Vision-Language-Action (VLA) models integrate visual perception, natural language understanding, and embodied control into a unified framework, enabling end-to-end task execution from multimodal instructions. While such models have demonstrated impressive generalization across tasks and environments, their direct outputs—often in the form of discrete action tokens or waypoint sequences—frequently overlook key physical constraints, such as trajectory feasibility, collision avoidance, and dynamic consistency. This limitation hinders deployment in safety-critical and dynamic real-world settings. Integrating motion planning into VLA systems offers a principled solution, embedding geometric and dynamic constraints into the control pipeline to transform high-level semantic goals into safe, smooth, and executable trajectories. This work examines representative integration strategies alongside the trade-offs between discrete tokenized outputs and continuous control policies. Applications are analyzed highlighting performance gains in generalization, safety, and execution efficiency. A discussion of current challenges—such as the balance between planning speed and precision, and generalization across embodiments—is followed by prospective research directions, including continuous prediction with hierarchical control, low-resource edge deployment, and multi-robot collaborative planning. The study underscores motion planning as a critical enabler for reliable, adaptable, and scalable embodied intelligence.

This study develops a biomimetic, vascularized skin model using advanced photopolymerization-based 3D bioprinting to address limitations in structural integrity, mechanical properties, and physiological functionality of current skin substitutes. The research synthesizes photocrosslinkable bioinks—methacrylated gelatin (GelMA) and methacrylated hyaluronic acid (HAMA)—at varying ratios (e.g., 5:1 GelMA:HAMA). These bioinks are processed via digital light processing (DLP) printing (405 nm wavelength, 25 μm XY resolution) to create stratified constructs mimicking epidermal topography and dermal layers, incorporating a 500 μm diameter vascular channel to enhance nutrient diffusion. Biomechanical evaluation through uniaxial compression testing reveals that the 5% GelMA/1% HAMA formulation achieves a compressive modulus of 193.09 kPa, aligning with human dermal properties (50–500 kPa). However, the embedded vascular architecture reduces stiffness due to mechanical discontinuity, and the bioink’s fracture toughness requires optimization to mitigate permanent deformation during inelastic phases. Comparisons with murine skin highlight methodological constraints, as untreated tissue exhibits unrepresentative modulus values (986.3 kPa) without preconditioning. While the bioprinted model demonstrates human-relevant mechanics, future work must refine vascular branching, implement crosslinking gradients, and validate long-term ECM remodeling to advance clinical applicability for chronic wound repair and personalized medicine.

We prove that Tietze Extension does not always exist in constructive mathematics if closed sets on which the function we are extending are defined as sequentially closed sets. Firstly, we take a discrete metric space as our topological space. Now all sets open and sequentially closed. Then, we form an unextendible algorithmic function transforming positive integers to 0 and 1, looking at the preimages of these values as our sequentially closed sets. Then we show that if the Tietze theorem conclusion holds for these closed sets then the unextendible function is extendible thus giving us a contradiction. Hence, topology in constructive mathematics have great differences compared to standard topology on Euclidean space. In addition, different definition of special topological space may have converse result on the same theory. Hence, topology in constructive mathematics have great differences compared to standard topology on Euclidean space. In addition, different definition of special topological space may have converse result on the same theory.

Large language models (LLMs) have demonstrated remarkable capabilities in code generation and semantic understanding, enabling ordinary users to generate their own software systems using natural language instructions. This study takes website systems as a case to investigate a user-centered paradigm for code generation and its evaluation. First, users submit their requirements to the LLM via a web interface, prompting the model to automatically generate website project code. Then, through a set of prompt engineering methods and quantitative evaluation techniques developed for this study, we conduct a multi-dimensional assessment of the quality and security of the generated website systems using different types of LLMs and varying system function weights. A hybrid evaluation strategy is proposed to integrate and optimize assessment results across different LLMs. Evaluation dimensions include the degree to which user requirements are satisfied, completeness of website functionality, potential security risks, and code reliability. This research introduces evaluation criteria such as automated review models, functional coverage, and static vulnerability analysis to explore the feasibility, advantages, and limitations of using LLMs as both code generators and reviewers. The findings contribute to our understanding of the practical value of multi-agent LLM collaboration in software development and reveal major current challenges such as functional hallucination, incomplete implementation, and overly optimistic evaluation mechanisms.

With the popularization of electronic payments and consumer credit, credit cards have become the core tool for global financial transactions, with transaction volumes exceeding $50 trillion by 2024. But at the same time as transaction growth, fraudulent methods have shown intelligent and covert characteristics, with frequent occurrences of theft, identity fraud, and false transactions. According to industry reports, global credit card fraud losses will exceed $35 billion in 2024, and fraud patterns will continue to evolve with the iteration of payment technology. To overcome the bottleneck of existing algorithms, this paper proposes a Transformer model that integrates LSTM and Kernel Extreme Learning Machine (KELM) optimization. In the study, correlation analysis was first conducted on various indicators of the data, and then multiple comparative models were used for testing to compare their effectiveness. The experimental results showed that the LSTM-KELM Transformer performed the best in all evaluation metrics, with accuracy, recall, precision, and F1 values reaching 0.999, and AUC reaching 1, significantly better than other models. Among other models, Random Forest, Adaboost, CatBoost, and BP neural network have similar performance, with Accuracy, Recall, and Precision mostly around 0.992, slightly lower F1 values, and AUC between 0.998-0.999, belonging to the suboptimal level; The various indicators of logistic regression are slightly weaker than the above model, about 0.99; The performance of Decision Tree and Gradient Boosting Tree (GBDT) is relatively poor, especially with GBDT's Accuracy, Recall and other indicators only reaching 0.985, and Decision Tree's AUC also only reaching 0.985. Overall, the LSTM-KELM Transformer outperforms other models in terms of classification accuracy, recognition ability for positive and negative samples, comprehensive performance, and ability to distinguish positive and negative classes, demonstrating stronger classification advantages and contributing to the correct classification of fraud detection. This has important practical significance for improving the efficiency of credit card fraud detection and reducing financial losses.

Large Language Models (LLMs) demonstrate remarkable capabilities but remain limited by their reliance on static training data. Retrieval-Augmented Generation (RAG) addresses this constraint by retrieving external knowledge during inference, though it still depends heavily on knowledge base quality. To explore potential improvements, we evaluated three RAG variants—Standard RAG, DA-RAG, and our proposed Prompt-Enhanced Parametric RAG (P-RAG), a hybrid architecture that integrates parametric knowledge within the LLM and retrieved evidence, guided by Chain-of-Thought (CoT) prompting and Low-Rank Adaptation (LoRA) fine-tuning—on both general and biomedical datasets. Using LLaMA-3.2-1B-Instruct fine-tuned via LoRA, we evaluate on PubMedQA and 2WikiMultihopQA. P-RAG outperforms Standard RAG on PubMedQA by 10.47 percentage points in F1 (93.33% vs. 82.86%; 12.64% relative). On 2WikiMultihopQA, P-RAG nearly doubles the overall score vs. Standard RAG (33.44% vs. 17.83%) and achieves 44.03% on the Compare subset (with 42.74% Bridge, 21.84% Inference, 8.60% Compose). CoT prompting substantially improves multi-hop reasoning but yields mixed results for simpler, single-hop queries. These findings underscore P-RAG’s potential for accurate, scalable, and contextually adaptive biomedical question answering. Our contributions include: (1) LoRA-based fine-tuning of LLaMA-3.2-1B-Instruct for biomedical QA, (2) introduction of P-RAG with Chain-of-Thought prompting, and (3) state-of-the-art results on PubMedQA and 2WikiMultihopQA.

As real-time live-streaming commerce has increasing applications of AI avatars, identity disclosure emerges as an important factor in shaping consumers’ short-term trust. An analytical model was constructed, integrating multimodal trust cues and causality inference to investigate the nonlinear threshold effects of AI identity disclosure. Based on large-scale real data and machine learning methods, the research establishes an optimal disclosure interval between 0.32 and 0.52, which significantly enhances trust while avoiding the trust decline caused by the “uncanny valley” effect. Depending on the age, different types of responses can be distinguished. Younger users have a lower tolerance for high-intensity information disclosure, while the middle-aged and elderly groups tend to prefer a moderate level of information disclosure intensity. Through double machine learning based on mediation analysis, parasocial intimacy and perceived truthfulness are established as prominent psychological mechanisms in cultivating trust. These findings provide a theoretical foundation for disclosing in a personalized form relative to distinctive user groups and provide practical expertise for designing trustworthy AI systems as well as for informing policymaking in governing such technologies.

Class imbalance poses a significant challenge in biomedical classification tasks, particularly when abnormal conditions such as arrhythmias occur infrequently. While oversampling methods like SMOTE, ADASYN, and Active SMOTE attempt to alleviate this by generating synthetic minority samples, they often overlook model uncertainty during sampling. In this paper, we propose an enhanced Active SMOTE framework that integrates a lightweight uncertainty-aware module. The module measures prediction confidence through softmax probabilities, identifies the most ambiguous minority-class instances—those with predicted probabilities close to 0.5—and prioritises them for synthetic augmentation. To generate new samples, a k-nearest-neighbour interpolation mechanism is applied, producing diverse yet informative synthetic data near decision boundaries. This design strengthens the classifier’s ability to learn from critical borderline cases and reduces wasted computation on confidently classified samples. We evaluate the method on two biomedical datasets with 12 features: a large-scale ECG dataset (80,000 samples) and a smaller Gas Sensor Drift dataset (~13,000 samples). Each dataset is processed in a five-stage incremental learning setup, simulating gradual data arrival as in real-world biomedical systems. Across both datasets, our uncertainty-aware strategy consistently outperforms traditional methods (SMOTE, ADASYN, Active SMOTE) in F1-score and recall, with particularly strong gains in early learning stages when data is scarce. The approach is efficient, interpretable, and easily integrable with existing classifiers, offering a practical and deployable improvement for biomedical applications such as arrhythmia detection or sensor drift monitoring.

This study investigates the impact of starting draw position (inner vs. outer tracks) on race outcomes at three distinct UK racecourses—Southwell, Newmarket, and Pontefract—examining how race distance and course topography modulate this effect. Utilizing linear regression and Spearman Rank Correlation Meta-Analysis, this study quantified draw-related performance biases across an extensive dataset of historical races. Races were systematically categorized into short, middle, and long-distance groups by identifying inflection points in draw effect trends through graphical analysis. The findings demonstrate a statistically significant relationship between stall number and finishing position across all three courses, with the magnitude and direction of bias varying by distance and track layout. Key results reveal that inner draws consistently provide an advantage in short-distance races, likely due to reduced travel distance on tighter turns. Middle-distance races exhibit pronounced course-dependent biases, with outer draws particularly disadvantaged at Newmarket, possibly due to its wide, sweeping turns. In contrast, long-distance races show diminished draw effects overall, though outer draws surprisingly improve outcomes at Southwell, suggesting terrain-specific adaptations. Meta-analysis further confirmed significant heterogeneity in draw biases across courses, highlighting the interplay between distance-governed turn frequency and unique topographic features. These findings underscore that track position bias is not universal but shaped by complex interactions between race dynamics and course design. The study provides actionable insights for strategic draw selection and proposes adjustments to handicapping models to account for these biases, ultimately enhancing competitive fairness in horse racing.

The major of the Rubik's Cube reduction algorithm is to construct an efficient operation sequence through mathematical tools (such as group theory). Different algorithms are based on the balance between the space division of the Rubik's Cube structure and the efficiency of operation, forming mainstream methods such as layer-first method, CFOP, ROUX, and bridge method. Starting from the underlying mathematical principles, this paper analyzes the design motivations and performance characteristics of different algorithms, and selects the CFOP algorithm for in-depth analysis.