Let A be any universal algebra. We say formula A is explicitly expressible on algebra A via system of formulas Σ, if A can be obtained on A of variables and formulas of Σ by means of superpositions. We say a system of formulas Σ is complete in A, if any formula is expressible via Σ. We say a system Σ is precomplete as to expressibility on A if Σ is not complete on A, but for any formula F , whi...

BACKGROUND The aim was to evaluate the efficacy of periocular intense pulsed light therapy combined with meibomian gland expression for chronic dry eye due to moderate to advanced meibomian gland dysfunction. METHODS This single-institution, open-label prospective study involved 26 participants who received bilateral treatments using a proprietary intense pulsed light device (E > Eye, E-Swin,...

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Abstract Random quantum circuits have been utilized in the contexts of supremacy demonstrations, variational algorithms for chemistry and machine learning, blackhole information. The ability random to approximate any unitaries has consequences on their complexity, expressibility, trainability. To study this property circuits, we develop numerical protocols estimating frame potential, distance b...

KAPLAN’S PUZZLE, DYNAMIC SENSES, AND DIACHRONIC PROPOSITIONS ! by ! Jack Kingston !! The University of Wisconsin-Milwaukee, 2014 Under the Supervision of Professor Michael N. Liston ! The Fregean encounters a few interconnected problems in his account of indexical sentences, each posed in one way or another by Kaplan’s puzzle of cognitive dynamics. For one, there’s a problem defending the doctr...

Rewriting Systems. An abstract rewriting system (ARS) is a quadruple ⟨A,Φ, src, tgt⟩ consisting of a set A of objects, a set Φ of steps, and src, tgt ∶ Φ → A, the source and target functions. We will always assume that A ∩Φ = ∅. For objects a ∈ A we denote by Φout(a) and by Φin(a) the set of steps in Φ that depart (are outgoing steps) Clemens Grabmayer and Jan Rochel 4 from a, and that arrive (...