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Across driven systems, a recurring empirical tension is observed: evolution remains coherent and produces durable structure, yet the underlying process cannot be reconstructed from local dissipation-based derivations. Observable trajectories persist longer and retain more organization than what local constraints alone would predict. This work treats this mismatch not as a modeling defect but as the starting phenomenon to be explained. We argue that under finite observation windows, what is accessed is necessarily a projection of ongoing irreversible change. Projection compresses continuous processes into finite, dimension-reduced representations, making time itself non-comparable across systems and shifting the basic object of comparison from time points to ordered paths. The observed contradiction between paths and local derivation then forces a separation: coherence can persist while phase reversibility fails. When relaxation is incomplete, prior change leaves retention that overlaps with subsequent driving, producing dislocated synchronization-new processes are imposed on unfinished remnants rather than replacing them. Most displacements dissipate, but a small subset survives, selected by coupling geometry. Under finite projection, this geometry becomes readable only statistically, yielding observable measures of coupling depth, orientation, and participation. The surviving outcomes appear as residuals: stable projected sections of high-dimensional dynamics. Lifespan differences among residuals lead to natural stratification, culminating in a durable topological skeleton that constrains future evolution. Persistence is thus explained as a consequence of irreversible projection, geometric selection, and stratified deposition, rather than optimization, design, or full process recoverability.

个性化学习路径规划通过分析学习者历史交互行为推荐有序的知识点序列，在提升在线教育效率与体验方面具有重要应用价值。然而，传统序列推荐方法（如SASRec、BERT4Rec）面临深层语义逻辑捕捉不足的问题，而直接应用大语言模型（LLM）则存在严重幻觉、长链路推理能力弱以及生成结果偏离教学大纲的局限。为此，提出一种基于检索增强图思维（RA-GoT）的个性化路径规划算法。该方法构建"相似路径检索 - 图式演化推理 - 候选约束映射"的结构化生成系统：利用 KNN 检索相似学习者的历史路径作为上下文参考，基于GoT框架执行"生成 - 批量对比打分 - 动态剪枝"的非线性规划，并通过模糊匹配机制将生成结果严格映射至知识库。在MOOCCubeX数据集上的实验表明，该方法的 Recall@10 和 NDCG@10 分别达到 65.81% 和 56.80%，相比 BERT4Rec 和 LLM-CoT等基线模型性能提升显著。该方法为大模型在教育推荐领域的落地提供了高可信、可解释的解决方案。

针对现有图像质量评估工具反馈单一、细粒度分析能力不足、缺乏成熟完整系统支持及模型适配性有限等问题，设计并实现一种融合自研微调模型与第三方开源模型的多模态细粒度图片质量评估系统。系统采用 C/S 与 B/S 混合架构及前后端分离设计，整合用户交互、业务处理、数据存储及多源 AI 模型推理等核心模块，支持多维度评分、可解释性评估报告生成、批量图像筛选、多模型适配切换等功能。通过显著物体识别、双图对比机制、动态损失函数优化及多模型协同推理策略，大幅提升细粒度曝光差异判别精度，同时保障系统的可靠性、易用性与扩展性。实际测试表明，系统在 KADID-10K、PIPAL 等基准数据集上表现优异，能有效满足专业摄影评估、摄影学习、商业图像筛选及日常图片管理等多场景需求，为图像质量评估提供高效、灵活、实用的解决方案。

Generalizing from limited data is particularly critical for models in domains such as material science, where task-relevant features in experimental datasets are often heavily confounded by measurement noise and experimental artifacts. Standard regularization techniques fail to precisely separate meaningful features from noise, while existing adversarial adaptation methods are limited by their reliance on explicit separation labels. To address this challenge, we propose the Adversarial Information Separation Framework (AdverISF), which isolates task-relevant features from noise without requiring explicit supervision. AdverISF introduces a self-supervised adversarial mechanism to enforce statistical independence between task-relevant features and noise representations. It further employs a multi-layer separation architecture that progressively recycles noise information across feature hierarchies to recover features inadvertently discarded as noise, thereby enabling finer-grained feature extraction. Extensive experiments demonstrate that AdverISF outperforms state-of-the-art methods in data-scarce scenarios. In addition, evaluations on real-world material design tasks show that it achieves superior generalization performance.

We provide proofs certifying that the structure theorem for vertex sets of bounded bidimensionality holds with polynomial bounds. The bidimensionality of vertex sets is a common generalisation of both treewidth and the face-cover-number of vertex sets in planar graphs. As such, it plays a crucial role in extensions of Courcelle's Theorem to $H$-minor-free graphs. Recently, bidimensionality and similar parameters have emerged as key for extensions of known parameterized algorithms for problems defined on a terminal set $R$. A prominent example for such a problem is Steiner Tree, which admits efficient algorithms on planar graphs whenever $R$ can be covered with few faces. Key to the algorithmic applications of bidimensionality is a structure theorem that explains how a graph $G$ can be decomposed into pieces where the behaviour of $R$ is highly controlled. One may see this structure theorem as a rooted analogue of Robertson and Seymour's celebrated Grid Theorem. Combining recent advances in obtaining polynomial bounds in the Graph Minors framework with new techniques for handling annotated vertex sets, we show that all parameters in the structure theorem above admit polynomial bounds. As an application, we also provide a sketch showing how our techniques imply polynomial bounds for the structure theorem for graphs excluding an apex minor.