Gerd Müller | Searcharxiv

arXiv2025

Capturing Road-Level Heterogeneity in Crash Severity on Rural Two-Lane Highways: A Multilevel Statistical and Machine-Learning Analysis

Crash severity may vary across roads because crashes on the same road share contextual characteristics not fully represented by observed variables. This study examined road-level heterogeneity using 19,956 police-reported crashes from 100 rural two-lane highways in Iran during 2021-2024. Single-level logistic regression was compared with random-intercept and random-coefficient multilevel logistic models. A regression-based mixed-effects random forest (MERF) was also used for an exploratory assessment of nonlinear predictive relationships and road-level patterns. The null multilevel model produced an intraclass correlation coefficient of 20.3 percent, indicating meaningful latent between-road variation in crash severity. Pavement condition had the largest estimated random-slope variance, followed by lighting condition, driver education, and driver age. Logistic road-level random intercepts ranged from -2.87 to +1.51 on the log-odds scale. In a comparison excluding road-specific information, the ten-variable MERF random-forest component achieved an AUC of 0.701, compared with 0.638 for single-level logistic regression. Retaining MERF road-level corrections for roads represented during training increased AUC to 0.763. MERF road-level corrections were strongly associated with logistic random intercepts (Pearson r = 0.892; Spearman rho = 0.931), indicating similar relative road patterns, although the estimates are not numerically equivalent. The findings support complementary use of multilevel and nonlinear models. Road-level estimates may help prioritize further investigation, but they do not measure crash frequency, total road risk, or causal effects.

stat.AP↗

arXiv1997

Derivation algebras of toric varieties

Normal affine algebraic varieties in characteristic 0 are uniquely determined (up to isomorphism) by the Lie algebra of derivations of their coordinate ring. This is not true without the hypothesis of normality. But, we show that (in general, non-normal) toric varieties defined by simplicial affine semigroups are uniquely determined by their Lie algebra if they are supposed to be Cohen-Macaulay of dimension at least 2 or Gorenstein of dimension 1. Moreover, every automorphism of the Lie algebra is induced from a unique automorphism of the variety and every derivation of the Lie algebra is inner, i.e., the first cohomology of the Lie algebra with coefficients in the adjoint representation vanishes.

alg-geom↗

arXiv1996

Symmetries of Surface Singularities

The automorphism group ${\rm Aut}\: X$ of a weighted homogeneous normal surface singularity $X$ has a maximal reductive algebraic subgroup $G$ which contains every reductive algebraic subgroup of ${\rm Aut}\: X$ up to conjugation. In all cases except the cyclic quotient singularities the connected component $G_1$ of the unit equals ${\Bbb C}^*$. The induced action of $G$ on the minimal good resolution of $X$ embeds the finite group $G/G_1$ into the automorphism group of the central curve $E_0$ of the exceptional divisor. We describe $G/G_1$ as a subgroup of ${\rm Aut}\: E_0$ in case $E_0$ is rational as well as for simple elliptic singularities. Moreover, sufficient conditions for $G$ to be a direct product $G_1 \times G/G_1$ are presented. Finally, it is shown that $G/G_1$ acts faithfully on the integral homology of the link of $X$.

alg-geom↗