Data scarcity remains a major obstacle to the application of deep learning techniques in medical imaging, particularly for rare neurodegenerative diseases. This study investigates the use of denoising diffusion probabilistic models (DDPMs) to generate synthetic 3D T1-weighted brain MRI images in this context. Addressing the dual challenges of limited training data and structural fidelity, we propose a generative pipeline trained on a multicenter dataset of healthy subjects. The model suggests the potential to produce anatomically coherent synthetic scans with realistic variability. Quantitative evaluation based on Maximum Mean Discrepancy confirms the similarity between real and generated data distributions, while visual assessments highlight the preservation of global and local brain structures. Despite limitations in high-frequency detail reconstruction, the results suggest that DDPMs hold promise as a tool for augmenting neuroimaging datasets and supporting downstream tasks such as classification and segmentation. This work lays the foundation for future research aimed at improving resolution and adapting generative models to the specific challenges of rare disease imaging.

This article focuses on the propensity to patent across Italian regions, considering data from ISTAT-BES between 2004 and 2019 to contribute to analyzing regional gaps and determinants of innovative performances. Results show how the North-South gap in innovative performance has persisted over time, confirming the relevance of research intensity, digital infrastructure, and cultural employment on patenting activity. These relations have been analyzed using the panel data econometric model. It allows singling out crucial positive drivers like R&D investment or strongly negative factors, such as limited mobility of graduates. More precisely, given the novelty of approaches applied in the used model, the following contributions are represented: first, the fine grain of regional differentiation, from which the sub-national innovation system will be observed. It also puts forward a set of actionable policy recommendations that would contribute to more substantial inclusive innovation, particularly emphasizing less-performing regions. By focusing on such dynamics, this study will indirectly address how regional characteristics and policies shape innovation and technological competitiveness in Italy. Therefore, it contributes to the debate on regional systems of innovation and their possible role in economic development in Europe since the economic, institutional, and technological conditions are differentiated between various areas in Italy.