Pólya trees are unlabeled rooted trees on n vertices. This paper gives a new way to generate Pólya trees, that conjecturally is very efficient. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with “reality.”

Our method is an application of the Burnside process, alternating two steps: from a labeled rooted tree, produce a uniform permutation fixing it; and from a permutation, produce a uniform labeled rooted tree fixed by it. This last step is linked to a product formula, refining Cayley’s, for the number of rooted labeled trees preserved by a given permutation.

This essay critically examines the relationship between antiracism, public policy, and liberal democratic accountability standards. Drawing on a set of standards derived from the political philosophies and constitutional structures of liberal democracies, the gap between these ideals and the realities of racial injustice are examined in light of Frederick Douglass’ position on the U.S. Constitution as an anti-slavery document, the persistence of a “racial contract,” and recent conceptualization of antiracism. By grounding antiracist policies in democratic accountability standards and recognizing the gap between the ideal and the real, the essay then examines the contemporary efforts of an “antiwoke” movement to purge policies and practices that focus on social equity and antiracism from government operations and assesses the efficacy of such efforts in light of core democratic standards and American ideals.

We present an efficient neural-based approach to estimate the instantaneous flow field around an airfoil from limited surface pressure measurements. The model, denoted SNN-POD, relies on two independent shallow neural networks to predict the instantaneous flow over a wide range of angles of attack $ \left[10{}^{\circ},20{}^{\circ}\right] $. At all angles the global model correctly recovers the average characteristics of the flow from single-time sensor data, thus allowing combination with local, angle-dependent models. The method is applied to 2D URANS simulations of a thick airfoil at a Reynolds number of $ \mathit{\operatorname{Re}}=4.5\times {10}^6 $. The training set consists of snapshots obtained from a coarse sampling $ \left(1-2{}^{\circ}\right) $ of the angle of attack range. A variance-based criterion is used to determine the number and positions of sensors. Tests are carried out for unseen snapshots at angles of attack within the set (sampled angles) as well as outside the set (interpolated angles). The maximum MSE error of attack for sampled and interpolated angles is respectively $ 2.9\% $ and $ 6.6\% $. This makes it possible to develop adaptive strategies to improve the estimation if necessary.

This study jointly considers two opportunistic behaviors among political incumbents that may be triggered by electoral uncertainty—policy myopia and policy moderation—which hitherto have been the focus of separate research traditions. We evaluate their prevalence in economic policy-making among Swedish local governments, using a new measure of electoral competitiveness, capturing the incumbent government’s re-election probability, for which plausibly exogenous variation is generated by exploiting national-level polls. We find a substantial moderating effect of competitiveness on incumbents’ tax rate decisions—shifting policy towards the political center—but little evidence of policy myopia, whether in taxation, budget balance, or public investment. Corroborated by evidence from a politician survey, these findings caution against the popular understanding of democratic policy-making as inherently short-sighted.

We introduce and study different compactifications of the moduli space of n distinct weighted labeled points in a flag of affine spaces. We construct these spaces via the weighted and generalized Fulton-MacPherson compactifications of Routis and Kim-Sato. For certain weights, our compactifications are toric and isomorphic to the polypermutohedral and polystellahedral varieties, which arise in the work of Crowley-Huh-Larson-Simpson-Wang and Eur-Larson on polymatroids, a generalization of matroids. Moreover, we show that these toric compactifications have a fibration structure, with fibers isomorphic to the Losev-Manin space, and are related to each other via a geometric quotient.

Insurance risk arising from natural catastrophes such as earthquakes is a key component of the minimum capital test for federally regulated property and casualty insurance companies. This paper proposes an integrated, open-source, simulation-based actuarial framework for the assessment of earthquake insurance risk and solvency capital requirements. The framework combines spatio-temporal earthquake occurrence modeling, physics-informed ground-shaking estimation based on Canadian seismic hazard maps, building exposure and vulnerability modeling, and detailed insurance loss and claim calculations within a unified pipeline. Spatial heterogeneity in seismic risk is captured through kernel-based spatio-temporal point process modeling, while Voronoi-based deviance residuals are employed as localized diagnostic tools to validate model adequacy. Simulated insured losses are used to estimate regional and country-wide probable maximum losses (PMLs), and a new capital aggregation formula is proposed that explicitly incorporates cross-provincial dependence in earthquake losses, in contrast to the current region-based regulatory aggregation. The proposed framework enables spatially resolved loss and capital assessment at a fine geographic scale and is implemented in a fully reproducible open-source environment. An interactive web application is also provided to allow users to simulate earthquake damage and the resulting financial losses and insurance claims at user-specified epicenter locations.

Through emerging interpretations of individual “medical freedoms,” a panoply of state legislative bills seeks to undermine long-standing public health and health care requirements including recommendations to test, screen, treat, and vaccinate persons. To the extent these bills could upend decades of laws and policies protecting individual and communal health, especially among vulnerable individuals, they threaten the health — and freedoms — of all persons.