Since their inception in the 1930s by von Neumann, operator algebras have been used to shed light on many mathematical theories. Classification results for self-adjoint and non-self-adjoint operator algebras manifest this approach, but a clear connection between the two has been sought since their emergence in the late 1960s. We connect these seemingly separate types of results by uncovering a hierarchy of classification for non-self-adjoint operator algebras and $C^{*}$-algebras with additional $C^{*}$-algebraic structure. Our approach naturally applies to algebras arising from $C^{*}$-correspondences to resolve self-adjoint and non-self-adjoint isomorphism problems in the literature. We apply our strategy to completely elucidate this newly found hierarchy for operator algebras arising from directed graphs.

In text, images, merged surveys, voter files, and elsewhere, data sets are often missing important covariates, either because they are latent features of observations (such as sentiment in text) or because they are not collected (such as race in voter files). One promising approach for coping with this missing data is to find the true values of the missing covariates for a subset of the observations and then train a machine learning algorithm to predict the values of those covariates for the rest. However, plugging in these predictions without regard for prediction error renders regression analyses biased, inconsistent, and overconfident. We characterize the severity of the problem posed by prediction error, describe a procedure to avoid these inconsistencies under comparatively general assumptions, and demonstrate the performance of our estimators through simulations and a study of hostile political dialogue on the Internet. We provide software implementing our approach.

This analysis identifies the significant problem of ambiguity, variation and vagueness in relation to the intervention described as ‘psychotherapy’. Its purpose is to raise international awareness of this problem and alternative solutions.

We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends [C. Bonatti, A. Gogolev, A. Hammerlindl and R. Potrie. Anomalous partially hyperbolic diffeomorphisms III: Abundance and incoherence. Geom. Topol., to appear] to the whole isotopy class. We relate the techniques to the study of certain partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds performed in [T. Barthelmé, S. Fenley, S. Frankel and R. Potrie. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part I: The dynamically coherent case. Preprint, 2019, arXiv:1908.06227; Partially hyperbolic diffeomorphisms homotopic to the identity in dimension 3, part II: Branching foliations. Preprint, 2020, arXiv: 2008.04871]. The appendix reviews some consequences of the Nielsen–Thurston classification of surface homeomorphisms for the dynamics of lifts of such maps to the universal cover.

In some non-international armed conflicts (NIACs) a foreign state is involved in favour of an armed group. This poses a challenge to classifying these armed conflicts under IHL. This article argues that evaluating the actions of a foreign state is best carried out by application of the ‘overall control’ test as developed by the Appeals Chamber of the International Criminal Tribunal for the former Yugoslavia in the Tadić case. The advantages of this approach are twofold. First, it is a more realistic benchmark for generating the required evidence than the complete dependency or effective control tests developed by the International Court of Justice. Second, using this test makes it less likely for a state to escape its responsibilities under IHL when it acts through armed groups in a prima facie NIAC on the territory of another state. To arrive at this conclusion, the article first critically discusses the different control tests. It then advances that Article 4 of Geneva Convention III 1949 and Article 29 of Geneva Convention IV 1949 themselves contain a threshold of control that can be used to identify foreign state participation in a prima facie NIAC.

The differentiation of pathological stress responses from responses that are appropriate and adaptive is a challenge with little to guide the clinician. This refreshment considers adjustment disorder and possible approaches to distinguishing those who have the disorder from those who are responding ‘normally’ to stressful events.

My recent article offered a model by which to better classify feasts by distinguishing between archaeological correlates of group size and sociopolitical competition. Applying this model to remains from a precontact mound site, I highlighted feasting's role in promoting group solidarity in the American South. Hayden's comment argues that my scheme does not accommodate certain types of events, and it questions my noncompetitive interpretation. I address both critiques here by citing further data from the Southeast, emphasizing the importance of interpreting feasts within their cultural and historical contexts, and highlighting Hayden's continued reliance on long-standing assumptions about feasting and monumental architecture.

While melancholic (according to DSM) or somatic syndrome (according to ICD) has strong historical roots and substantial empirical verification, the concept of atypical features is relatively new and not sufficiently studied. The aim of the current study was to investigate the reliability of these diagnostic subcategories in patients suffering from major depression in Greece. Forty patients (eight males and 32 females) aged 19-60 years (mean 39.3, sd 12.2) suffering from major depression according to DSM-IV criteria were studied. SCAN v.2.0 was used to assess symptomatology. The presence of each criterion according to DSM-IV and ICD-10 was registered. Frequency tables were developed and factor and cluster analysis were performed. The results of the analysis suggest the existence of three syndromes which roughly reflect the melancholic and atypical but also propose a third, which can be considered as an ‘undifferentiated’ syndrome. The DSM demand that the existence of melancholic features be excluded first and then that diagnosis of atypical features be made was confirmed.

We examined the item properties of the Two Peas Questionnaire (TPQ) among a sample of same-sex twin pairs from the Washington State Twin Registry. With the exception of the ‘two peas’ item, three of the mistakenness items showed differential item functioning. Results showed that the monozygotic (MZ) and dizygotic (DZ) pairs may differ in their responses on these items, even among those with similar latent traits of similarity and confusability. Upon comparing three classification methods to determine the zygosity of same-sex twins, the overall classification accuracy rate was over 90% using the unit-weighted pair zygosity sum score, providing an efficient and sufficiently accurate zygosity classification. Given the inherent nature of twin-pair similarity, the TPQ is more accurate in the identification of MZ than DZ pairs. We conclude that the TPQ is a generally accurate, but by no means infallible, method of determining zygosity in twins who have not been genotyped.