is available at: https://github.com/QinLab-WFU/MCRDH.

In dynamic multi-objective optimization, environmental changes can rapidly invalidate converged solution sets. Therefore, achieving fast convergence recovery while maintaining solution-set distribution stability remains a key challenge. Existing methods often lack effective coordination between change response and subsequent optimization, which limits their recovery speed and long-term tracking stability. To address this issue, this paper proposes a dynamic multi-objective evolutionary algorithm with direction-guided hybrid response and sensitive-dimension-based two-stage evolution. First, a direction-guided hybrid response strategy is developed to improve post-change recovery. It estimates the population migration direction from the elite centroid and the population centroid, and then generates a response population through directional translation, change-intensity-related perturbation, and small-scale random reinitialization. The response population then provides the decision-space basis for sensitive-dimension identification. The identified dimensions further provide search guidance for the subsequent two-stage evolution. Second, a sensitive-dimension identification mechanism is constructed to locate decision variables that are more sensitive to environmental changes. Based on the dispersion characteristics of elite solutions in the decision space, the identified sensitive dimensions are used to guide a two-stage evolutionary process. Predictive search is performed on sensitive dimensions to accelerate Pareto-front tracking, while local refinement is conducted on relatively stable dimensions to improve solution-set distribution. Finally, a multi-source fusion elite recombination strategy is introduced to enhance the robustness of population updating. It removes duplicates and performs controlled replacement among the original population, two-stage candidate solutions, and elite information. Experimental results on FDA, DF, and JY benchmark problems under different change-frequency settings show that the proposed algorithm outperforms the competing algorithms on most test problems and remains competitive on the others. Further studies on aluminum electrolysis operating-parameter optimization and the dynamic multi-objective knapsack problem demonstrate its practical applicability in both continuous- and discrete-variable decision scenarios.

Due to the scarcity of Thermal Infrared (TIR) datasets, PEFT-based TIR tracking methods are gaining popularity. However,existing PEFT-based TIR trackers pursue lightweight adaptation but often ignore the thermophysical degradation of infrared imaging. Existing frequency-based and MoE-based methods exploit high-frequency cues or adaptive routing, yet rarely model heat-diffusion-induced attenuation or inject TIR-specific physical priors. To this end, we propose PPAT, a physics-prior adapter tuning framework for TIR tracking. Specifically, we first design a physics prior adapter that utilizes the solution of the heat diffusion partial differential equation in the frequency domain. This adapter can recover high-frequency structural details submerged by thermal blurring, which is crucial to TIR tracking. We further design a Mixture-of-Experts (MoE)-based injector to adaptively reweight useful physical priors before injecting them into a frozen RGB foundation tracker for fine-tuning. Extensive experiments on four TIR tracking benchmarks demonstrate that our PPAT achieves state-of-the-art performance. Compared to other PEFT-based methods (e.g., Head Probe, LoRA, Adapter), PPAT yields superior results with significantly fewer trainable parameters and outperforms the full fine-tuning paradigm, demonstrating exceptional training efficiency and stability.