We use spectral theory and algebraic geometry to establish a higher-degree analogue of a Szemerédi–Trotter-type theorem over finite fields, with an application to polynomial expansion.

Attention-deficit-hyperactivity disorder (ADHD) medication effects and their putative role in shortening the lifespan of adults with ADHD remain unclear. This is largely because ADHD’s diagnostic foundation lacks validity. Thus we argue that, until this is resolved, neither diagnosis nor treatment will serve patients’ needs effectively, and estimates of mortality will remain as conjecture.

This article considers the function of American food and its exchange at the time of the Allied occupation of Italy to revisit the complexity of the encounter with the local population. Through unpublished diaries and confidential reports of the Psychological Warfare Branch, as well as video materials, published interviews and published diaries, the article makes the issues around food central to the understanding of the dynamics of the Italian occupation. While contributing to the growing literature on food availability in the Second World War, the article expands in particular on the historic function of American comfort food and rations, to explore the experience of the Italian occupation through the interactions of gifting, bartering and black market trade. It illuminates the complexity of mutual perceptions shaped by hope, nostalgia, supremacy, and fairness. It concludes with a reading of John Hersey’s A Bell for Adano, which, as a cultural product, brings together and makes valid for future generations, the contrasting image of a benign and a damaging occupation explored in the article.

The global rise of deliberative democratic innovations, particularly minipublics such as citizens’ assemblies and deliberative polls, has been marked by uneven adoption across advanced democracies. While some countries have integrated these mechanisms into their democratic frameworks, others remain hesitant, raising questions about the institutional conditions that facilitate or hinder their adoption. This study employs qualitative comparative analysis (QCA) to examine how configurations of three key institutional dimensions – consensus democracy, federalism, and direct democracy – shape the adoption of minipublics. Our findings reveal that minipublics are more likely to be adopted in majoritarian systems with strong federalism and limited direct democracy, where they address participatory gaps. Conversely, systems combining high consensus democracy and extensive direct democratic mechanisms, such as Switzerland, often exhibit lower adoption rates, as existing power-sharing structures fulfil similar deliberative functions.

The health crisis of COVID-19 has provoked a pivotal moment of global health law reform that comes against larger shifts against international law, democracy, and human rights. In this light, it is perhaps not surprising that state-led amendments to the International Health Regulations (IHR)—international law’s primary instrument governing state responses to public health crises—and a prospective Pandemic Agreement—designed to remedy the former’s defects—have shifted away from the language of human rights and toward the sweeping principle of equity. While these changes appear to herald an important normative and legal shift in international law, they also raise longer-standing questions about coherence and fragmentation in international law, and about the future of human rights within international law. In this essay, I first explore larger concerns around coherence and fragmentation in international law, and the practical manifestation of these threats in disparities in access to COVID-19 vaccines. Second, I consider the legal and political implications of the shift to equity in both instruments. I conclude by considering what this move may mean for coherence and human rights in international law.

Placing Lauren Berlant’s concept of “cruel optimism,” in conversation with Tuck and Yang’s work, “Decolonization is Not a Metaphor,” this paper examines affective attachments to mass tree-planting efforts, which encourage unquestioned faith in these initiatives, serving to enable their persistence despite their consistent failures. This paper questions how affective attachments to mass tree-plantings teach publics to remain invested in the ability of settler-colonial institutions to solve climate crises, thereby ensuring that climate crises remain meaningfully unaddressed. Drawing together decolonial scholarship, affect theory, Indigenous thought and scholarship on environmental education, I demonstrate that mainstream tree-planting initiatives do not challenge the logics that permit forest and land degradation, but in fact, reproduce these logics. Rejecting a model which considers the act of planting trees as a success in and of itself, I instead ask what is missed when the planting of a tree is more important than the life of the forest.

We consider d-dimensional stochastic differential equations (SDEs) of the form $\textrm{d}U_t = b(U_t)\,\textrm{d}t + \sigma\,\textrm{d}Z_t$. Let $X_t$ denote the solution if the driving noise $Z_t$ is a d-dimensional rotationally symmetric $\alpha$-stable process ($1\lt \alpha\lt 2$), and let $Y_t$ be the solution if the driving noise is a d-dimensional Brownian motion. Continuing the work started in Deng et al. (2025), we derive an estimate of the total variation distance $\|\textrm{law}(X_{t})-\textrm{law}(Y_{t})\|_\textrm{TV}$ for all $t \gt 0$, and we show that the ergodic measures $\mu_\alpha$ and $\mu_2$ of $X_t$ and $Y_t$, respectively, satisfy $\|\mu_\alpha-\mu_2\|_\textrm{TV} \leq {Cd\log(1+d)}(2-\alpha)/({\alpha-1})$. We show that this bound is optimal with respect to $\alpha$ by an Ornstein–Uhlenbeck SDE. Combining this bound with a recent interpolation result from Huang et al. (2023), we can derive a bound in the Wasserstein-p distance ($0 \lt p \lt 1$): $\|\mu_\alpha-\mu_2\|_{W_p} \leq {Cd^{(p+3)/2}\log(1+d)}(2-\alpha)/{\alpha-1}$.

It is well known that the dynamical behavior of a rational map $f:\widehat {\mathbb C}\to \widehat {\mathbb C}$ is governed by the forward orbits of the critical points of f. The map f is said to be postcritically finite if every critical point has finite forward orbit, or equivalently, if every critical point eventually maps into a periodic cycle of f. We encode the orbits of the critical points of f with a finite directed graph called a ramification portrait. In this article, we study which graphs arise as ramification portraits. We prove that every abstract polynomial ramification portrait is realized as the ramification portrait of a postcritically finite polynomial and classify which abstract polynomial ramification portraits can only be realized by unobstructed maps.

Researchers have struggled to identify heirs’ property (HP) via the use of real estate records for years. This paper evaluates seven distinct methodological approaches to identify HP using CoreLogic’s national property database. We find minimal convergence among these algorithms, with different methods flagging largely non-overlapping sets of properties. Certain approaches show promise – particularly in identifying properties with characteristics consistent with documented HP patterns. The lack of agreement across methods, however, makes estimating the prevalence of HP difficult. Several paths exist forward to identify HP such as adding extra property characteristics into existing algorithms, developing more sophisticated algorithms, and establishing protocols for cross-jurisdictional validation.