Skew-closed categories

Spurred by the new examples found by Kornel Szlach\'anyi of a form of lax monoidal category, the author felt the time ripe to publish a reworking of Eilenberg-Kelly's original paper on closed categories appropriate to the laxer context. The new examples are connected with bialgebroids. With Stephen Lack, we have also used the concept to give an alternative definition of quantum category and quantum groupoid. Szlach\'anyi has called the lax notion {\em skew monoidal}. This paper defines {\em skew closed category}, proves Yoneda lemmas for categories enriched over such, and looks at closed cocompletion.Comment: Version 2 corrects a mistake in axiom (2.4) noticed by Ignacio Lopez Franco. Only the corrected axiom was used later in the paper so no other consequential change was needed. A few obvious typos have been corrected. Some material on weighted colimits, composite modules and skew-promonoidal categories has been added. Version 3 adds Example 23 and corrects a few typos.

Closed-loop Identification of an Industrial Extrusion Process

This paper deals with the challenging problem of closed-loop identification for multivariable chemical processes and particularly the estimation of an open-loop plant model for a lab-scale industrial twin-screw extruder used in a powder coatings manufacturing line. The aim is to produce a low order efficient model in order to assist the scaling-up and the model-based control design of the manufacturing process. To achieve this goal, a two-stage indirect approach has been deployed which relies on the a-priori knowledge of the controller parameters in order to extract good estimates of the open-loop dynamics of the underlying process. As input excitation signals we have used multiple single variable step tests at various operating conditions (current industrial practice) carried out manually in order to generate the data-set which captures the dynamics of the extrusion process. In order to increase the efforts for obtaining a suitable plant model, we have employed various identification techniques, such as Prediction Error Methods (PEM) and Subspace Identification Methods (SIM) in order to generate candidate closed-loop models that fit to the original input-output process data. Then, a comparison of the estimated models was performed by means of the mean square error and data fitting criteria in order to select the model that best describes the dynamic behaviour of the extrusion process. Model validation based on closed-loop step responses also used as verification of the results

Closed timelike curves and chronology protection in quantum and classical simulators

In principe, General Relativity seems to allow the existence of closed timelike curves (CTC). However, when quantum effects are considered, it is likely that their existence is prevented by some kind of chronological protection mechanism, as Hawking conjectured. Confirming or refuting the conjecture would require a full quantum theory of gravity. Meanwhile, the use of simulations could shed some light on this issue. We propose simulations of CTCs in a quantum system as well as in a classical one. In the quantum simulation, some restrictions appear that are not present in the classical setup, which could be interpreted as an analogue of a chronology protection mechanism.Comment: 6 pages, 4 figures. v2: published versio

Geometrically closed rings

We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several connections between finitely presented rings and ultraproducts, affine varieties and definable sets, and we introduce the key notion of an arithmetic theory as a purely algebraic version of coherent logic for rings.Comment: 18 page