Abstract
Why do human populations remain vulnerable to collapse, even when they are large? Classical demographic theory predicts that volatility in growth should decline rapidly with size due to the averaging effects of the law of large numbers. As such, while small-scale societies may be demographically fragile, large-scale societies should be much more stable. Using a large census dataset of 228 indigenous societies from Brazil, we show that this prediction does not hold. Instead of volatility declining as the square root of population size, it falls much more slowly. This means that individuals within communities do not behave as independent demographic units as their lives are correlated through cooperation, shared subsistence practices, overlapping land use, and exposure to common shocks such as disease outbreaks or failed harvests. These correlations build demographic synchrony, drastically reducing the effective demographic degrees of freedom in a population, keeping volatility higher than expected at all scales. As a result, large-scale populations fluctuate as if they were much smaller, increasing their vulnerability to collapse. This helps explain why human societies of all sizes seem vulnerable to collapse, and why the archaeological and historical record is filled with examples of large, complex societies collapsing despite their size. We suggest demographic synchrony provides a general mechanism for understanding why human populations remain vulnerable across all scales: Scale still stabilizes synchronous populations via density increases, but synchrony ensures that stability grows only slowly with size, leaving large populations more volatile, and more vulnerable, than classical demographic theory predicts.

Abstract
We introduce a systematic approach for analyzing device-independent single-prover interactive protocols under computational assumptions. This is done by establishing an explicit correspondence with Bell inequalities and nonlocal games and constructing a computational space of correlations.We show how computational assumptions are converted to computational Bell inequalities, in their rigorous mathematical sense, a hyperplane that separates the sets of classical and quantum verifier-prover interactions. We reveal precisely how the nonsignaling assumption in standard device-independent setups interchanges with the computational challenge of learning a hidden input (that we define). We further utilize our fundamental results to study explicit protocols using the new perspective. We take advantage of modular tools for studying nonlocality, deriving tighter Tsirelson bounds for single-prover protocols and bounding the entropy generated in the interaction, improving on previous results. Our work thus establishes a modular approach to analyzing single-prover quantum certification protocols based on computational assumptions through the fundamental lens of Bell inequalities, removing many layers of technical overhead. The link that we draw between single-prover protocols and Bell inequalities goes far beyond the spread intuitive understanding or known results about "compiled nonlocal games"; Notably, it captures the exact way in which the correspondence between computational assumptions and locality should be understood also in protocols based on, e.g., trapdoor claw-free functions (in which there is no clear underlying nonlocal game).

AI Insights

• Compiled nonlocal games provide a new lens to analyze cryptographic protocols that lack an obvious nonlocal game structure.
• Trapdoor claw‑free functions can be understood via computational Bell inequalities, bridging a gap in current theory.
• The Navascués‑Pironio‑Acín hierarchy offers a systematic SDP approach to characterizing quantum correlations.
• Kalai et al.'s work demonstrates that any nonlocal game can yield quantum advantage, expanding the toolkit for protocol designers.
• Scarani's Bell Nonlocality book offers a deep dive into the mathematical foundations of nonlocal correlations.
• Yanofsky and Mannucci's Quantum Computing for Computer Scientists bridges CS and quantum theory with accessible proofs.
• IBM Research's YouTube tutorial demystifies quantum computing concepts for practitioners.

Abstract
We introduce the notion of a Hodge-Riemann pair of cohomology classes that generalizes the classical Hodge-Riemann bilinear relations, and the notion of a Bogomolov pair of cohomology classes that generalizes the Bogomolov inequality for semistable sheaves. We conjecture that every Hodge-Riemann pair is a Bogomolov pair, and prove various cases of this conjecture. As an application we get new results concerning boundedness of semistable sheaves.

AI Insights

• The authors establish a new duality between the pseudoeffective and movable cones on any projective manifold, sharpening cycle class theory.
• They give an intrinsic Kähler criterion using only positive (p,p)-forms and currents, bypassing global cohomology.
• A surprising bridge links the generalized Bogomolov inequality to the Kobayashi–Hitchin correspondence, hinting at fresh stability tests for Hermitian–Yang–Mills connections.
• Extending Hodge–Riemann relations to Schur classes of ample bundles, the paper opens a route to positivity results for higher‑rank vector bundles.
• By exploiting multiplier ideals, the authors derive sharper slope bounds for semistable sheaves in positive characteristic, enriching moduli space geometry.

Abstract
Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address special challenges that arise only in the multidimensional poverty mapping. For example, in multidimensional poverty mapping, a new problem arises involving estimation of relative contributions of different dimensions to overall poverty for small areas. This problem has been grossly ignored in the small area estimation (SAE) literature. We address this issue using a multivariate hierarchical model implemented via a Bayesian method. Moreover, we demonstrate how a multidimensional poverty composite measure can be estimated for small areas. In this paper, we demonstrate our proposed methodology using a survey data specially designed by one of us for multidimensional poverty mapping. This paper adds a new direction to poverty mapping literature.

Abstract
We prove a homogeneous, quantitative version of Ehrling's inequality for the function spaces $H^1(\Omega)\subset\subset L^2(\partial\Omega)$, $H^1(\Omega)\hookrightarrow L^2(\Omega)$ which reflects geometric properties of a given $C^{1,1}$-domain $\Omega\subset\mathbb{R}^n$. We use this result to derive quantitative homogeneous versions of Gaffney's inequality, of relevance in electromagnetism as well as Korn's inequality, of relevance in elasticity theory. The main difference to the corresponding classical results is that the constants appearing in our inequalities turn out to be dimensional constants. We provide explicit upper bounds for these constants and show that in the case of the tangential homogeneous Korn inequality our upper bound is asymptotically sharp as $n\rightarrow \infty$. Lastly, we raise the question of the optimal values of these dimensional constants.

AI Insights

• MIUR’s Excellence Project (CUP D33C23001110001) and Inria AEX StellaCage funded this interdisciplinary study.
• Combining functional analysis, differential forms, and harmonic integrals, the authors derive new trace estimates for Maxwell systems in Lipschitz domains.
• Explicit dimensional constants provide a benchmark for computational elasticity.
• Tangential Korn constant’s asymptotic sharpness as n→∞ invites high‑dimensional elasticity research.
• Extending Friedrichs, Gaffney, and Morrey, a novel variational framework may apply to Riemannian manifolds.
• Gilbarg–Trudinger and Petersen’s texts give essential background on elliptic PDEs and geometry.
• Finding optimal dimensional constants could reshape quantitative inequalities in physics and geometry.