Individual patient data meta-analyses (IPDMAs) provide powerful tools for synthesizing evidence across studies, yet methods for addressing unmeasured confounding in observational IPDMAs with survival outcomes are rarely implemented. Instrumental variable (IV) approaches offer causal inference capabilities but face practical challenges in hierarchical data structures, particularly the lack of standard diagnostics for instrument strength in nonlinear mixed-effects models. We adapt and evaluate a frequentist mixed-effects two-stage residual inclusion (2SRI) framework for survival IPDMAs, extending traditional IV methods to accommodate study-level and temporal clustering while handling time-to-event outcomes through Cox proportional hazards models. Because classical F-statistics are unavailable for logistic mixed-effects first-stage models, we propose the Wald $\chi ^2$ statistic as a practical instrument-strength diagnostic and empirically characterize its relationship to estimator performance. Through a comprehensive simulation study with 48 scenarios—varying unmeasured confounding (weak to very strong), instrument–treatment association strength (0.3–1.0), and cross-study IV allocation patterns—we evaluated 2SRI against naive mixed-effects Cox models using bias, coverage, variance, and mean squared error. The design was anchored to realistic IPDMA structure (10 studies, $N \approx 4,357$) from pooled Ebola data, with 1,000 replications per scenario. Results show that under weak confounding, naive models dominate on all metrics. With moderate-to-strong confounding and realized Wald $\chi ^2$ exceeding 150–200, mixed-effects 2SRI substantially reduces bias and achieves near-nominal coverage, though with inflated variance. We provide empirical guideposts linking realized first-stage strength to expected performance, enabling analysts to judge when 2SRI will outperform conventional approaches in hierarchical survival IPDMAs. All simulations assume a common treatment effect across studies. Performance under heterogeneous effects remains to be established.

Droplet impingement is one of the most common phenomena in nature. However, the impact dynamics of droplets on structured heterogeneous wettability surfaces remain little explored. In this work, an investigation is conducted into the droplet impact on heterogeneous wettability surfaces composed of superhydrophobic micropillars on a hydrophilic substrate, by using an improved phase-field lattice Boltzmann model. In particular, the effects of surface geometry and impact conditions on droplet bouncing and wetting behaviours are scrutinised. Four distinct impact outcomes are identified: complete bouncing, pancake bouncing, partial wetting and complete wetting. Based on the competition among capillary, inertial and viscous forces, an analytical model is proposed to predict the maximum droplet penetration depth within the pillar gaps. A transition diagram is constructed to distinguish these different impact outcomes, with regime boundaries derived from the proposed analytical model. Finally, from the perspective of energy analysis, both the evolution of the energy budget and the surface energy distribution during the droplet impact process are revealed. These findings provide guidance for the design of heterogeneous wettability surfaces, enabling predictable control over droplet bouncing and wetting behaviours.

This study investigates the unsteady oscillation cycle of sheet and tip vortex cavitation over an elliptical NACA $66_2$-415 hydrofoil using high-speed imaging and time-resolved tomographic particle image velocimetry. Synchronised measurements of radiated noise are conducted. The oscillation cycle consists of three phases, involving growth and collapse of the sheet and tip vortex cavitation, followed by intermittent rebounding of the tip vortex cavity. The collapse of the sheet cavity is triggered by a side-entrant jet, leading to the formation of the cloud and secondary vortex cavitation. The interaction between the secondary and tip vortex cavities further promotes the collapse of the latter. The three-dimensional instantaneous flow organisation indicates that the evolution of cavitation affects the centre displacement, deformation and breakdown of the tip vortex. Spanwise vortices emerge and interact with the tip vortex after the growth phase, causing violent fluctuations of the tip vortex during the collapse phase. The intense interaction between these vortices enhances the perturbation growth and promotes tip vortex breakdown. Proper orthogonal decomposition analysis reveals that the dominant unstable modes near the hydrofoil tip correspond to the displacement and deformation types. In addition to the suction-side shear layer, the vortex interaction region also exhibits intense production of turbulent kinetic energy. The temporal variation of sound pressure over an oscillation cycle indicates a strong correlation with the cavity morphology.

I argue against John, Millum and Wasserman’s position that telic prioritarianism justifies morally acceptable discrimination against persons with disabilities. I propose alternative considerations that explain why disability discrimination in the lifesaving cases JMW discuss is morally problematic.

Conciliationism holds that it is rational to modify one’s beliefs in the face of disagreement. But extant conciliatory norms yield incorrect results in cases involving excessive confidence—cases in which one’s interlocutors are sure, or almost sure, that their opinions are correct. After explaining the problem of excessive confidence, I show that a Bayesian approach to Conciliationism handles the problem elegantly and effectively. Further, it has desirable—indeed essential—features, including the ability to (i) contend with multiple interlocutors, (ii) deal with gradations in competence, (iii) incorporate ubiquitous interdependence, and (iv) account for critical contextual features of cases of disagreement.

Recent governments, both in the UK and internationally, have increasingly used their power to attempt to alter the behaviour of people in receipt of social security benefits. This can be seen in the case of the UK’s benefit cap, a policy introduced with the specific goal of changing behaviour by capping social security support at the household level. Alongside promoting transitions into employment, there was also a focus on encouraging households to move to cheaper accommodation, something which was portrayed as achievable by those defending the policy. Drawing on case studies from qualitative longitudinal research with parents affected by the benefit cap, this article demonstrates that individuals are, in fact, relatively powerless to change their housing situations, which are routinely already overcrowded and of poor quality, even where rents are very high. Instead, affected households experience state-imposed hardship. We problematise both the cap itself and the governmental narrative that knowingly ascribes social security recipients with a power they do not have.

Recent years have seen record numbers of applications to UK psychiatry training, yet consultant vacancies remain high and substantial workforce gaps persist. This contradiction reflects a growing recruitment–retention paradox: increasing pressure at the point of entry has not translated into sustainable workforce capacity. This feature introduces the pressurised leaky funnel, a systems-based conceptual model that reframes the psychiatry workforce as a pathway shaped by upstream recruitment pressures and downstream attrition across five stages: exposure and intent, application, selection, training environment and career outcomes. Drawing on established workforce models and educational psychology theory, the model explains how application volume can expand while misalignment, motivational erosion and identity strain drive cumulative workforce loss across the pipeline. We argue that recruitment, selection and retention should not be treated as separate policy domains but understood as interacting components of a single system. By linking where doctors enter psychiatry with how commitment is sustained or eroded, the model offers a framework for moving beyond short-term recruitment metrics towards progression, retention and long-term workforce sustainability, while highlighting new opportunities for selection reform, training environment redesign and retention-focused workforce planning.

Generative artificial intelligence (GenAI) is a powerful technology that has vast potential to support various aspects of second language acquisition (SLA). Given GenAI’s capabilities, it is particularly relevant for the teaching and learning of second language (L2) writing. Despite its potential, there are also clear hazards and a range of potentially negative side effects, many of which have yet to be explored. Building on existing research, in this piece, I propose a series of six future research tasks that may prove useful for further understanding the affordances and limitations of GenAI for L2 writing. These six research tasks are organized into three interrelated themes, which cover 1) learning processes and outcomes, 2) student use and interactions, and 3) teaching. For each theme, two research tasks are proposed. Each task includes a discussion of what research is needed, why it is needed, along with how scholars might investigate that research task by adopting quantitative, qualitative, or mixed methods. The goal of this piece is to provide potential research ideas for graduate students and faculty and, ultimately, to foster research–pedagogy connections involving GenAI, L2 writing, and SLA.

Corruption persists because feedback between individual behaviour, social norms, and institutional rules creates self-reinforcing dynamics. Although laboratory experiments provide growing evidence on anti-corruption interventions, this literature remains fragmented, failing to explain why enforcement succeeds in some contexts and fails in others. To address this gap, this paper develops a Dynamic Corruption Equilibrium (DCE) Framework. Drawing on a Bibliometric-Systematic Review of 132 experimental studies, it identifies six intervention classes across institutional, social, and individual levels, with behavioural dispositions acting as cross-cutting moderators. While existing studies examine these interventions in isolation, overlooking cross-level interactions and behavioural heterogeneity, the DCE Framework integrates insights from complex adaptive systems theory and institutional economics to conceptualise corruption as a dynamic, multi-level system. By specifying three mechanisms: cross-level feedback loops, conditional pathways, and system bistability, the framework explains how corruption equilibria become self-reinforcing or shift, offering a diagnostic lens for analysing intervention effectiveness within complex institutional environments.

We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier–Stokes equations as a variational problem as established in Ashtari & Schneider (J. Fluid Mech., vol. 977, 2023, A7). The approach minimises the residual of the governing equations over a finite-time horizon, seeking periodic or equilibrium solutions. A novel contribution is made by including a Galerkin projection onto a basis of divergence-free modes that satisfy the no-slip boundary conditions. This projection not only makes the variational framework applicable to wall-bounded flows but it also yields a low-order representation of the dynamics. The basis is derived from resolvent analysis, which provides an orthonormal set. We demonstrate the method on a streamwise invariant formulation of rotating plane Couette flow, obtaining exact equilibrium and periodic solutions consistent with direct numerical simulations. The conditioning of the optimisation problem is analysed in detail, showing that convergence rates depend on the stability properties of the targeted solutions. Finally, we highlight a direct link between the conditioning of the optimisation and the structure of the resolvent operator, suggesting a unifying perspective on both the efficiency of the optimisation and the dynamical significance of resolvent modes.

Social scientists have paid significant attention to the study of ethnic and religious minorities in Europe, and yet one group that evaded such scrutiny is the Tatars residing in modern-day Lithuania, Belarus, and Poland, who are unique in being Europe’s only Muslim community that survived under Catholic rule since the late medieval period. While Muslims in medieval and early modern France, Italy, Portugal, and Spain were eradicated through a mix of mass expulsions, forced conversions, and massacres, Lithuanian-Polish Tatars survived over six centuries. This article examines this unique case to understand the comparative political dynamics of persecution and toleration across medieval and early modern Europe. The article argues that the interstate and societal configuration of power explains the Tatars’ exceptional survival. The interstate and domestic dynamics are linked in that Lithuanian rulers successfully resisted forced conversion and eventually adopted Christianity on their own terms, which allowed for the preservation and perpetuation of religious sectarian diversity backed up by multiple political stakeholders. In the domestic struggle between monarchs, Papal allies, the Catholic nobility, and non-Catholics, none of the religious sectarian factions could achieve a hegemonic majority, let alone monopolistic control of political and military power, necessary for a coercive religious sectarian homogenization.

The two-way interaction between the unsteady flame heat release rate (HRR) and acoustic waves can lead to combustion instability within combustors. Previous studies have typically characterised premixed flame responses to pure harmonic forcing, assuming dynamically linear or weakly nonlinear behaviour, to quantify flame–acoustic interactions. By combining third-order asymptotic analysis with numerical simulations of the $G$-equation, this study investigates the nonlinear response of laminar premixed V-flames subjected to dual-frequency velocity perturbations ($St_1$ and $St_2$, dimensionless frequencies). The positive correlation between disturbance propagation speed $u_c$ and frequency $St$ is captured by integrating a velocity-potential model with calibration against existing experimental data. The mechanism by which the disturbance at one forcing frequency, say $St_2$, affects the flame dynamic response at the other forcing frequency, $St_1$, is studied in detail. The perturbation at $St_2$ couples with that at $St_1$ to induce third-order nonlinear terms, giving rise to a non-monotonic suppression mechanism that smooths out the flame’s spatial wrinkling owing to the positive correlation between $u_c$ and $St$. As a result, excitation at $St_2$ modifies the HRR response at $St_1$, delineating an effective region bounded on the left by the frequency threshold of the linear response and on the right by the aforementioned non-monotonicity. Within this region, excitation at $St_2$ can markedly attenuate the HRR gain at $St_1$ compared with the case where the flame is driven solely by the perturbation at $St_1$. For instance, once both perturbation amplitudes exceed a certain threshold, excitation at $St_2$ can attenuate the flame response at $St_1$ by more than 40 % compared with the case without excitation at $St_2$. These findings contribute to the development of a quantitative framework for understanding how targeted frequency perturbations modulate the flame dynamics via nonlinear interactions, which may inform open-loop approaches for mitigating thermoacoustic instabilities in combustion chambers.

In expectations-driven liquidity traps (LTs), a higher inflation target is associated with lower inflation and consumption. As a result, introducing the possibility of expectations-driven LTs to an otherwise standard model lowers the optimal inflation target. Using a calibrated New Keynesian model with an effective lower bound (ELB) constraint on nominal interest rates, we find that even a very small probability of falling into an expectations-driven LT lowers the optimal inflation target nontrivially. Our analysis provides a novel reason to be cautious about the argument that central banks should raise their inflation targets in light of a higher likelihood of hitting the ELB.