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COLENGTH, MULTIPLICITY, AND IDEAL CLOSURE OPERATIONS II

Ma, L.; Pham, H.Q.; Smirnov, I. (2024-01-01)

Let (R,m) be a Noetherian local ring. This paper concerns several extremal invariants arising from the study of the relation between colength and (Hilbert–Samuel or Hilbert–Kunz) multiplicity of an m-primary ideal. We intr...

The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality

Sahil, I.; Merelli, E.; Rodrigues, S. (2025-01-01)

We propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the forma...

Explosive neural networks via higher-order interactions in curved statistical manifolds

Aguilera, M.; Morales, P.A.; Rosas, F.E.; Shimazaki, H. (2025-12-01)

Higher-order interactions underlie complex phenomena in systems such as biological and artificial neural networks, but their study is challenging due to the scarcity of tractable models. By leveraging a generalisation of the...

The theory of F-rational signature

Smirnov, I.; Tucker, K. (2024-07-01)

F-signature is an important numeric invariant of singularities in positive characteristic that can be used to detect strong F-regularity. One would like to have a variant that rather detects F-rationality, and there are two ...