Norm-Controlled Inversion in Smooth Banach Algebras, I

Every differential subalgebra of a unital $C^*$-algebra is spectrally invariant. We derive a quantitative version of this well-known fact and show that a minimal amount of smoothness, as given by a differential norm, already implies norm control. We obtain an explicit estimate for the differential norm of an invertible element $a$. This estimate depends only on the condition number of $a$ and the ratio of two norms

Spectral invariance of Besov–Bessel subalgebras

AbstractUsing principles of the theory of smoothness spaces, we give systematic constructions of scales of inverse-closed subalgebras of a given Banach algebra with the action of a d-parameter automorphism group. In particular, we obtain the inverse-closedness of Besov algebras, Bessel potential algebras and approximation algebras of polynomial order in their defining algebra. By a proper choice of the group action, these general results can be applied to algebras of infinite matrices and yield inverse-closed subalgebras of matrices with off-diagonal decay of polynomial order. Besides alternative proofs of known results we obtain new classes of inverse-closed subalgebras of matrices with off-diagonal decay.This work is a continuation and extension of results presented by Gröchenig and Klotz (2010) [23]

Conformal Prediction for Time Series with Modern Hopfield Networks

To quantify uncertainty, conformal prediction methods are gaining continuously more interest and have already been successfully applied to various domains. However, they are difficult to apply to time series as the autocorrelative structure of time series violates basic assumptions required by conformal prediction. We propose HopCPT, a novel conformal prediction approach for time series that not only copes with temporal structures but leverages them. We show that our approach is theoretically well justified for time series where temporal dependencies are present. In experiments, we demonstrate that our new approach outperforms state-of-the-art conformal prediction methods on multiple real-world time series datasets from four different domains.Comment: presented at NeurIPS 202

Causing factors, outcomes, and governance of Shadow IT and business-managed IT: a systematic literature review

Shadow IT and Business-managed IT describe the autonomous deployment/procurement or management of Information Technology (IT) instances, i.e., software, hardware, or IT services, by business entities. For Shadow IT, this happens covertly, i.e., without alignment with the IT organization; for Business-managed IT this happens overtly, i.e., in alignment with the IT organization or in a split responsibility model. We conduct a systematic literature review and structure the identified research themes in a framework of causing factors, outcomes, and governance. As causing factors, we identify enablers, motivators, and missing barriers. Outcomes can be benefits as well as risks/shortcomings of Shadow IT and Business-managed IT. Concerning governance, we distinguish two subcategories: general governance for Shadow IT and Business-managed IT and instance governance for overt Business-managed IT. Thus, a specific set of governance approaches exists for Business-managed IT that cannot be applied to Shadow IT due to its covert nature. Hence, we extend the existing conceptual understanding and allocate research themes to Shadow IT, Business-managed IT, or both concepts and particularly distinguish the governance of the two concepts. Besides, we find that governance themes have been the primary research focus since 2016, whereas older publications (until 2015) focused on causing factors