Consider a quadratic polynomial $Q(\xi_{1},\ldots,\xi_{n})$ of independent Rademacher random variables $\xi_{1},\ldots,\xi_{n}$. To what extent can $Q(\xi_{1},\ldots,\xi_{n})$ concentrate on a single value? This quadratic version of the classical Littlewood–Offord problem was popularised by Costello, Tao and Vu in their study of symmetric random matrices. In this paper, we obtain an essentially optimal bound for this problem, as conjectured by Nguyen and Vu. Specifically, if $Q(\xi_{1},\ldots,\xi_{n})$ ‘robustly depends on at least m of the $\xi_{i}$’ in the sense that there is no way to pin down the value of $Q(\xi_{1},\ldots,\xi_{n})$ by fixing values for fewer than m of the variables $\xi_{i}$, then we have $\mathrm{Pr}[Q(\xi_{1},\ldots,\xi_{n})=0]\le O(1/\sqrt{m})$. This also implies a similar result in the case where $\xi_{1},\ldots,\xi_{n}$ have arbitrary distributions. Our proof combines a number of ideas that may be of independent interest, including an inductive decoupling scheme that reduces quadratic anticoncentration problems to high-dimensional linear anticoncentration problems. Also, one application of our main result is the resolution of a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn related to graph inducibility.

This article challenges historians’ recent Russian-Ukrainian war-related claims that the field of Russian history in the west, and in the United States in particular, has overlooked the imperial and colonial dimensions of Russia’s past. It argues that far from overlooking Russian and Soviet imperialism and colonialism and marginalizing the histories of non-Russian peoples in that context, Anglophone historians have been documenting and explaining them for almost a century. It shows that as early as the 1940s and 50s, Michael Karpovich and his former Harvard University students emphasized the need to pay greater attention to the history of Russian imperial expansion and colonization, Russia’s borderlands and its non-Russian peoples. By tracing the ways in which Anglophone historians over the next fifty years sought to make sense of Russian and Soviet empire, it becomes possible to see the so-called “imperial turn” in Russian historiography as a return to research agendas that had been established decades earlier and helped make possible the production of historical accounts of Russia arguably free from what Mykhailo Hrushevsʹkyi famously dubbed the “traditional scheme of ‘Russian’ history.”

Datasets from around the world suggest that people completed early monumental construction projects without long-term structures of hierarchy or authority. In the Maya area, some of the first monuments produced by semisedentary societies, such as those at Yaxuna and Ceibal, were built in the absence of substantial social inequality. The focus of these monuments was a relatively inclusive plaza. This article presents evidence of an eighth-century BC monumental construction at Ucí, another site that was probably not fully sedentary. At Ucí, however, the first large architecture is not inclusive. Structure 14sub5 lacks a front stairway, separating people in the plaza from those who could ascend the building from the back. The difference between the inclusivity at Ceibal and Yaxuna and exclusivity at Ucí suggests variation in degrees of inequality. Different societies experimented creatively with social and political organization. This aligns with the inherent complexity of egalitarian societies as well as the possibility that not all complex societies began as egalitarian. Consonant with the idea that people had power to act otherwise, early exclusivity at Ucí developed into inclusive forms of governance in the Late Preclassic.

This article proposes queernotation as a lens to understanding existing works and as a way forward for composers and musicians who find themselves limited by traditional forms of music notation. Applying queer ways of knowing and creating, I investigate the inherent boundaries in notation and how queer theory can guide us to break out of them. Queernotation connects score types to three key areas of queer theory: queer erotics, queer temporalities and queer futurity. Extending these theoretical approaches to their musical possibilities, I identify three modes of queering notation. These approaches are demonstrated in this article through existing historical and recent works and practically applied in a chamber opera that tests concepts of queernotation in directing improvisers to perform conceptual ideas on the stage. Notation for electronic instruments and with digital mediums demonstrates how technology facilitates new approaches that can queer music notation.

Radziwiłł and Soundararajan unveiled a connection between low-lying zeros and central values of L-functions, which they instantiated in the case of quadratic twists of an elliptic curve. This article addresses the case of the family of modular forms in the level aspect, and proves that the logarithms of central values of associated L-functions approximately distribute along a normal law with mean $-\tfrac 12 \log \log c(f)$ and variance $\log \log {c(f)}$, where $c(f)$ is the analytic conductor of f, as predicted by the Keating–Snaith conjecture.

In this paper, I argue that we do not know how to implement abstract principles of liberal egalitarian justice. Starting with Scheffler’s Rawlsian diagnosis of the retreat of liberal democracy in the United States, I argue that it may be due to our lack of knowledge about how to institutionalize a Rawlsian just liberal society. To illustrate the difficulty or challenge, I examine several policy proposals to help build human capital for property-owning democracy and argue that they can fail for various reasons. The main problem is that the changing ways in which diverse individuals respond to policies and interact with one another affect policy consequences, but their complexity surpasses our limited knowledge. The ignorance gives us reason to be patient with the slow pace of building an ideal liberal society, tolerant of those who are sceptical about interventions to implement liberal egalitarian principles, and open to policy experimentation and learning. I further argue that we should publicly acknowledge our ignorance about policy outcomes, as it can reduce political polarization, by moderating policy positions and interpreting policy disagreements as empirical rather than moral, and counter democratic backsliding.

This paper addresses the comprehensive regulation of artificial intelligence (“AI”) across its entire lifecycle in the health care sector. It builds on a proposal for a True Lifecycle Approach (“TLA”) to address governance gaps across three phases of AI and expands the framework with detailed practical insights for governing health care AI, drawing on pioneering examples from Qatar, Saudi Arabia, and the United Arab Emirates (“UAE”) as models for global implementation. Beginning with the research and development phase, it highlights the urgent need for robust guidelines and certification processes to ensure that AI technologies are developed in compliance with ethical and safety standards. Moving into the approval stage, the discussion explores how AI systems can be effectively regulated under existing medical device frameworks, emphasizing the need for tailored regulations that consider the unique challenges posed by AI. Finally, the paper delves into the deployment of AI in clinical practice, examining the gaps in current laws and the need for a coherent and consistent regulatory framework that can adapt to AI advancements. The paper argues that the existing legal structures are inadequate, often inconsistent, and fail to address the complexities of AI in health care. It argues for a broader regulatory approach focused on patient safety throughout the AI lifecycle.

La guerre d’Algérie est entrée dans l’ère des réparations. Face à la pression de groupes mémoriels (appelés, rapatriés, harkis), l’État a pris des mesures compensatrices ciblées avant de nommer cette guerre en 1999. Mais cette histoire partielle marginalise les familles des 4 000 tués et 10 000 blessés qui, sans s’être constituées en groupes, n’ont pas moins œuvré à bas bruit dès le début de la guerre pour une reconnaissance de leur expérience : une guerre en métropole faite d’affrontements fratricides entre Algériens, de répressions policières et de menées OAS. À partir de questions écrites à l’Assemblée nationale, de textes réglementaires, de milliers de dossiers de successions montés par des familles algériennes et de centaines de demandes d’indemnisations adressées aux autorités, cet article propose une ethnographie historique de l’État pris dans les transactions réparatrices d’une guerre non déclarée. Il redéfinit alors la chronologie, les modalités et les stratégies déployées par les victimes civiles de la guerre d’Algérie pour obtenir réparation. Il remarque d’abord que la fiction d’une guerre sans nom n’a pas été simplement imposée par l’État, mais a été renforcée par en bas, à travers les négociations engagées sous la forme d’accidents de travail ou de trajet. Il souligne ensuite que la lutte menée par les victimes collatérales françaises a suscité un élan de solidarité nationale à l’origine d’une des premières lois d’indemnisation pour les victimes du terrorisme en France, rejetant les « inexcusables » algériens. Il démontre enfin que les amnisties, les frontières nationales, la définition rétroactive du maintien de l’ordre et la reconnaissance progressive par l’État de la guerre en Algérie ont achevé de créer une nouvelle guerre sans nom, la guerre en métropole, avec son lot d’exclus des réparations.

Conversational theatre is a medium for facilitating dialog on race, privilege, and discrimination in Swedish society. Du Contrat Social, a performance based on Jean-Jacques Rousseau’s social contract, demonstrates how theatre can create an interactive space where audience members actively reflect on their social positioning and implicit biases. By guiding the audience through exercises that expose implicit stereotypes and encourage self-reflection, the performance fosters a unique setting for transformative learning.

Reflections on Claire O’Callaghan and Brendan Parent’s article “Withdrawal of Life-Sustaining Treatment and Organ Donation After Circulatory Death: Consequences of Legislative Separation.”