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A dichotomy result about Hessenberg matrices associated with measures in the unit circle

We characterize Hessenberg matrices D associated with measures in the unit circle ν, which are matrix representations of compact and actually Hilbert Schmidt perturbations of the forward shift operator as those with recursion coefficients urn:x-wiley:mma:media:mma5716:mma5716-math-0001 verifying urn:x-wiley:mma:media:mma5716:mma5716-math-0002, ie, associated with measures verifying Szegö condition.

Forecasting Promotional Sales within the Neighbourhood

Promotions are a widely used strategy to engage consumers and as such, retailers dedicate immense effort and resources to their planning and forecasting. This paper introduces a novel interpretable machine learning method specifically tailored to the automatic prediction of promotional sales in real-market applications.

Quantum error correction with the semion code

We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double-semion model. We construct open-string operators that recover the quantum memory from arbitrary errors and closed-string operators that implement the basic logical operations for information processing.