We study the noise sensitivity of the minimum spanning tree (MST) of the $n$-vertex complete graph when edges are assigned independent random weights. It is known that when the graph distance is rescaled by $n^{1/3}$ and vertices are given a uniform measure, the MST converges in distribution in the Gromov–Hausdorff–Prokhorov (GHP) topology. We prove that if the weight of each edge is resampled independently with probability $\varepsilon \gg n^{-1/3}$, then the pair of rescaled minimum spanning trees – before and after the noise – converges in distribution to independent random spaces. Conversely, if $\varepsilon \ll n^{-1/3}$, the GHP distance between the rescaled trees goes to $0$ in probability. This implies the noise sensitivity and stability for every property of the MST that corresponds to a continuity set of the random limit. The noise threshold of $n^{-1/3}$ coincides with the critical window of the Erdős-Rényi random graphs. In fact, these results follow from an analog theorem we prove regarding the minimum spanning forest of critical random graphs.

Hagiographical writing promotes a vision of Egyptian monasticism in which pious ascetic figures are isolated from the world. Peter Brown highlighted the role of the holy man as patron, but nonetheless reinforced a traditional view of Egyptian monasticism based on his readings of works such as the sixth-century Aphothegmata Patrum. Surviving monastic correspondence, in contrast, demonstrates that there was a highly individualized approach to the monastic vocation. In this article, I turn to documentary material to consider the complexities of the early development of the movement. As a case study, I use the Greek and Coptic correspondence of a fourth-century monk called Apa John. My conclusion is that activities and behaviours described in the texts do not always accord with any known typology or ideal, but they are invaluable for exploring aspects of the early monastic impulse and the role played by the movement in wider society.

Bedford and Smillie [A symbolic characterization of the horseshoe locus in the Hénon family. Ergod. Th. & Dynam. Sys. 37(5) (2017), 1389–1412] classified the dynamics of the Hénon map $f_{a, b} : (x, y)\mapsto (x^2-a-by, x)$ defined on $\mathbb {R}^2$ in terms of a symbolic dynamics when $(a, b)$ is close to the boundary of the horseshoe locus. The purpose of the current article is to generalize their results for all $b\ne 0$ (including the case $b < 0$ as well). The method of the proof is first to regard $f_{a, b}$ as a complex dynamical system in $\mathbb {C}^2$ and second to introduce the new Markov-like partition in $\mathbb {R}^2$ constructed by us [On parameter loci of the Hénon family. Comm. Math. Phys. 361(2) (2018), 343–414].

This article explores the theme of hypocrisy in a multi-volume collection of hitherto unstudied manuscript sermons by Exeter Dissenting ministers from the Restoration to the mid-eighteenth century, held by the Devon and Exeter Institution. In these sermons, the theme of hypocrisy is addressed in a variety of senses and contexts, including the imposition by conformists of forms of worship not required by Scripture; the false accusations of hypocrisy made against Dissenters; the insincere performance of piety; the tendency of sinners to justify vice as virtue and virtue as vice; and the incompatibility of persecution with true New Testament Christianity. These sermons trace a move from Reformed orthodoxy towards rational Dissent, with a soteriology that increasingly makes moral performance a condition of final salvation. The possibility of insincere performance of piety and virtue by hypocrites may have created increased anxiety in a context in which soteriology and ethics were increasingly entangled.

Many scholars have told the story of how John Davenport (bap. 1597, d. 1670), a prominent Congregationalist minister in New England, was fatally discredited as a fraudster when a letter he had forged was exposed in 1669. However, no one has analyzed how this extraordinary scandal fits into the larger narrative of puritan providentialism and its disenchantment. Focusing on the manipulation of providential language, this article shows that intra-Congregationalist conflicts over church polity could often be more political than theological. God-talk, or ‘providential pragmatism’, empowered New Englanders to navigate the ecclesiological ambiguities inherent in the Congregational system in a way that most benefited themselves. Davenport's scandal, precisely because it was the most blatant form of such pragmatism, offers a case study of a pattern of self-contradiction and double standard already observable in similar cases of schisms over church membership and infant baptism in late seventeenth-century New England.

The status of hypocrisy as a vice has varied historically, but analysis has tended to stress the issue in relation to individuals, rather than institutions. Taking Judith Shklar and Boccaccio as points of departure, this article explores how and why hypocrisy mattered in the context of the early fourteenth-century church. Analysing charges of hypocrisy made by and against Pope Boniface VIII at the papal Curia; Angelo Clareno within the Franciscan Order; and the later Capetian court in relation to the Roman de Fauvel allows us to see how anxiety about hypocrisy became especially acute across a range of early fourteenth institutions. Contemporaries questioned what their institutions meant and increasingly put their claims to the test, often in heightened apocalyptic terms. In and around the early fourteenth-century church, worry about institutional hypocrisy shows how responsibility was increasingly on trial.

This article considers The Turncoats (1711), an anti-Dissent graphic satire published after the Tory victory in the 1710 General Election. The print ridiculed the hypocrisy of those Dissenters who abandoned their principles and conformed to the Church of England after that election, and pointed to the pervasiveness of religious hypocrisy in early eighteenth-century England more generally. This article contextualizes the print within the tense religious and political rivalries that developed after the 1688 Revolution and the trial of Henry Sacheverell. The Turncoats’ ridicule resonated because it built on older traditions of stereotypes in anti-popery and anti-puritanism, which used mockery to attack those perceived to be hypocrites. Mockery is analyzed by considering how early modern culture understood laughter. It is argued that ridicule in The Turncoats expressed superiority over hypocrites by subjecting them to contempt and provided relief from anxieties about the prevalence of hypocrisy during the rage of parties.

Let $\mathbf {D}$ be a bounded homogeneous domain in ${\mathbb {C}}^n$. In this note, we give a characterization of the Stein domains in $\mathbf {D}$ which are invariant under a maximal unipotent subgroup N of $Aut(\mathbf {D})$. We also exhibit an N-invariant potential of the Bergman metric of $\mathbf {D}$, expressed in a Lie theoretical fashion. These results extend the ones previously obtained by the authors in the symmetric case.

The political messaging of Leoluca Orlando, who served five terms as mayor of Sicily's capital, Palermo (most recently, until 2022), articulates a cosmopolitan vision of local identity. Orlando seeks to emphasise Palermo's ‘tolerant’ values, invoking the city's history to foster this image, as well as using a variety of rhetorical strategies. He portrays Palermo as having a true ‘essence’, which is necessarily multicultural. I analyse Orlando's pronouncements on his official Facebook page, as well as observing his audience's reactions to his messaging, both supportive and critical. I examine how Orlando articulates the narrative that Palermo has historically been a ‘mosaic’ of various cultural influences, proposing that the contemporary city is the ‘true’, welcoming face of the Mediterranean. As well as exploring the political utility Orlando sees in such arguments, I analyse the risks inherent in this essentialising project.

During the antebellum period and American Civil War, ‘puritan’ was a contested identity, fraught with layers of meaning and interpretation. Historians have charted the ways Southern intellectuals cast the differences between North and South as an outplaying of the old conflict between Cavalier and puritan. This article highlights the ways Southern ministers claimed the puritan identity for the South and accused the North of hypocrisy, for having fallen far from the theological ideals of their puritan forebears. Furthermore, Southern ministers noted the hypocrisy of Northern puritans for having escaped religious tyranny only to impose it upon those who did not conform to their form of Christianity; they had thus fallen into the very sin which they had decried. This came from Southern ministers whose attempt to appropriate the memory of puritanism as liberty-loving revealed their own hypocrisy in fighting for the ‘liberty’ to maintain a system of racial slavery.

The brief but bitter campaign to expose the hidden homosexuality of Anglican bishops in the mid-1990s was framed as a contest about hypocrisy, with bishops – whether suspected of homosexuality or not – condemned as hypocrites, and the Church of England as hypocritical. However, the activists behind this ‘outing’, and the media which covered the story with such enthusiasm, were similarly attacked for hypocrisy. A neglected moment in recent ecclesiastical history, it reveals the ongoing importance of hypocrisy in debates about the nature of faith and the authority of the church. Still more, it sheds light on how contemporary assumptions about authenticity both intensified the perceived importance of hypocrisy and increased the chances of being accused of acting hypocritically.

While nonspeech communication and “metaphorical” silence (in opposition to voice) have benefited from a considerable academic attention, less is known about quiet environments and the intentional practice of silence. We theorize these silences as potential catalysts of internal and collective reflection. Such silences can strongly impact individual and organizational processes and outcomes, notably in the workplace. The meaning, valence, and effects of these silences are highly context- and perspective-dependent. By characterizing and studying these silences and their effects, we show how they are functional or dysfunctional to individuals or organizations. These silences can notably serve as emotion regulators and generate an environment favorable to individual and collective decision making. Examining what is lost by individuals and organizations due to a lack of these silence and what can be gained with a better harnessing of their power is promising.