A widely used Agile practice for requirements is to produce a set of user stories (also called ``agile product backlog''), which roughly includes a list of pairs (role, feature), where the role handles the feature for a certain purpose. In the context of Software Product Lines, the requirements for a family of similar systems is thus a family of user-story sets, one per system, leading to a 3-dimensional dataset composed of sets of triples (system, role, feature). In this paper, we combine Triadic Concept Analysis (TCA) and Large Language Model (LLM) prompting to suggest the user-story set required to develop a new system relying on the variability logic of an existing system family. This process consists in 1) computing 3-dimensional variability expressed as a set of TCA implications, 2) providing the designer with intelligible design options, 3) capturing the designer's selection of options, 4) proposing a first user-story set corresponding to this selection, 5) consolidating its validity according to the implications identified in step 1, while completing it if necessary, and 6) leveraging LLM to have a more comprehensive website. This process is evaluated with a dataset comprising the user-story sets of 67 similar-purpose websites.

The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those from Hilbert geometry, Peano arithmetic, or ZFC - we offer a new way to visualize, compare, and analyze mathematical knowledge. This vector-based formalism not only captures the logical foundation of theorems but also enables quantitative similarity metrics - such as cosine distance - between mathematical results, offering a new analytic layer for structural comparison. Using heatmaps, vector clustering, and AI-assisted modeling, this atlas enables the grouping of theorems by logical structure, not just by mathematical domain. We also introduce a prototype assistant (Atlas-GPT) that interprets natural language theorems and suggests likely proof vectors, supporting future applications in automated reasoning, mathematical education, and formal verification. This direction is partially inspired by Terence Tao's recent reflections on the convergence of symbolic and structural mathematics. The Axiom-Based Atlas aims to provide a scalable, interpretable model of mathematical reasoning that is both human-readable and AI-compatible, contributing to the future landscape of formal mathematical systems.

Dependencies among attributes are a common aspect of tabular data. However, whether existing tabular data generation algorithms preserve these dependencies while generating synthetic data is yet to be explored. In addition to the existing notion of functional dependencies, we introduce the notion of logical dependencies among the attributes in this article. Moreover, we provide a measure to quantify logical dependencies among attributes in tabular data. Utilizing this measure, we compare several state-of-the-art synthetic data generation algorithms and test their capability to preserve logical and functional dependencies on several publicly available datasets. We demonstrate that currently available synthetic tabular data generation algorithms do not fully preserve functional dependencies when they generate synthetic datasets. In addition, we also showed that some tabular synthetic data generation models can preserve inter-attribute logical dependencies. Our review and comparison of the state-of-the-art reveal research needs and opportunities to develop task-specific synthetic tabular data generation models. Keywords: Synthetic tabular data, Logical dependencies, Functional dependencies, Generative models 1. Introduction Dependencies among attributes are a common aspect of tabular data. A well-known fact in Database Management Systems is that if one wants to remove redundancies by dividing larger tables into smaller ones (Normalization) [1], one needs tools to identify functional dependencies present among the attributes of the larger table [2]. Preserving functional dependencies in synthetic tabular data is an area that has not been explored. Dependencies exist in both tabular and image data.

Many fields could benefit from the rapid development of the large language models (LLMs). The end-to-end autonomous driving (e2eAD) is one of the typically fields facing new opportunities as the LLMs have supported more and more modalities. Here, by utilizing vision-language model (VLM), we proposed an e2eAD method called SimpleLLM4AD. In our method, the e2eAD task are divided into four stages, which are perception, prediction, planning, and behavior. Each stage consists of several visual question answering (VQA) pairs and VQA pairs interconnect with each other constructing a graph called Graph VQA (GVQA). By reasoning each VQA pair in the GVQA through VLM stage by stage, our method could achieve e2e driving with language. In our method, vision transformers (ViT) models are employed to process nuScenes visual data, while VLM are utilized to interpret and reason about the information extracted from the visual inputs. In the perception stage, the system identifies and classifies objects from the driving environment. The prediction stage involves forecasting the potential movements of these objects. The planning stage utilizes the gathered information to develop a driving strategy, ensuring the safety and efficiency of the autonomous vehicle. Finally, the behavior stage translates the planned actions into executable commands for the vehicle. Our experiments demonstrate that SimpleLLM4AD achieves competitive performance in complex driving scenarios.