We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse hazard rates; it therefore remains tractable even when density derivatives are intractable. Our main application concerns the approximation of normalized extremes by Fréchet laws. In this setting, the new discrepancy provides a quantitative measure of distributional proximity in terms of the average regular variation at infinity of the underlying cumulative distribution function. We illustrate the approach through explicit computations for maxima of Pareto, Cauchy, and Burr~XII distributions.

Carbon-enhanced metal-poor (CEMP) stars are ancient stars enriched in carbon and heavy elements. Some of these stars exhibit enhanced s-process and/or r-process elements, hence are classified as CEMP-s, CEMP-rs, or CEMP-r. This classification is challenging due to the limited availability of heavy element abundances, particularly among r-process elements. Heavy r-process elements such as terbium, holmium, thulium, ytterbium, lutetium, tantalum, and iridium have rarely been measured because their sensitive lines are located in the ultraviolet. However, they provide sensitive diagnostics of the s-, r-, and i- nucleosynthetic processes. In this work, we aim to obtain a secure classification of CEMP-s and -rs stars and investigate whether the i-process can account for the measured abundance patterns in CEMP-rs stars. We derive the abundance profiles, notably for twelve heavy r-elements, including, in some cases, tantalum, using high-resolution UVES spectra of seventeen CEMP-s and -rs stars. Based on indicators such as the [s/r] abundance ratio or the model-independent 'abundance distance', nine stars are confirmed as CEMP-rs and six as CEMP-s. The classification of two objects remains uncertain. The i-process satisfactorily reproduces the abundance patterns of CEMP-rs stars. However, larger samples are needed to confirm trends with metallicity and clarify how CEMP-rs stars differ from CEMP-s stars.

Quantum theory admits ensembles of quantum nonlocality without entanglement (QNLWE). These ensembles consist of seemingly classical states (they are perfectly distinguishable and non-entangled) that cannot be perfectly discriminated with local operations and classical communication (LOCC). Here, we analyze QNLWE from a causal perspective, and show how to perfectly discriminate some of these ensembles using local operations and classical communication without definite causal order. Specifically, three parties with access to an instance of indefinite causal order-the AF/BW process-can perfectly discriminate the states in a QNLWE ensemble--the SHIFT ensemble--with local operations. Hence, this type of quantum nonlocality disappears at the expense of definite causal order while retaining classical communication. Our results thereby leverage the fact that LOCC is a conjunction of three constraints: local operations, classical communication, and definite causal order. Moreover, we show how multipartite generalizations of the AF/BW process are transformed into multiqubit ensembles that exhibit QNLWE. Such ensembles are of independent interest for cryptographic protocols and for the study of separable quantum operations unachievable with LOCC.

Given a tesselation of the plane, defined by a planar straight-line graph $G$, we want to find a minimal set $S$ of points in the plane, such that the Voronoi diagram associated with $S$ "fits" \ $G$. This is the Generalized Inverse Voronoi Problem (GIVP), defined in \cite{Trin07} and rediscovered recently in \cite{Baner12}. Here we give an algorithm that solves this problem with a number of points that is linear in the size of $G$, assuming that the smallest angle in $G$ is constant.

Interstellar linear polarization occurs when starlight passes through elongated dust grains aligned by interstellar magnetic fields. The observed polarization can come from different dust structures along the line of sight (LOS). By combining polarization measurements with stellar distances, we can study the plane-of-sky Galactic magnetic field (GMF) between the observer and the star and separate the contributions of clouds with different GMF properties. We used optical and near-infrared (NIR) polarization data from three regions in the Galactic plane (|b|<1^{\circ} and $19.\!\!^{\circ}8

In this work, we study the effects of $\Lambda$-hyperons on neutron star properties employing a metamodel framework for the equation of state (EoS). Different choices for defining the hyperonic couplings with different levels of parametric freedom are discussed. In all models, the predicted NS maximum masses are reduced compared with the purely nucleonic composition as expected. In the case of relating hyperonic couplings via $SU(6)$-symmetry arguments to the nucleonic ones, we find that NS radii for intermediate mass stars are shifted to higher values compared with purely nucleonic stars, in agreement with the existing literature. However, allowing for more freedom for the hyperonic couplings, the effect is strongly reduced, and the distributions in the NS mass-radius plane of models with and without hyperons become very close. We have also investigated how different nucleonic density functionals influence the hyperon matter composition and neutron star properties.