Menger systems of idempotent cyclic and weak near-unanimity multiplace functions

Multiplace functions, which are also called functions of many variables, and their algebras called Menger algebras have been studied in various fields of mathematics. Based on the theory of many-sorted algebras, the primary aim of this paper is to present the ideas of Menger systems and Menger systems of full multiplace functions which are natural generalizations of Menger algebras and Menger algebras of [Formula: see text]-ary operations, respectively. Two specific types of [Formula: see text]-ary operations, which are called idempotent cyclic and weak near-unanimity generated by cyclic and weak near-unanimity terms, are provided. The Menger algebras under consideration have a two-element universe, the elements of which are two specific [Formula: see text]-ary operations. Additionally, we provide necessary and sufficient conditions in which the abstract Menger algebra and the Menger algebras of these two [Formula: see text]-ary operations are isomorphic. An abstract characterization of unitary Menger systems via systems of idempotent cyclic and weak near-unanimity multiplace functions is generally investigated. A strong connection between clone of terms and Menger systems of full multiplace functions is also investigated.

What’s so special about born globals, their entrepreneurs or their business model?

There is near unanimity among international business scholars that it takes more time to expand internationally than domestically. Hence, this is why some are puzzled by born globals (BGs), firms that make large foreign sales at birth or shortly afterwards. Explanations given for this “anomaly” are that BGs have exceptional resources—advanced technologies and a high international orientation on the part of their entrepreneurs, and that they rely on cheaper internationalization strategies like the Internet and networks. What is almost completely overlooked is the role of the BG’s business model (BM). We analyze the time it took for a sample of Italian SMEs to reach BG status (25% foreign over total sales) within a three-year time span. Entering both international entrepreneurship (IE) and BM variables, we find that, among the IE variables, a firm’s technological intensity, the number of years their founders studied abroad and their foreign language fluency, as well as their use of domestic networks, are statistically insignificant. Variables measuring a firm’s focus on a niche BM, on the other hand, are statistically significant, along with the international work experience of the founders, with the niche BM explaining a higher level of variance with greater accuracy.

Delphi consensus survey on how to document bilingual experience

While most investigations of bilingualism document participants’ language background, there is an absence of consensus on how to quantify bilingualism. The high number of different language background questionnaires used by researchers and practitioners jeopardises data comparability and cross-pollination between research and practice. Using the Delphi method, we asked 132 panellists (researchers, speech and language therapists, teachers) from 29 countries to rate 124 statements on a 5-point agreement scale. Consensus was pre-defined as 75% agreement threshold. After two survey rounds, 79% of statements reached consensus, revealing near-unanimity regarding the need for common methods to quantify bilingualism. Agreement was reached to document: language exposure and use, language difficulties, proficiency (when it cannot be assessed directly), education and literacy, input quality, language mixing practices, and attitudes (towards languages and language mixing). We discuss the implications of these findings for the creation of a new tool to quantify bilingual experience.

The Ordinary Legislative Procedure in a Post-Brexit EU: The Case of Social Europe

This article assesses the political and power dynamics of the Ordinarily Legislative Procedure (OLP) in social Europe and the likely impact of the UK’s departure in the field for future integration. It provides a detailed analysis of the OLP in social Europe during two recent periods of integration in the field—the first Barroso Commission (2004–2009) and the Juncker Commission (2014–2019). It finds the dynamics of the OLP have shifted from intergovernmental deadlock during the Barroso Commission to the characteristics of a new intergovernmental core state power during the Juncker Commission, even though the policy area is not a core state power <em>per se</em>. Despite the use of qualified majority voting policy agreements can only be achieved when there is near unanimity support in the Council, the Commission remains a neutral broker, and the Parliament shifts its position to that of the Council. As a result, continued opposition to integration in social Europe by Northern and Eastern Members means the removal of UK political agency will have only a marginal impact on the slow and piecemeal approach to integration in the field.

Galois Connections for Patterns: An Algebra of Labelled Graphs

A pattern is a generic instance of a binary constraint satisfaction problem (CSP) in which the compatibility of certain pairs of variable-value assignments may be unspecified. The notion of forbidden pattern has led to the discovery of several novel tractable classes for the CSP. However, for this field to come of age it is time for a theoretical study of the algebra of patterns. We present a Galois connection between lattices composed of sets of forbidden patterns and sets of generic instances, and investigate its consequences. We then extend patterns to augmented patterns and exhibit a similar Galois connection. Augmented patterns are a more powerful language than flat (i.e. non-augmented) patterns, as we demonstrate by showing that, for any $$k \ge 1$$ k ≥ 1 , instances with tree-width bounded by k cannot be specified by forbidding a finite set of flat patterns but can be specified by a finite set of augmented patterns. A single finite set of augmented patterns can also describe the class of instances such that each instance has a weak near-unanimity polymorphism of arity k (thus covering all tractable language classes).We investigate the power of forbidding augmented patterns and discuss their potential for describing new tractable classes.

Cohorting of Non-Critically Ill COVID-19 Patients: A Multicenter Survey Study (COVID-COHORT)

The COVID-19 pandemic has posed novel infection-control challenges for hospitals around the globe. One infection-control strategy that has been widely used in the context of other outbreaks is patient cohorting. This strategy refers to the placement of all patients exposed to the same laboratory-confirmed infectious agent in one location within the hospital. Little is known about the current utilization of this strategy with non-critically ill COVID-19 patients. An international multicenter, survey study was conducted to identify what strategies are planned or in place for patients with COVID-19 who are not critically ill. The survey was distributed from March 23-29th, 2020 to GIM physicians in Canada, USA, Denmark, Singapore, Hong Kong, and England. Of the 31 hospitals, 29 (94%) indicated that they plan on cohorting all GIM patients with COVID-19 to one location in the hospital. Among these 29 hospitals, 23 (79%) had implemented the plan at the time of the survey. The primary reasons for this decision were to limit the spread of COVID-19 and conserve PPE use. In conclusion, in the face of a novel virus there is near unanimity in the practice of patient cohorting as a potential mitigation strategy.

THE DISTRIBUTIVITY SPECTRUM OF BAKER’S VARIETY

For every n, we evaluate the smallest k such that the congruence inclusion $\alpha (\beta \circ _n \gamma ) \subseteq \alpha \beta \circ _{k} \alpha \gamma $ holds in a variety of reducts of lattices introduced by K. Baker. We also study varieties with a near-unanimity term and discuss identities dealing with reflexive and admissible relations.

n-Permutability is not join-prime for n ≥ 5

Let [Formula: see text] be the variety generated by an order primal algebra of finite signature associated with a finite bounded poset [Formula: see text] that admits a near-unanimity operation. Let [Formula: see text] be a finite set of linear identities that does not interpret in [Formula: see text]. Let [Formula: see text] be the variety defined by [Formula: see text]. We prove that [Formula: see text] is [Formula: see text]-permutable for some [Formula: see text]. This implies that there is an [Formula: see text] such that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties. In fact, it follows that [Formula: see text]-permutability where [Formula: see text] runs through the integers greater than 1 is not prime in the lattice of interpretability types of varieties. We strengthen this result by making [Formula: see text] and [Formula: see text] more special. We let [Formula: see text] be the 6-element bounded poset that is not a lattice and [Formula: see text] the variety defined by the set of majority identities for a ternary operational symbol [Formula: see text]. We prove in this case that [Formula: see text] is 5-permutable. This implies that [Formula: see text]-permutability is not join-prime in the lattice of interpretability types of varieties whenever [Formula: see text]. We also provide an example demonstrating that [Formula: see text] is not 4-permutable.