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Related Articles from SNS
On Effective Banach-Mazur Games and an application to the Poincar\'e Recurrence Theorem for Category
arXiv:2506.11118v2 Announce Type: replace-cross Abstract: The classical Banach-Mazur game characterizes sets of first category in a topological space. In this work, we show that an effectivized version of the game yields a characterization of sets of effective first category. Using this, we give a proof for the effective Banach Category Theorem.
Complex Bounded Operators in Isabelle/HOL
Announce Type: replace Abstract: We present a formalization of bounded operators on complex vector spaces in Isabelle/HOL. Our formalization contains material on complex vector spaces (normed spaces, Banach spaces, Hilbert spaces) that complements and goes beyond the developments of real vectors spaces in the Isabelle/HOL standard library. We define the type of bounded operators between complex vector spaces (cblinfun) and develop the theory of unitaries, projectors, extension of bounded...
Boundary-compatible interacting approximations of quasilinear PDEs on bounded domains
arXiv:2606.04049v1 Announce Type: new Abstract: We develop a general operator-theoretic route that turns Kato-type quasilinear evolution systems on a Banach scale $(Z,X)$ into finite-dimensional interacting approximations. The construction proceeds in two steps. First, one introduces a regularized family $(A_\varepsilon,f_\varepsilon)$ indexed by a scale parameter $\varepsilon>0$, for which the drift $A_\varepsilon[t,z]z+f_\varepsilon[t,z]$ takes values in an output space $Y$ suitable for...
Weighted universal approximation of differentiable maps on infinite-dimensional manifolds
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Locally Adaptive Conformal Inference for Operator Models
arXiv:2507.20975v5 Announce Type: replace-cross Abstract: Operator models are regression algorithms between Banach spaces of functions. They have become an increasingly critical tool for spatiotemporal forecasting and physics emulation, especially in high-stakes scenarios where robust, calibrated uncertainty quantification is required. We introduce Local Sliced Conformal Inference (LSCI), a distribution-free framework for generating function-valued, locally adaptive prediction sets for...
Metric-Free Riemannian Optimization
Announce Type: cross Abstract: Riemannian optimization provides a powerful framework for constrained optimization by incorporating problem-specific structure directly into the geometry of the search space. In many applications, however, the explicit evaluation or application of the Riemannian metric can be computationally expensive or numerically unstable, limiting the practical efficiency of otherwise well-founded algorithms. Motivated by such settings, this work investigates to what extent...