This paper develops an autonomous agentic framework called V-Math that aims to assist Vietnamese high school students in preparing for the National High School Graduation Mathematics Exams (NHSGMEs). The salient framework integrates three specialized AI agents: a specification-matrix-conditioned question generator, a solver/explainer for detailed step-by-step reasoning, and a personalized tutor that adapts to student performance. Beyond enabling self-paced student practice, V-Math supports teachers by generating innovative, compliant exam questions and building diverse, high-quality question banks. This reduces manual workload and enriches instructional resources. We describe the system architecture, focusing on practice modes for learners and teacher-oriented features for question generation. Preliminary evaluations demonstrate that V-Math produces matrix-aligned exams with high solution accuracy, delivers coherent explanations, and enhances the variety of practice materials. These results highlight its potential to support scalable, equitable mathematics preparation aligned with national standards while also empowering teachers through AI-assisted exam creation.

Lt. Gov. Jay Collins, R-Fla., joins'America's Newsroom' to discuss Florida's crackdown on illegal immigrant truck drivers after the death of three Americans. In an apparent effort to address the millions of backlogged immigration cases, the Justice Department made a rule change to allow attorneys without immigration law experience to act as temporary immigration judges. The DOJ's Office of Immigration Review published the rule in the federal register Thursday, which removes the requirement that temporary immigration judges have substantive prior experience in immigration law. Jurists who are approved by Attorney General Pam Bondi may serve as immigration judges, which represents a tide change after more than 100 judges were fired or bought out by the Trump administration earlier in 2025. The DOJ hopes that by expanding the net as to who may hear immigration-related cases, the more than three million case backlog may finally be assuaged.

The advancement of technology and information has led to a rapid growth in various fields. Undoubtedly, the global community extensively relies on technology as a solution to address the myriad challenges of the contemporary world. One prominent application is the search systems, which offer efficient methods for locating specific information within vast data collections. For instance, a search system can be employed to locate titles of student practical work [1]. A search engine is the practical application of information retrieval techniques for large the term "search engine" was originally term "Search Engine" was originally used to refer to specialized hardware for text searching [2]. Among the problem-solving techniques rooted in historical knowledge, Case-Based Reasoning stands out.

Efficient motion planning algorithms are essential in robotics. Optimizing essential parameters, such as batch size and nearest neighbor selection in sampling-based methods, can enhance performance in the planning process. However, existing approaches often lack environmental adaptability. Inspired by the method of the deep fuzzy neural networks, this work introduces Learning-based Informed Trees (LIT*), a sampling-based deep fuzzy learning-based planner that dynamically adjusts batch size and nearest neighbor parameters to obstacle distributions in the configuration spaces. By encoding both global and local ratios via valid and invalid states, LIT* differentiates between obstacle-sparse and obstacle-dense regions, leading to lower-cost paths and reduced computation time. Experimental results in high-dimensional spaces demonstrate that LIT* achieves faster convergence and improved solution quality. It outperforms state-of-the-art single-query, sampling-based planners in environments ranging from R^8 to R^14 and is successfully validated on a dual-arm robot manipulation task. A video showcasing our experimental results is available at: https://youtu.be/NrNs9zebWWk

Optimal path planning aims to determine a sequence of states from a start to a goal while accounting for planning objectives. Popular methods often integrate fixed batch sizes and neglect information on obstacles, which is not problem-specific. This study introduces Adaptively Prolated Trees (APT*), a novel sampling-based motion planner that extends based on Force Direction Informed Trees (FDIT*), integrating adaptive batch-sizing and elliptical $r$-nearest neighbor modules to dynamically modulate the path searching process based on environmental feedback. APT* adjusts batch sizes based on the hypervolume of the informed sets and considers vertices as electric charges that obey Coulomb's law to define virtual forces via neighbor samples, thereby refining the prolate nearest neighbor selection. These modules employ non-linear prolate methods to adaptively adjust the electric charges of vertices for force definition, thereby improving the convergence rate with lower solution costs. Comparative analyses show that APT* outperforms existing single-query sampling-based planners in dimensions from $\mathbb{R}^4$ to $\mathbb{R}^{16}$, and it was further validated through a real-world robot manipulation task. A video showcasing our experimental results is available at: https://youtu.be/gCcUr8LiEw4

Path planning has long been an important and active research area in robotics. To address challenges in high-dimensional motion planning, this study introduces the Force Direction Informed Trees (FDIT*), a sampling-based planner designed to enhance speed and cost-effectiveness in pathfinding. FDIT* builds upon the state-of-the-art informed sampling planner, the Effort Informed Trees (EIT*), by capitalizing on often-overlooked information in invalid vertices. It incorporates principles of physical force, particularly Coulomb's law. This approach proposes the elliptical $k$-nearest neighbors search method, enabling fast convergence navigation and avoiding high solution cost or infeasible paths by exploring more problem-specific search-worthy areas. It demonstrates benefits in search efficiency and cost reduction, particularly in confined, high-dimensional environments. It can be viewed as an extension of nearest neighbors search techniques. Fusing invalid vertex data with physical dynamics facilitates force-direction-based search regions, resulting in an improved convergence rate to the optimum. FDIT* outperforms existing single-query, sampling-based planners on the tested problems in R^4 to R^16 and has been demonstrated on a real-world mobile manipulation task.

CNN (Zheng et al., ICCV 2017) uses aggregated conv-feature maps as "part attentions."

This is indeed an omission, but it is not terribly complicated and we will add it to the paper.

Approximate nearest neighbor (ANN) search is a fundamental algorithmic problem.

Falconn++ is also competitive with HNSW, an efficient representative of graph-based solutions on high search recall regimes.