In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this article, we give exact logical characterizations of recurrent GNNs in two scenarios: (1) in the setting with floating-point numbers and (2) with reals. For floats, the formalism matching recurrent GNNs is a rule-based modal logic with counting, while for reals we use a suitable infinitary modal logic, also with counting. These results give exact matches between logics and GNNs in the recurrent setting without rel-ativising to a background logic in either case, but using some natural assumptions about floating-point arithmetic. Applying our characterizations, we also prove that, relative to graph properties definable in monadic second-order logic (MSO), our infinitary and rule-based logics are equally expressive. This implies that recurrent GNNs with reals and floats have the same expressive power over MSO-definable properties and shows that, for such properties, also recurrent GNNs with reals are characterized by a (finitary!)

The full-day workshop on AI and Agile at XP 2025 convened a diverse group of researchers and industry practitioners to address the practical challenges and opportunities of integrating Artificial Intelligence into Agile software development. Through interactive sessions, participants identified shared frustrations related to integrating AI into Agile Software Development practices, including challenges with tooling, governance, data quality, and critical skill gaps. These challenges were systematically prioritized and analyzed to uncover root causes. The workshop culminated in the collaborative development of a research roadmap that pinpoints actionable directions for future work, including both immediate solutions and ambitious long-term goals. The key outcome is a structured agenda designed to foster joint industry-academic efforts to move from identified frustrations to successful implementation.

The electrocardiogram (ECG) is a key diagnostic tool in cardiovascular health. Single-lead ECG recording is integrated into both clinical-grade and consumer wearables. While self-supervised pretraining of foundation models on unlabeled ECGs improves diagnostic performance, existing approaches do not incorporate domain knowledge from clinical metadata. We introduce a novel contrastive learning approach that utilizes an established clinical risk score to adaptively weight negative pairs: clinically-guided contrastive learning. It aligns the similarities of ECG embeddings with clinically meaningful differences between subjects, with an explicit mechanism to handle missing metadata. On 12-lead ECGs from 161K patients in the MIMIC-IV dataset, we pretrain single-lead ECG foundation models at three scales, collectively called CLEF, using only routinely collected metadata without requiring per-sample ECG annotations. We evaluate CLEF on 18 clinical classification and regression tasks across 7 held-out datasets, and benchmark against 5 foundation model baselines and 3 self-supervised algorithms. When pretrained on 12-lead ECG data and tested on lead-I data, CLEF outperforms self-supervised foundation model baselines: the medium-sized CLEF achieves average AUROC improvements of at least 2.6% in classification and average reductions in MAEs of at least 3.2% in regression. Comparing with existing self-supervised learning algorithms, CLEF improves the average AUROC by at least 1.8%. Moreover, when pretrained only on lead-I data for classification tasks, CLEF performs comparably to the state-of-the-art ECGFounder, which was trained in a supervised manner. Overall, CLEF enables more accurate and scalable single-lead ECG analysis, advancing remote health monitoring. Code and pretrained CLEF models are available at: github.com/Nokia-Bell-Labs/ecg-foundation-model.