Publications SISSA

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https://ricerca.unityfvg.it/handle/123456789/239342

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Ora in mostra 1 - 5 di 14797
  • Pubblicazione
    On Dold-Whitney's parallelizability of 4-manifolds
    ( 2025)
    Bais V.
    We present a proof of a theorem by Dold and Whitney, according to which a closed orientable 4-manifold is parallelizable if and only if its second Stiefel-Whitney class, first Pontryagin class and Euler characteristics vanish. This follows from a stronger result due to Dold and Whitney on the classification of oriented sphere bundles over a 4-complex. Our proof is based on an argument by R. Kirby on the classification of SO(4)-principal bundles over the 4-sphere by means of their Euler and first Pontryagin classes.
  • Pubblicazione
    On Stiefel's parallelizability of 3-manifolds
    ( 2023)
    Bais, V.
    ;
    Zuddas, D.
    We give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting.
  • Pubblicazione
    BARNN: A Bayesian Autoregressive and Recurrent Neural Network
    (ML Research Press, 2025)
    Coscia D.
    ;
    Welling M.
    ;
    Demo N.
    ;
    Rozza G.
    Autoregressive and recurrent networks have achieved remarkable progress across various fields, from weather forecasting to molecular generation and Large Language Models. Despite their strong predictive capabilities, these models lack a rigorous framework for addressing uncertainty, which is key in scientific applications such as PDE solving, molecular generation and Machine Learning Force Fields. To address this shortcoming we present BARNN: a variational Bayesian Autoregressive and Recurrent Neural Network. BARNNs aim to provide a principled way to turn any autoregressive or recurrent model into its Bayesian version. BARNN is based on the variational dropout method, allowing to apply it to large recurrent neural networks as well. We also introduce a temporal version of the “Variational Mixtures of Posteriors” prior (tVAMPprior) to make Bayesian inference efficient and well-calibrated. Extensive experiments on PDE modelling and molecular generation demonstrate that BARNN not only achieves comparable or superior accuracy compared to existing methods, but also excels in uncertainty quantification and modelling long-range dependencies.
  • Pubblicazione
    Homogenization of vectorial free-discontinuity functionals with cohesive type surface terms
    ( 2025)
    Dal Maso G.
    ;
    Donati D.
    The results on Gamma-limits of sequences of free-discontinuity functionals with bounded cohesive surface terms are extended to the case of vector-valued functions. In this framework, we prove an integral representation result for the Gamma-limit, which is then used to study deterministic and stochastic homogenization problems for this type of functional.
  • Pubblicazione
    Pin±-structures on non-oriented 4-manifolds via Lefschetz fibrations
    ( 2025)
    Bais V.
    We study necessary and sufficient conditions for a 4-dimensional Lefschetz fibration over the 2-disk to admit a Pin±-structure, extending the work of A. Stipsicz in the orientable setting. As a corollary, we get existence results of Pin+ and Pin−-structures on closed non-orientable 4-manifolds and on Lefschetz fibrations over the 2-sphere. In particular, we show via three explicit examples how to read-off Pin±-structures from the Kirby diagram of a 4-manifold. We also provide a proof of the well-known fact that any closed 3-manifold M admits a Pin−-structure and we find a criterion to check whether or not it admits a Pin+-structure in terms of a handlebody decomposition. We conclude the paper with a characterization of Pin+-structures on vector bundles.