The bidimensionality of a set of vertices $X$ in a graph $G$ is the maximum $k$ for which $G$ contains as a $X$-rooted minor the $(k \times k)$-grid. This notion allows for the following version of the Graph Minors Structure Theorem (GMST) that avoids the use of apices and vortices: $K_k$-minor free graphs are those that admit tree decompositions whose torsos contain sets of bounded bidimensionality whose removal yield a graph embeddable in some surface $Σ$ of bounded Euler-genus. We next fix the target condition by demanding that $Σ$ is some particular surface. This defines a "surface extension" of treewidth, where $Σ$-${\sf tw}$ is the minimum $k$ for which $G$ admits a tree decomposition whose torsos become embeddable in $Σ$ after the removal of a set of bidimensionality at most $k$. We identify a finite collection $\mathfrak{D}_Σ$ of parametric graphs and prove that the minor-exclusion of the graphs in $\mathfrak{D}_Σ$ determines the behavior of $Σ$-${\sf tw},$ for every surface $Σ.$ It follows that the collection $\mathfrak{D}_Σ$ bijectively corresponds to the "surface obstructions" for $Σ,$ i.e., surfaces that are minimally non-contained in $Σ.$ Our results are tight in the sense that $Σ$-${\sf tw}$ cannot be bounded for all parametric graphs in $\mathfrak{D}_Σ$.

Auscultation provides a rich diversity of information to diagnose cardiovascular and respiratory diseases. However, sound auscultation is challenging due to noise. In this study, a modified version of the affine non-negative matrix factorization (NMF) approach is proposed to blindly separate lung and heart sounds recorded by a digital stethoscope. This method applies a novel NMF algorithm, which embodies a parallel structure of multilayer units on the input signal, to find a proper estimation of source signals. Another key innovation is the use of the periodic property of the signals which improves accuracy compared to previous works. The method is tested on 100 cases. Each case consists of two synthesized mixtures of real measurements. The effect of different parameters is discussed, and the results are compared to other current methods. Results demonstrate improvements in the source-to-distortion ratio (SDR), source-to-interference ratio (SIR), and source-to-artifacts ratio (SAR) of heart and lung sounds, respectively.

Neutrino masses may have evolved dynamically throughout the history of the Universe, potentially leading to a mass spectrum distinct from the normal or inverted ordering observed today. While cosmological measurements constrain the total energy density of neutrinos, they are not directly sensitive to a dynamically changing mass ordering unless future surveys achieve exceptional precision in detecting the distinct imprints of each mass eigenstate on large-scale structures. In this work, we investigate the impact of a dynamic neutrino mass spectrum on the diffuse supernova neutrino background (DSNB), which is composed of neutrinos from all supernova explosions throughout cosmic history and is on the verge of experimental detection. The dynamic evolution of neutrino masses with redshift changes the propagation of neutrinos inside the supernova. Since neutrino oscillations are highly sensitive to the mass spectrum, we show that the electron neutrino survival probability carries distinct signatures of the evolving neutrino mass spectrum. Our results show that a dynamic neutrino mass spectrum can modify the DSNB flux in an energy-dependent way. However, we find that the current level of spectral shape uncertainty in DSNB modeling makes a direct detection beyond the reach of present and near-future experiments. Nonetheless, our study highlights the DSNB as a probe of redshift-dependent neutrino properties once the astrophysical systematics are brought under control.

We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithmapplied to a class of non convex functions called strongly quasar convex functions. We show thatNAG can achieve an accelerated convergence speed at the cost of a lower curvature assumption.We provide a continuous analysis through high resolution ODEs, where we show that despite thatnegative friction may appear, the solution of the system achieves accelerated rate of convergenceto the minimum. Finally, we identify the key geometrical property that, if dropped, theoreticallycancels the acceleration phenomenon.

We introduce a new contraction property, which we call the generalized $p$-contraction property, for $p$-energy forms as generalizations of many well-known inequalities, such as $p$-Clarkson's inequality, the strong subadditivity and the Markov property in the theory of nonlinear Dirichlet forms, and show that any $p$-energy form satisfying $p$-Clarkson's inequality is Fréchet differentiable. We also verify the generalized $p$-contraction property for $p$-energy forms on fractals constructed by Kigami [Mem. Eur. Math. Soc. 5 (2023)] and by Cao--Gu--Qiu [Adv. Math. 405 (2022), no. 108517]. As a general framework of $p$-energy forms taking the generalized $p$-contraction property into consideration, we introduce the notion of $p$-resistance form and investigate fundamental properties of $p$-harmonic functions with respect to $p$-resistance forms. In particular, some new estimates on scaling factors of self-similar $p$-energy forms on self-similar sets are obtained by establishing Hölder regularity estimates for $p$-harmonic functions, and the $p$-walk dimensions of any generalized Sierpiński carpet and the $D$-dimensional level-$l$ Sierpiński gasket are shown to be strictly greater than $p$.

Accurate attribution of authorship is crucial for maintaining the integrity of digital content, improving forensic investigations, and mitigating the risks of misinformation and plagiarism. Addressing the imperative need for proper authorship attribution is essential to uphold the credibility and accountability of authentic authorship. The rapid advancements of Large Language Models (LLMs) have blurred the lines between human and machine authorship, posing significant challenges for traditional methods. We present a comprehensive literature review that examines the latest research on authorship attribution in the era of LLMs. This survey systematically explores the landscape of this field by categorizing four representative problems: (1) Human-written Text Attribution; (2) LLM-generated Text Detection; (3) LLM-generated Text Attribution; and (4) Human-LLM Co-authored Text Attribution. We also discuss the challenges related to ensuring the generalization and explainability of authorship attribution methods. Generalization requires the ability to generalize across various domains, while explainability emphasizes providing transparent and understandable insights into the decisions made by these models. By evaluating the strengths and limitations of existing methods and benchmarks, we identify key open problems and future research directions in this field. This literature review serves as a roadmap for researchers and practitioners interested in understanding the state of the art in this rapidly evolving field.

We propose a novel approach which implements the relativistic calculations of the photon travel time into a robust timing model for pulsars orbiting supermassive black holes. We demonstrate that timing models relying on the lowest-order (1PN) post-Newtonian approximation can produce significant discrepancies in strong-field configurations, affecting the predicted relativistic times of arrival at an Earth-based observatory. We also show how a misestimation of the pulsar parameters can lead to the appearance of phase-dependent residual, which hints at a tremendous constraining power of the binary and intrinsic parameters for timing observations of potential pulsars at the Galactic Center.

Mandatory waiting periods have been instituted for medical procedures, gun purchases, and other high-stakes decisions. Are these softly paternalistic policies substitutes for harder restrictions, and are delayed decisions more respected? In a general population survey experiment, Choice Architects make rules for decision-makers facing a high-stakes Bomb Risk Elicitation Task. Treatments vary when the decision is made: on the spot or after one day, and whether the initial decision can be revised. Choice Architects set a cap on the decision-maker's risk taking; in one treatment, they can additionally implement a mandatory waiting period. Exogenous deliberation has no effect on the cap; equivalence testing (TOST) and Bayesian analysis ($\text{BF}_{01} \approx 12$) provide strong positive evidence for the absence of an effect. Endogenously prescribed waiting periods are add-on restrictions that do not substitute for the cap. Choice Architects believe that, with time, the average decision-maker will take less risk and -- because of the distribution of Choice Architects' bliss points -- come closer to Choice Architects' subjective ideal choice; the resulting reduction in forecasted errors is small. Soft and hard paternalistic instruments are not substitutes: waiting periods are deployed as add-on restrictions.

To ensure their safe use, autonomous vehicles (AVs) must meet rigorous certification criteria that involve executing maneuvers safely within (arbitrary) scenarios where other actors perform their intended maneuvers. For that purpose, existing scenario generation approaches optimize search to derive scenarios with high probability of dangerous situations. In this paper, we hypothesize that at road junctions, potential danger predominantly arises from overlapping paths of individual actors carrying out their designated high-level maneuvers. As a step towards AV certification, we propose an approach to derive a complete set of (potentially dangerous) abstract scenarios at any given road junction, i.e. all permutations of overlapping abstract paths assigned to actors (including the AV) for a given set of possible abstract paths. From these abstract scenarios, we derive exact paths that actors must follow to guide simulation-based testing towards potential collisions. We conduct extensive experiments to evaluate the behavior of a state-of-the-art learning-based AV controller on scenarios generated over two realistic road junctions with increasing number of external actors. Results show that the AV-under-test is involved in increasing percentages of unsafe behaviors in simulation, which vary according to functional- and logical-level scenario properties.

It is shown that the Hamiltonian formalism proposed previously in [1] to describe the nonlinear dynamics of only {\it soft} fermionic and bosonic excitations contains much more information than initially assumed. In this paper, we have demonstrated in detail that it also proved to be very appropriate and powerful in describing a wide range of other physical phenomena, including the scattering of colorless plasmons off {\it hard} thermal (or external) color-charged particles moving in a hot quark-gluon plasma. A generalization of the Poisson superbracket including both anticommuting variables for hard modes and normal variables of the soft Bose field, is presented for the case of continuous medium. The corresponding Hamilton equations are defined, and the most general form of the third- and fourth-order interaction Hamiltonians is written out in terms of the normal boson field variables and hard momentum modes of the quark-gluon plasma. The canonical transformations involving both bosonic and hard mode degrees of freedom of the system under consideration, are discussed. The canonicity conditions for these transformations based on the Poisson superbracket, are derived. The most general structure of canonical transformations in the form of integro-power series up to sixth order in a new normal field variable and a new hard mode variable, is presented. For the hard momentum mode of quark-gluon plasma excitations, an ansatz separating the color and momentum degrees of freedom, is proposed. The question of approximation of the total effective scattering amplitude when the momenta of hard excitations are much larger than those of soft excitations of the plasma, is considered. The self-consistent system of Boltzmann-type kinetic equations taking into account the time evolution of the mean value of the color charge of the hard particle is obtained.

In this paper, we propose Intelligent Environmental Empathy (IEE) as a new driver for climate peace and justice, as an emerging issue in the age of big data. We first show that the authoritarian top-down intergovernmental cooperation, through international organizations (e.g., UNEP) for climate justice, could not overcome environmental issues and crevices so far. We elaborate on four grounds of climate injustice (i.e., teleological origin, axiological origin, formation cause, and social epistemic cause), and explain how the lack of empathy and environmental motivation on a global scale causes the failure of all the authoritarian top-down intergovernmental cooperation. Addressing all these issues requires a new button-up approach to climate peace and justice. Secondly, focusing on the intersection of AI, environmental empathy, and climate justice, we propose a model of Intelligent Environmental Empathy (IEE) for climate peace and justice at the operational level. IEE is empowered by the new power of environmental empathy (as a driver of green obligation for climate justice) and putative decentralized platform of AI (as an operative system against free riders), which Initially, impact citizens and some middle-class decision makers, such as city planners and local administrators, but will eventually affect global decision-makers as well.

We present a model predictive control (MPC) framework for linear switched evolution equations arising from a parabolic partial differential equation (PDE). First-order optimality conditions for the resulting finite-horizon optimal control problems are derived. The analysis allows for the incorporation of convex control constraints and sparse regularization. Then, to mitigate the computational burden of the MPC procedure, we employ Galerkin reduced-order modeling (ROM) techniques to obtain a low-dimensional surrogate for the state-adjoint systems. We derive recursive a-posteriori estimates for the ROM feedback law and the ROM-MPC closed-loop state and show that the ROM-MPC trajectory evolves within a neighborhood of the true MPC trajectory, whose size can be explicitly computed and is controlled by the quality of the ROM. Such estimates are then used to formulate two ROM-MPC algorithms with closed-loop certification.

This paper proposes V2Sim, an open source Pythonbased simulation platform designed for advanced vehicle-to-grid (V2G) analysis in coupled urban power and transportation networks. By integrating a microscopic urban transportation network (MUTN) with a power distribution network (PDN), V2Sim enables precise modeling of electric vehicle charging loads (EVCL) and dynamic V2G operations. The platform uniquely combines SUMO for MUTN simulations and an optimized DistFlow model for PDN analysis, with dedicated models for fast charging stations (FCS) and slow charging stations (SCS), capturing detailed charging dynamics often overlooked in existing simulation tools. V2Sim supports a range of customizable V2G strategies, advanced fault-sensing in charging stations, and parallel simulation through multi-processing to accelerate large-scale case studies. Case studies using a real-world MUTN from Nanjing, China, demonstrate V2Sim's capability to analyze the spatial-temporal distribution of EVCL and evaluate V2G impacts, such as fault dissemination and pricing variations, in unprecedented detail. Unlike traditional equilibrium models, V2Sim captures single-vehicle behavior and charging interactions at the microscopic level, offering unparalleled accuracy in assessing the operational and planning needs of V2G-compatible systems. This platform serves as a comprehensive tool for researchers and urban planners aiming to optimize integrated power and transportation networks.

We investigate an odd-sized fermionic open tight-binding chain subjected to stochastic projective measurements at its central site, effectively inducing localized dephasing. Focusing initially on the single-particle regime, we demonstrate that when the system is prepared in an even-parity state, the dynamics under central-site dephasing drive it toward a nontrivial steady state, which we characterize through both analytical and numerical approaches. Remarkably, this steady state exhibits long-range quantum correlations in the form of symmetrically positioned, pairwise entangled sites across the chain. We further show that the degree of pairwise entanglement can be significantly enhanced by increasing the particle number, provided the system is initialized within a specific symmetry sector associated with an underlying strong symmetry operator. Our results identify a minimal measurement-induced route for generating symmetry-selected long-range pairwise entanglement, with possible implications for quantum communication and distributed quantum information processing.

The question of how Algebra can be used to solve dynamical systems and characterize chaos was first posed in a fertile mathematical context by Ziglin, Morales, Ramis and Simó using differential Galois theory. Their study was aimed at first-order, later higher-order, variational equations of Hamiltonian systems. Recent work by this author formalized a compact yet comprehensive expression of higher-order variationals as one infinite linear system, thereby simplifying the approach. More importantly, the dual of this linear system contains all information relevant to first integrals, regardless of whether the original system is Hamiltonian. This applicability to formal calculation of conserved quantities is the centerpiece of this paper, following an introduction to the requisite context. Three important examples, namely particular cases of Dixon's system, the SIR epidemiological model with vital dynamics and the Van der Pol oscillator, are tackled, and explicit convergent first integrals are provided for the first two.

We examine the impact of various Initial Mass Function (IMF) sampling and supernova (SN) feedback injection methods on the star formation and metal enrichment histories of Ultra-Faint Dwarf (UFD) galaxy analogs. These analogs, characterized by M_vir~10^8 solar mass and M_star < 10^4.5 solar mass at z=0, are simulated using high-resolution cosmological hydrodynamic zoom-in simulations with a gas particle mass resolution of ~63 solar mass. We compare three approaches: the burst model, stochastic IMF sampling, and individual IMF sampling. These methods differ not only in how star particles are sampled following the IMF, but also in how SN feedback energy is injected -- specifically in the degree of temporal and spatial discreteness, with the individual IMF sampling method being the most discrete SN feedback and thus the most physically realistic. Our findings indicate that, despite variations in sampling and SN feedback injection, the final stellar masses across methods are generally similar. However, star formation is notably more continuous in the individual sampling runs due to the weaker suppression from discrete SN events, which enables star formation in denser environments. This sustained star formation leads to more frequent self-enrichment of star-forming gas, resulting in stellar metallicities that are 0.2 to 0.5 dex higher in individual sampling runs compared to burst and stochastic models. These findings highlight the importance of considering both IMF sampling and SN feedback implementation when modeling the star formation and chemical evolution of UFD galaxies.

Confinement prohibits isolation of color charges, e.g., quarks, in nature via a process called string breaking: the separation of two charges results in an increase in the energy of a color flux, visualized as a string, connecting those charges. Eventually, creating additional charges is energetically favored, hence breaking the string. Such a phenomenon can be probed in simpler models, including quantum spin chains, enabling enhanced understanding of string-breaking dynamics. A challenging task is to understand how string breaking occurs as time elapses, in an out-of-equilibrium setting. This work establishes the phenomenology of dynamical string breaking induced by a gradual increase of string tension over time. It, thus, goes beyond instantaneous quench processes and enables tracking the real-time evolution of strings in a more controlled setting. We focus on domain-wall confinement in a family of quantum Ising chains. Our results indicate that, for sufficiently short strings and slow evolution, string breaking can be described by the transition dynamics of a two-state quantum system akin to a Landau-Zener process. For longer strings, a more intricate spatiotemporal pattern emerges: the string breaks by forming a superposition of bubbles (domains of flipped spins of varying sizes), which involve highly excited states. We finally demonstrate that string breaking driven only by quantum fluctuations can be realized in the presence of sufficiently long-ranged interactions. This work holds immediate relevance for studying string breaking in quantum-simulation experiments.

For the group $\mathrm{GL}_{n}$ and the anisotropic elements, we confirm the purity hypothesis of Goresky, Kottwitz and MacPherson, which states that the affine Springer fibers are cohomologically pure in the sense of Grothendieck-Deligne.

In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It is desirable to know the eigenvalue decay properties of these matrices without explicitly forming them, such as when determining if a low-rank approximation is feasible. In this work, we introduce a new eigenvalue quantile estimation framework for some kernel matrices. This framework gives meaningful bounds for all the eigenvalues of a kernel matrix while avoiding the cost of constructing the full matrix. The kernel matrices under consideration come from a kernel with quick decay away from the diagonal applied to uniformly-distributed sets of points in Euclidean space of any dimension. We prove the efficacy of this framework given certain bounds on the kernel function, and we provide empirical evidence for its accuracy. In the process, we also prove a general interlacing-type theorem for finite sets of numbers. Additionally, we indicate an application of this framework to the study of the intrinsic dimension of data, as well as several other directions in which to generalize this work.

Stellar mass governs stellar evolution and the distribution of stellar masses plays a central role in the dynamical evolution of stellar clusters. Using high-precision astrometry and photometry from Gaia DR3, we investigate mass segregation and the present-day mass function (PDMF) in fifteen nearby open clusters. Single and binary stars are identified from the color magnitude diagram, and stellar masses for single stars are derived from a cubic spline relation with G-band magnitude, while binary component masses are estimated via a simulation-based inference method. Based on these mass estimates, mass segregation is quantified using the minimum spanning tree technique, and the PDMF is characterized through power-law fitting. We detect significant mass segregation in all clusters. Systems lacking very massive stars exhibit weaker segregation affecting a larger fraction of the population, whereas clusters hosting a small number of very massive stars show strong central concentration of these objects. The PDMF follows a power law with a slope of 2.01, consistent with the canonical Kroupa initial mass function. The strength of mass segregation correlates with the mass of the most segregated stars. Strong segregation observed in very young clusters supports a primordial origin, while older clusters display signatures of dynamical mass segregation at lower masses and evidence of binary disruption. A low-mass break in the PDMF observed in most clusters, if not due to incompleteness, may reflect early gas expulsion in initially mass-segregated systems.

In analogy with the 290-Theorem of Bhargava-Hanke, a criterion set is a finite subset $C$ of the totally positive integers in a given totally real number field such that if a quadratic form represents all elements of $C$, then it necessarily represents all totally positive integers, i.e., is universal. We use a novel characterization of minimal criterion sets to show that they always exist and are unique, and that they must contain certain explicit elements. We also extend the uniqueness result to the more general setting of representations of a given subset of the integers.

The physical properties of the intracluster medium (ICM) reflect signatures of the underlying gravitational potential, mergers and strong interactions with other halos and satellite galaxies, as well as galactic feedback from supernovae and supermassive black holes (SMBHs). Traditionally, clusters have been characterized in terms of summary statistics, such as halo mass, X-ray luminosity, cool-core state, luminosity of AGN, and number of merging components. In this paper of the Extracting Reality from Galaxy Observables with Machine Learning series (ERGO-ML), we instead consider the full information content available in maps of X-ray emission from the ICM. We employ Nearest Neighbour Contrastive Learning (NNCLR) to identify and populate a low-dimensional representation space of such images. Using idealized X-ray maps of the 352 clusters of the TNG-Cluster cosmological magnetohydrodynamical simulation suite, we take three orthogonal projections of each cluster at eight snapshots within the redshift range $0\leq z<1$, resulting in a dataset of $\sim$8,000 images. Our findings reveal that this representation space forms a continuous distribution from relaxed to merging objects, and from centrally-peaked to flat emission profiles. The representation also exhibits clear trends with redshift, with halo, gas, stellar, and SMBH mass, with time since a last major merger, and with indicators of dynamical state. We show that an 8-dimensional representation can be used to predict a variety of cluster properties, find analogs, and identify correlations between physical properties, thereby suggesting causal relationships. Our analysis demonstrates that contrastive learning is a powerful tool for characterizing galaxy clusters from their images alone, allowing us to derive constraints on their physical properties and formation histories using cosmological hydrodynamical galaxy simulations.

In many image processing applications (e.g. computational anatomy) a groupwise registration is performed on a sample of images and a template image is simultaneously generated. From the template alone it is in general unclear to which extent the registered images are still spatially misaligned. The local spatial variation left after registration may be seen as the resolution of the resulting template. In this sense we develop the first template resolution measure (TRM) quantifying the misalignment at each location of the template. The TRM is based on the key insight that the size of such misalignments can be determined as the amount of smoothing required to bring the registered images in agreement. This relationship is mathematically derived from characteristic examples in one dimension. This way, the TRM quantifies the remaining spatial variation in the template's units of length. Furthermore we propose to enhance the template by an effective visualization of its resolution measure. Finally we demonstrate the TRM's applicability and validate its interpretability for example datasets in two and three dimensions. The corresponding code is publicly available on GitHub.

In this article, we investigate the focal locus of closed (not necessarily compact) submanifolds in a forward complete Finsler manifold. The main goal is to show that the associated normal exponential map is \emph{regular} in the sense of F.W. Warner (Am. J. of Math., 87, 1965). As a consequence, we show that the normal exponential is non-injective near any tangent focal point. Extending the ideas of Warner, we study the connected components of the regular focal locus. This allows us to identify an open and dense subset, on which the focal time maps are smooth, provided they are finite. We explicitly compute the derivative at a point of differentiability. As an application of the local form of the normal exponential map, following R.L. Bishop's work (Proc. Amer. Math. Soc., 65, 1977), we express the tangent cut locus as the closure of a certain set of points, called the separating tangent cut points. This strengthens the results from the present authors' previous work (J. Geom. Anal., 34, 2024).

We prove an injectivity theorem for the cohomology of the Du Bois complexes of varieties with isolated singularities. We use this to deduce vanishing statements for the cohomologies of higher Du Bois complexes of such varieties. Besides some extensions and conjectures in the non-isolated case, we also provide analogues for intersection complexes.

This lecture note is hopefully helpful to undergraduate and postgraduate students or beginning Ph.D students both in theoretical physics and in applied mathematics. Modern terminology in differential geometry has been discussed in the book with the motivation of geometrical or pictorial way of thinking. This note is an effort of teaching differential geometry and shows its wide applicability to relativity theory. The problems in this lecture note may be useful to the students

We prove convergence and compatibility of iterated bulk and boundary operator product expansions (OPEs) in two-dimensional conformal field theory with locally $C_1$-cofinite chiral symmetry. For each tree, we give an explicit domain of convergence for the corresponding iterated OPE. These local expansions glue to single-valued real analytic functions on the configuration spaces, which are the correlation functions of the theory. The proof uses an action of the parenthesized permutation-braid operad on $C_1$-cofinite module categories of a vertex operator algebra. This operad models the fundamental groupoid of the two-dimensional Swiss-cheese operad, and under this action the operadic generators correspond to the genus-zero bootstrap equations of boundary CFT.

We study $Ξ$-$^4{\mathrm{He}}$ ($α$) momentum correlation functions in the high-energy nuclear collisions to investigate the nature of the $ΞN$ interactions. We employ the folding $Ξα$ potential based on the lattice QCD $ΞN$ interactions to compute the correlation function. The $Ξα$ potential supports a Coulomb-assisted bound state ${}^5_Ξ\mathrm{H}$ in the $Ξ^-α$ channel, while the $Ξ^0α$ channel is unbound. To examine the sensitivity of the correlation function to the nature of the $Ξα$ interaction, we vary the potential strength simulating stronger and weaker interactions. The result of the correlation function is sensitive to the existence of the bound state in the $Ξ^0 α$ channel, and the characteristic behavior of the bound state remains also in the $Ξ^-α$ correlation with the Coulomb interaction. The effect of the repulsive core of the $Ξα$ potential can be found in the correlation from the small source as the distinctive dip in the intermediate momentum region.

We provide a rigorous analysis of the generalized Jang equation in the asymptotically anti-de Sitter setting modelled on constant time slices of anti-de Sitter spacetimes in dimensions $3\leq n \leq 7$ for a very general class of asymptotics. Potential applications to spacetime positive mass theorems for asymptotically anti-de Sitter initial data sets are discussed.

How informative are job ads about the actual pay and non-pay attributes offered by employers? Using a comprehensive database of job ads posted by Norwegian employers, we develop a methodology to systematically classify the pay and non-pay job attributes advertised in vacancy texts. About 60% of job ads provide pay-related information and nearly all ads feature information on non-pay attributes. We link these advertised attributes to the employers posting the ads and validate this information against revealed-preference measures of employer quality, realized attributes, and choices from a survey experiment. All three strategies confirm that job ads provide reliable signals of employer quality. We then incorporate the detailed job attributes in a monopsony framework and quantify their contribution to labor market inequality.