Management of the high rates of medical and psychiatric complications, including self-harm and suicide, associated with anorexia nervosa requires regular clinical review. However, during the current pandemic, face-to-face clinical assessments carry the risk of infection and transmission in this vulnerable cohort already compromised by low weight and lowered immunity. This paper describes how one service has had to adapt usual care during the COVID-19 pandemic without contributing excessively to carer burden or compromising patient safety.

Let \unicode[STIX]{x1D6E4}\leqslant \text{Aut}(T_{d_{1}})\times \text{Aut}(T_{d_{2}})$\unicode[STIX]{x1D6E4}\leqslant \text{Aut}(T_{d_{1}})\times \text{Aut}(T_{d_{2}})$ be a group acting freely and transitively on the product of two regular trees of degree d_{1}$d_{1}$ and d_{2}$d_{2}$. We develop an algorithm that computes the closure of the projection of \unicode[STIX]{x1D6E4}$\unicode[STIX]{x1D6E4}$ on \text{Aut}(T_{d_{t}})$\text{Aut}(T_{d_{t}})$ under the hypothesis that d_{t}\geqslant 6$d_{t}\geqslant 6$ is even and that the local action of \unicode[STIX]{x1D6E4}$\unicode[STIX]{x1D6E4}$ on T_{d_{t}}$T_{d_{t}}$ contains \text{Alt}(d_{t})$\text{Alt}(d_{t})$. We show that if \unicode[STIX]{x1D6E4}$\unicode[STIX]{x1D6E4}$ is torsion-free and d_{1}=d_{2}=6$d_{1}=d_{2}=6$, exactly seven closed subgroups of \text{Aut}(T_{6})$\text{Aut}(T_{6})$ arise in this way. We also construct two new infinite families of virtually simple lattices in \text{Aut}(T_{6})\times \text{Aut}(T_{4n})$\text{Aut}(T_{6})\times \text{Aut}(T_{4n})$ and in \text{Aut}(T_{2n})\times \text{Aut}(T_{2n+1})$\text{Aut}(T_{2n})\times \text{Aut}(T_{2n+1})$, respectively, for all n\geqslant 2$n\geqslant 2$. In particular, we provide an explicit presentation of a torsion-free infinite simple group on 5 generators and 10 relations, that splits as an amalgamated free product of two copies of F_{3}$F_{3}$ over F_{11}$F_{11}$. We include information arising from computer-assisted exhaustive searches of lattices in products of trees of small degrees. In an appendix by Pierre-Emmanuel Caprace, some of our results are used to show that abstract and relative commensurator groups of free groups are almost simple, providing partial answers to questions of Lubotzky and Lubotzky–Mozes–Zimmer.

Non-n-ampleness as denned by Pillay [20] and Evans [5] is preserved under analysability. Generalizing this to a more general notion of Σ-ampleness, this gives an immediate proof for all simple theories of a weakened version of the Canonical Base Property (CBP) proven by Chatzidakis [4] for types of finite SU-rank. This is then applied to the special case of groups.

Simple games cover voting systems in which a single alternative, such as a bill or anamendment, is pitted against the status quo. A simple game or a yes-no voting system is aset of rules that specifies exactly which collections of “yea” votes yield passage of theissue at hand. Each of these collections of “yea” voters forms a winning coalition. We areinterested in performing a complexity analysis on problems defined on such families ofgames. This analysis as usual depends on the game representation used as input. Weconsider four natural explicit representations: winning, losing, minimal winning, andmaximal losing. We first analyze the complexity of testing whether a game is simple andtesting whether a game is weighted. We show that, for the four types of representations,both problems can be solved in polynomial time. Finally, we provide results on thecomplexity of testing whether a simple game or a weighted game is of a special type. Weanalyze strongness, properness, weightedness, homogeneousness, decisiveness andmajorityness, which are desirable properties to be fulfilled for a simple game. Finally,we consider the possibility of representing a game in a more succinct and natural way andshow that the corresponding recognition problem is hard.

There is an unfortunate error in Theorem 4.1 of our paper. However, the statement of the theorem remains true with a correct construction of adding a tail to enlarge the dynamical system.

We give a new very concrete description of the C*-envelope of the tensor algebra associated to a multivariable dynamical system. In the surjective case, this C*-envelope is described as a crossed product by an endomorphism and as a groupoid C*-algebra. In the non-surjective case, it is a full corner of such an algebra. We also show that when the space is compact the C*-envelope is simple if and only if the system is minimal.

This paper deals with the SIMPLE-DK lexicon, a computational lexicon for Danish developed at the Centre for Language Technology in Copenhagen within the European Union project SIMPLE. The general SIMPLE model, on which the Danish lexicon is based, is presented, and the way in which several specific aspects of Danish, such as nominal compounds and time expressions, are accommodated in this model is then described. Phrasal verbs – in particular phrasal motion verbs – are shown to be a challenging phenomenon since they are difficult to place in the SIMPLE event ontology, and pose problems regarding the interpretation of the directional particle they combine with. The encoding strategy that is proposed here accounts for compositional and non-compositional types of phrasal verb, and captures the relation between act-denoting and transition-denoting senses of the same verb in terms of regular polysemy. The final part of the paper deals with the exploitation of SIMPLE-DK as an ontological and lexical source in the Danish project on content-based querying OntoQuery. In the OntoQuery ontology, the structured concepts in SIMPLE-DK are combined with nutrition concepts, and the resulting ontology is used for matching evaluation. It is also discussed how selectional restrictions and qualia roles from SIMPLE-DK can be included in a conceptual grammar to be used for query and text analysis.

A type analysable in one-based types in a simple theory is itself one-based.

We study smooth classes without the algebraic closure property. For such smooth classes we investigate the simplicity of the class of generic structures, in the context of Robinson theories.