Alex Conway

Michael A. Bender, Aaron Bernstein, Nairen Cao et al.

The issue of internal fragmentation in data structures is a fundamental challenge in database design. A seminal result of Yao in this field shows that evenly splitting the leaves of a B-tree against a workload of uniformly random insertions achieves space utilization of around 69%. However, many database applications perform batched insertions, where a small run of consecutive keys is inserted at a single position. We develop a generalization of Yao's analysis to provide rigorous treatment of such batched workloads. Our approach revisits and reformulates the analytical structure underlying Yao's result in a way that enables generalization and is used to argue that even splitting works well for many workloads in our extended class. For the remaining workloads, we develop simple alternative strategies that provably maintain good space utilization.

António Farinhas, Nuno M. Guerreiro, José Pombal et al.

Large language models are increasingly used for mental health support, yet their conversational coherence alone does not ensure clinical appropriateness. Existing general-purpose safeguards often fail to distinguish between therapeutic disclosures and genuine clinical crises, leading to safety failures. To address this gap, we introduce a clinically grounded risk taxonomy, developed in collaboration with PhD-level psychologists, that identifies actionable harm (e.g., self-harm and harm to others) while preserving space for safe, non-crisis therapeutic content. We release MindGuard-testset, a dataset of real-world multi-turn conversations annotated at the turn level by clinical experts. Using synthetic dialogues generated via a controlled two-agent setup, we train MindGuard, a family of lightweight safety classifiers (with 4B and 8B parameters). Our classifiers reduce false positives at high-recall operating points and, when paired with clinician language models, help achieve lower attack success and harmful engagement rates in adversarial multi-turn interactions compared to general-purpose safeguards. We release all models and human evaluation data.