We find that firms enlarge the executive pay gap when executive mobility is constrained by more enforceable noncompete agreements. We interpret this finding as evidence that firms increase tournament incentives to keep executives incentivized after the loss of valuable outside employment options. Consistent with this argument, we observe more significant increases in pay gaps for executives with greater ex ante mobility options. However, shocks reducing enforceability have a weaker, less robust impact on pay gaps, contributing to asymmetric effects. Following restrictions to mobility, equity portfolios that long (short) firms that boost (do not boost) executive pay gaps generate positive alphas.

We prove an ergodic theorem for Markov chains indexed by the Ulam–Harris–Neveu tree over large subsets with arbitrary shape under two assumptions: (i) with high probability, two vertices in the large subset are far from each other, and (ii) with high probability, those two vertices have their common ancestor close to the root. The assumption on the common ancestor can be replaced by some regularity assumption on the Markov transition kernel. We verify that these assumptions are satisfied for some usual trees. Finally, with Markov chain Monte Carlo considerations in mind, we prove that when the underlying Markov chain is stationary and reversible, the Markov chain, that is the line graph, yields minimal variance for the empirical average estimator among trees with a given number of nodes. In doing so, we prove that the Hosoya–Wiener polynomial is minimized over $[{-}1,1]$ by the line graph among trees of a given size.

We analyse a Markovian SIR epidemic model where individuals either recover naturally or are diagnosed, leading to isolation and potential contact tracing. Our focus is on digital contact tracing via a tracing app, considering both its standalone use and its combination with manual tracing. We prove that as the population size n grows large, the epidemic process converges to a limiting process, which, unlike with typical epidemic models, is not a branching process due to dependencies created by contact tracing. However, by grouping to-be-traced individuals into macro-individuals, we derive a multi-type branching process interpretation, allowing computation of the reproduction number R. This is then converted to an individual reproduction number $R^\mathrm{(ind)}$, which, in contrast to R, decays monotonically with the fraction of app-users, while both share the same threshold at 1. Finally, we compare digital (only) contact tracing and manual (only) contact tracing, proving that the critical fraction of app-users, $\pi_{\mathrm{c}}$, required for $R=1$ is higher than the critical fraction manually contact-traced, $p_{\mathrm{c}}$, for manual tracing.

This article asks why states choose to explicitly label themselves as feminist and critically examines the case of Canada. Drawing on constructivist insights, I suggest that identity insecurity is a key contextual factor driving states’ decision to adopt a feminist branding. Through a thematic analysis of 1,551 statements from the Canadian House of Commons and additional documents published by the Standing Committee on Foreign Affairs and International Development from 2006 to 2017, I find that Canada’s choice to adopt a feminist brand occurred within a broader context of identity insecurity, with gender equality emerging as a strategic area to enhance the country’s role through strengthened leadership in this sector. This article advances the study of feminist foreign policies by highlighting the strategic motivations behind the adoption of the feminist label, offering insights into its diffusion despite differing levels of commitment to gender equality.

Plant-based diets, with limited quantities of animal foods, are increasingly promoted for sustainability and health. In many countries, animal-source foods provide the majority of several micronutrients at a population level; in the UK, milk and dairy products contribute around one third of total calcium, vitamin B12 and iodine intake in adults. Recommendations for a predominantly plant-based diet may have the unintended consequence of reducing intake of micronutrients, particularly in groups with an already-low intake of these nutrients, such as women of reproductive age. Furthermore, young women are the group most likely to replace dairy products with plant-based alternatives. Milk alternatives are often fortified to match the nutrient content of cows’ milk for some micronutrients (e.g. calcium), but not of others (e.g. iodine or vitamin B2). Unfortified alternatives have an iodine concentration that is just 2 % of that of UK cows’ milk, and the rise in popularity of these products may increase iodine-deficiency risk in consumers. Low nutrient intake is of concern prior to, and during, pregnancy, when many of the micronutrients at risk (iron/calcium/iodine) are essential for foetal development. While there may be awareness of some at-risk nutrients on a plant-based diet, this may not be the case for all. At-risk nutrients should be considered in nutrition guidelines and advice given by healthcare professionals to ensure that the diets are well planned and supplemented when necessary. This review focuses on the provision of micronutrients (particularly iodine) from plant-based diets in the UK.

Veto rights are a prominent institutional feature in ethnically divided societies, especially power-sharing democracies. Yet while vetoes are intended to protect the vital interests of each ethnic community, they can give rise to serious concerns about political deadlock and instability. In response, we argue that vetoes should be subject to a justificatory test grounded in public reason. On the face of it, one troubling consequence of this approach is that a community’s assessment of its own vital interests cannot be decisive. Yet as we explain, the critical issue is not who should be the arbiter of an interest but the need to be fair to the interests of all concerned. To illustrate how a public reason approach of this sort might be rendered sufficiently specific to be of practical use, we take human rights law as our example. Having considered a number of potential difficulties that this example throws up, we conclude by noting how a justificatory test can help to deliver not just greater political stability but a more democratically progressive form of politics.

This article argues that there are two different types of ‘past potential’ relevant to the Classical Greek tense and mood system. First, the past-tense indicative with ἄν can signal that a designated past event was once possible but not realized (retrospective root potential: ἐποίει ἄν ‘could have done’). Second, the optative with ἄν can express uncertainty about whether a designated past event actually occurred (retrospective epistemic potential: ποιοȋ ἄν ‘may have done’). While such usages are recognized in the traditional grammars, they have been dismissed in modern discussions. The article presents a detailed theoretical argument, backed up by both close readings of individual passages and broader discussions of corpus data, in favour of establishing these past potential usages as an integral part of Classical Greek grammar.

Food insecurity (FIS) is a critical public health issue, particularly among older adults. This study investigates the association between FIS with diet quality and anthropometric indices in the US older adults. A cross-sectional analysis was conducted using NHANES data from 2017 to 2020, involving 2592 participants aged ≥ 60 years. FIS was assessed using the USDA Household Food Security Survey Module. Diet quality was assessed using the Healthy Eating Index (HEI)-2020 and adherence to Mediterranean diet (MedDiet) score. Anthropometric measures were calculated following standardised protocols. Multivariable logistic regression models, adjusted for demographic, socio-economic and behavioural factors examined the association between FIS and the higher quartile and tertile of anthropometric and diet quality indices, respectively. Of the participants, 27·4 % experienced FIS. FIS participants were younger and had lower education and income levels compared with FS individuals (P < 0·05). In the adjusted model, FIS was associated with lower adherence to both the Mediterranean Diet (OR: 0·48, 95 % CI: 0·31, 0·67) and HEI-2020 (OR: 0·61, 95 % CI: 0·37, 0·84), indicating poorer diet quality in older adults. In adjusted analyses, FIS was significantly associated with higher A Body Shape Index quartiles (Q3: OR: 1·44, 95 % CI: 1·06, 1·95; Q4: OR: 1·46, 95 % CI: 1·07, 2·01), the waist-to-hip ratio (Q4: OR: 1·44, 95 % CI: 1·01, 2·06) and the Conicity index (Q4: OR: 1·36, 95 % CI: 1·02, 1·81). FIS in older adults is associated with unfavourable diet quality and body composition patterns, particularly central obesity measures. Addressing FIS may mitigate health risks related to obesity and its complications.

This article examines how statecraft (jingshi 經世) policies were implemented in the Late Qing period. It focuses on Dai Zhaochen, a prefect who served in Shandong and Guangdong in the 1860s. Dai was from a noted family of officials and had numerous “weak ties” with prominent jingshi officials. One of his handbooks, this paper shows, drew primarily on the Collected Statecraft Writings from the Qing Dynasty (Huangchao jingshi wenbian 皇朝經世文編). In office, Dai adapted policies from it and other collections, appealing to practicability and simplicity as the criteria for policymaking. More generally, he insisted that he was just a humble practitioner of the art of governance. The conclusion reflects on that disavowal, arguing that existing definitions of “statecraft” do not attend to Dai’s core concerns. I propose, therefore, that we stop seeking an essential definition of “statecraft” and instead pursue a broader socio-intellectual history of policy in the Qing.

Aspectual verbs with infinitival complements are often considered ambiguous when it comes to the question of whether they should be classified as raising or control verbs. In present-day German, argument structure properties seem to favor a raising analysis, but arguments for a control analysis cannot be dismissed. Word order properties do not provide conclusive evidence either and seem to support the ambiguity of aspectual verbs in present-day German. However, new diachronic evidence on word order properties of infinitival complements in uncontested raising and control constructions shows that well-established word order differences between raising and control constructions are a fairly recent development in the history of infinitival constructions (De Cesare 2021): Until about the mid eighteenth century, infinitival complements of both raising and control verbs tend to precede the finite verb in final position, with the preference of control verbs for extraposition developing only later. In present-day German, the extraposition of infinitival complements is considered a strong criterion for the sentential nature of the postposed infinitive and thus of the biclausal structure of the infinitival pattern, at least since the influential work of Bech (1983). In the present article, we look into the word order properties of ingressive aspectualizers over time and evaluate them against the emergence of a systematic distinction of raising and control verbs in the recent history of German, aiming at a deeper understanding of the syntactic behavior of aspectual verbs in present-day German.

This study develops a two-country New Keynesian model incorporating deep habits in consumption to analyze macroeconomic dynamics under the optimal coordinated monetary policy. The central bank adjusts interest rates more aggressively in response to structural shocks in an open economy than in a closed economy. Deep habits strengthen the central bank’s incentive to adjust terms of trade through interest rates due to habit formation and counter-cyclical markup behavior, creating price inelasticity in demand. Deep habits also lead to deviations from the law of one price, reflected in goods-specific real exchange rates, which the degree of home bias influences. Finally, this study compares international policy coordination to noncoordination to analyze welfare gains, showing that they depend on key structural factors like price rigidity, deep habits, and home bias. Policy coordination stabilizes domestic output and inflation by internalizing externalities in terms of trade and consumption.

This paper studies quasiconformal non-equivalence of Julia sets and limit sets. We proved that any Julia set is quasiconformally different from the Apollonian gasket. We also proved that any Julia set of a quadratic rational map is quasiconformally different from the gasket limit set of a geometrically finite Kleinian group.

In Democratic Theory (1962), Sartori argued that the key challenge for liberal-democratic regimes is to reconcile liberty and equality. However, his focus was primarily on the concept of liberty. In the Theory of Democracy Revisited (1987a), he elaborated a richer conception of equality, taking into account the thriving Anglo-Saxon debate. Sartori made two main contributions to this debate. First, he provided a clear conceptual framework for identifying different types of equalities and the various criteria for egalitarian distributions. Second, he laid the groundwork for an empirical theory of equality politics in contemporary democracies, warning against their potential threats. He also proposed to address the risk by means of an “efficient system of reciprocal compensations among inequalities.” The paper reconstructs and discusses Sartori's arguments on these important topics.

As societal conceptions of gender have evolved, so too have survey-based approaches to the measurement of gender. Yet, most research innovations and insights regarding the measurement of gender come from online or phone surveys in the Global North. We focus on face-to-face surveys in the Global South, specifically in the Latin America and Caribbean (LAC) region. Through in-person interviews, an online experiment, and survey experiments, we identify and assess an open-ended approach to incorporating respondent-provided gender identity in face-to-face interviews. Our results affirm that the measure is comparatively effective in minimizing discomfort and does not have substantial consequences for data quality across a diverse set of LAC countries. We discuss the potential traveling capacity of our approach and identify paths for further research on best practices in recording interviewee gender in face-to-face surveys in the LAC region and beyond.