Let g be an element of a group G. For a positive integer n, let $R_n(g)$ be the subgroup generated by all commutators $[\ldots [[g,x],x],\ldots ,x]$ over $x\in G$, where x is repeated n times. Similarly, $L_n(g)$ is defined as the subgroup generated by all commutators $[\ldots [[x,g],g],\ldots ,g]$, where $x\in G$ and g is repeated n times. In the literature, there are several results showing that certain properties of groups with small subgroups $R_n(g)$ or $L_n(g)$ are close to those of Engel groups. The present article deals with orderable groups in which, for some $n\geq 1$, the subgroups $R_n(g)$ are polycyclic. Let $h\geq 0$, $n>0$ be integers and G be an orderable group in which $R_n(g)$ is polycyclic with Hirsch length at most h for every $g\in G$. It is proved that there are $(h,n)$-bounded numbers $h^*$ and $c^*$ such that G has a finitely generated normal nilpotent subgroup N with $h(N)\leq h^*$ and $G/N$ nilpotent of class at most $c^*$. The analogue of this theorem for $L_n(g)$ was established in 2018 by Shumyatsky [‘Orderable groups with Engel-like conditions’, J. Algebra 499 (2018), 313–320].

Political scientists regularly rely on a selection-on-observables assumption to identify causal effects of interest. Once a causal effect has been identified in this way, a wide variety of estimators can, in principle, be used to consistently estimate the effect of interest. While these estimators are all justified by appeals to the same causal identification assumptions, they often differ greatly in how they make use of the data at hand. For instance, methods based on regression rely on an explicit model of the outcome variable but do not explicitly model the treatment assignment process, whereas methods based on propensity scores explicitly model the treatment assignment process but do not explicitly model the outcome variable. Understanding the tradeoffs between estimation methods is complicated by these seemingly fundamental differences. In this paper we seek to rectify this problem. We do so by clarifying how most estimators of causal effects that are justified by an appeal to a selection-on-observables assumption are all special cases of a general weighting estimator. We then explain how this commonality provides for diagnostics that allow for meaningful comparisons across estimation methods—even when the methods are seemingly very different. We illustrate these ideas with two applied examples.

This essay takes as its point of departure the so-called ‘Verdi A’, 432Hz. From the late 1860s through to the 1880s, the opera composer was intensely preoccupied with the question of tuning, weighing in several times on the matter of where A should sit. Verdi was concerned for the strain that high tunings should place on singers’ voices. He advocated on multiple occasions for global acceptance of an A well below 440, and sent Arrigo Boito to argue in favour of A=432 at the Congresso dei Musicisti Italiani, held in Milan on 16–21 June 1881. In the 1880s, Italy remained one of the only nations in Europe that had not adopted equal temperament wholesale for fixed-tone instruments; as in the case of its spoken languages during this same period, and the locations of its A, temperament varied by region, with the southern part of the peninsula clinging to meantones. This article argues that ‘Verdi tuning’ represents the end point of a number of longer shifts in the conceptualization of musical sound, particularly in the Italian context: from temperament to tuning (accordatura); from relative conceptions of musical pitch to an absolute one; from local and regional variations towards a standardized system; from an older notion of all-encompassing nature to a presumed separation between nature and culture. Tracing this history through the Italian long nineteenth century will involve concentrating on what this article calls music-adjacent sound: that is, interrogative play with musical pitch; sound experiments from musical materials and operatic voices; instrument tuning by ear; listening for overtones; legislating preferred ratios and (eventually) frequencies for musical use; and constructing a theory of music that draws together these means of sounding. Music-adjacent sound is where the conditions for music-making were and still are established. This article argues that an attention to these sonic and nearly musical moments can demonstrate how listening and the musical imagination were cultivated outside the boundaries of any work or performance.

In this editorial, we draw insights from a special collection of peer-reviewed papers investigating how new data sources and technology can enhance peace. The collection examines local and global practices that strive towards positive peace through the responsible use of frontier technologies. In particular, the articles of the collection illustrate how advanced techniques—including machine learning, network analysis, specialised text classifiers, and large-scale predictive analytics—can deepen our understanding of conflict dynamics by revealing subtle interdependencies and patterns. Others assess innovative approaches reinterpreting peace as a relational phenomenon. Collectively, they assess ethical, technical, and governance challenges while advocating balanced frameworks that ensure accountability alongside innovation. The collection offers a practical roadmap for integrating technical tools into peacebuilding to foster resilient societies and non-violent conflict transformations.

Would you prioritize assembling a group of more competent individuals or a more diverse group? According to the well-known Diversity-Trumps-Ability Theorem (DTA), when two groups of similar size are compared, the more diverse group generally outperforms the more competent group. Despite considerable criticism regarding the DTA’s mathematical rigor, it has sparked substantial interdisciplinary discussion. While most research on the DTA focuses on its implications within specific fields or on empirical simulations to test its validity, we aim to establish precise conditions under which diversity indeed surpasses ability in a particular decision-making context: voting. To this end, we integrate the DTA into a voting model inspired by the Condorcet Jury Theorem (CJT) and model diversity based on the classic dependency model in the CJT literature, namely the influence of an opinion leader.

Numerous studies show that women are less likely than men to express attitudes and opinions about politics. To explore the origins of this gender gap, we use data from a series of surveys of the general public and international relations scholars in the United States between 2014 and 2023. These data show that the gender gap in political expression exists, even among knowledge elites; female IR scholars say they don’t know the answer to survey questions at higher rates than their male colleagues. We also find that differences in political knowledge explain a significant part of the gap in political expression; the highly educated female scholars we surveyed were less likely than women in the general public to say they didn’t know the answer to survey questions. At the same time, factors other than knowledge, including confidence, also matter. Our public opinion survey shows that women select extreme answers, such as “strongly agree/disagree” rather than simply “agree/disagree,” at lower rates than men. Despite high levels of education among the female scholars we surveyed, they too are more hesitant than their male counterparts to select extreme answers. These findings have important implications for civic participation as well as for the recognition of women’s expertise within the academy and society more broadly.

This paper examines how, in politically polarized contexts, people reconstruct the biographies of contested memorialized figures to challenge or reproduce dualistic metanarratives of national history. We analyze two sites of recent controversy in Scotland and Lithuania which have been engaged in struggles over how to memorialize individuals who, at various points in their lives, engaged in acts of both anti-imperial resistance and collaboration in those same empires’ systems of oppression. Their moral liminality—a term we employ to refer to the transgression of moral categories—blurs the boundaries between perpetrators and victims of imperial violence, calling into question binary frameworks underpinning broader national narratives. Based on a comparative media analysis of debates over the legacies of David Livingstone and Jonas Noreika, we find that though some people in both Scotland and Lithuania have embraced these figures’ moral liminality, others have, instead, suppressed aspects of their biographies to uphold traditional distinctions between national “heroes” and foreign “villains.” We argue that such moral binaries are either blurred or reproduced through the manipulation of three aspects of liminal figures’ biographical records: their agency, motives, and social impact.

The boom in survey experiments in international relations has allowed researchers to make causal inferences on longstanding foreign policy debates such as democratic peace, and audience costs. However, most of these experiments rely on mass samples, whereas foreign policy is arguably more technocratically driven. We probe the validity of generalizing from mass to elite preferences by exploring preferences of ordinary U.S. citizens and foreign policy experts (employees of the U.S. Department of State) in two identical conjoint experiments on democratic peace. We find that experts are not only more opposed to military actions against other democracies than members of the public—but also that overall preferences about the matters of war and peace are stronger among foreign policy professionals.

Though the use of court documents as data is widespread within US sociolegal scholarship, their use remains surprisingly undertheorized as a methodological practice. This article, therefore, asks, what differentiates court materials from other forms of documentary data, and how do these attributes impact claimsmaking in law and society scholarship? Drawing on varied empirical examples from existing scholarship, we uncover five distinctive attributes: their multitemporality, their dialogic nature, the multiple truths they house, their multivocality, and their social productivity. Considering these attributes, we argue that court documents unite our diverse field of scholarship in two important ways. First, as an essential output of the legal system, they are arguably “our” data, shaping law and society as we know it today. Second, they both reify and obscure the power dynamics that make social inequality so durable, helping inequality appear “just.” Despite their underexploited promise for theory-building in sociolegal research, we also discuss the practical, epistemic, and ethical pitfalls to their use. Ultimately, ignoring these rich yet complex documents is to our field’s analytic peril.

In this article, I argue that the musical landscape in Panama during the nineteenth century was much more active, diverse and globally connected than previously observed by authors of traditionally accepted music historiography of the country. Particularly, I discuss the heightened activity in the second half of the century through primary sources concerning violinist Miguel Iturrado (d. 1879). I further argue that the violin culture fostered by Iturrado and his contemporaries became a solid platform for cultural exchange which allowed for the development of early-twentieth-century music production in Panama. I conclude that the flourishing of numerous fin-de-siècle concert violinists, as well as the advent of the violinist-composers of dance music now known as the Azuero School in the first third of twentieth-century Panama, are directly related to Iturrado’s –and his colleagues’– musical and cultural achievements.

Discourse on the existence of Ghanaian English (GhE) has provided several works leading to the descriptions of GhE pronunciations, especially vowels. However, the major challenge is that most of these studies, impressionistically, have provided different numbers of the English monophthongal vowels used in the Ghanaian context and often discount the existence of certain vowels used in GhE. Consequently, the present study employed the acoustic approach to investigate the English monophthongs produced by 40 educated Ghanaian speakers of English. The purposive sampling was used to select those with first degree to study. The descriptive research design was used to study the formant one and two of the vowels. The vowels were studied within three different contextual realisations: in citation, in sentences and in spontaneous speech. The results revealed that the Ghanaian speakers of English employed in this study realised the English vowels /iː, ɪ, e, a, ɑː, ɒ, ɔː, ʊ, uː ʌ, ə/. The /ɜː/ vowel was shortened while the /æ/ was replaced with the /a/ vowel. This suggests that most of the Ghanaian speakers of English in this study could produce more RP vowels, contrary to earlier studies.

Barricaded incidents, hostage-taking and sieges occur in the community, where police negotiators are usually called on to bring about a peaceful resolution. They occur also in prisons and psychiatric hospitals, where they will be managed by the institution’s staff, with police support if needed. Psychiatrists and other mental health professionals have been involved in providing training and on-call support for negotiators and decision makers in these crisis situations. This article describes definitions and goals in relation to such incidents, and outlines a five-phase framework for their management (training; first responders, preliminary interventions and inquiries; negotiations; resolution; aftercare), indicating the psychiatrist’s role during each phase. Ethical issues are also discussed.

A central question in foreign language (LX) learning is how vocabulary acquisition is affected by using image versus orthographic referents. According to the picture superiority effect (PSE) and bilingual/dual coding theory (b/DCT), images should lead to better novel word encoding and retrieval. We tested this prediction using behavioral and event-related potential (ERP) measures. Thirty Polish native speakers learned 40 LX (artificial language) words using either image or L1/orthographic referents. After 24 hours, participants were tested using a translational priming paradigm in congruent and incongruent training-testing modalities. Behavioral results showed higher accuracy and faster responses for LX words learned and tested with images, in line with the PSE and b/DCT. ERP results revealed smaller Late Positive Complex (LPC) amplitudes for words preceded by image compared to lexical primes, likely reflecting less cognitively demanding lexical retrieval. These results provide converging evidence that visual referents provide a more salient modality for L2 learning.