Single-photon emission computed tomography for myocardial perfusion imaging (MPI SPECT) is a widely used diagnostic tool for coronary artery disease. However, the procedure requires considerable scanning time, leading to patient discomfort and the potential for motion-induced artifacts. Reducing the number of projection views while keeping the time per view unchanged provides a mechanism to shorten the scanning time. However, this approach leads to increased sampling artifacts, higher noise, and hence limited image quality. To address these issues, we propose sparseview SPECT image enhancement (SPASHT), inherently training the algorithm to improve performance on defect-detection tasks. We objectively evaluated SPASHT on the clinical task of detecting perfusion defects in a retrospective clinical study using data from patients who underwent MPI SPECT, where the defects were clinically realistic and synthetically inserted. The study was conducted for different numbers of fewer projection views, including 1/6, 1/3, and 1/2 of the typical projection views for MPI SPECT. Performance on the detection task was quantified using area under the receiver operating characteristic curve (AUC). Images obtained with SPASHT yielded significantly improved AUC compared to those obtained with the sparse-view protocol for all the considered numbers of fewer projection views. To further assess performance, a human observer study on the task of detecting perfusion defects was conducted. Results from the human observer study showed improved detection performance with images reconstructed using SPASHT compared to those from the sparse-view protocol. The results provide evidence of the efficacy of SPASHT in improving the quality of sparse-view MPI SPECT images and motivate further clinical validation.

We consider steady water waves in a two-dimensional channel bounded below by a flat, rigid bottom and above by a free surface. Surface tension is neglected, and the flow is rotational with constant vorticity $a$. We analyze an analytic branch of Stokes waves bifurcating from a subcritical laminar flow, with the wave period serving as the bifurcation parameter. Along this branch, the first eigenvalue of the Fréchet derivative remains negative. Our main focus is the second eigenvalue; its sign plays a crucial role in the analysis of subharmonic bifurcations. This small eigenvalue determines the validity of the principle of exchange of stabilities: a positive sign confirms it, while a negative sign indicates its violation. Furthermore, a positive second eigenvalue corresponds to an increasing period along the bifurcation curve near the critical point, whereas a negative sign implies period decrease. We investigate how the sign of the second eigenvalue depends on the Bernoulli constant $R$ (equivalently, the laminar flow depth $d$) and the vorticity $a$. We show that for each $a$ there exists a critical depth $d_0(a)$ such that the second eigenvalue is positive for $d<d_0(a)$ and negative for $d>d_0(a)$. In the laminar flow, a stagnation point forms when the depth exceeds a threshold $d_s(a)$. We demonstrate that $d_0(a) < d_s(a)$ for $a > a_0 \approx -1.01803$, whereas $d_0(a) > d_s(a)$ for $a < a_0$. We also verify the property of formal stability by a description of the domain in $(a,d)$ variables, where this property holds. Numerical illustrations of these properties are presented in the paper.

We prove well-posedness of the analytic Cauchy problem for gradient generalized Ricci solitons on an abelian bundle gerbe and solve the initial data equations on every compact Riemann surface. Along the way, we provide a novel characterization of the self-similar solutions of the generalized Ricci flow by means of families of automorphisms of the underlying abelian bundle gerbe covering families of diffeomorphisms isotopic to the identity.

Generated networks are widely used in network-based research as a convenient simulation environment. Generating universal networks that more accurately reflect real-world patterns is a cornerstone task. This study proposes a vari-linear network generation model that incorporates two core mechanisms: exponential probabilistic growth and vari-linear preferential attachment. It concurrently overcomes the limitations of traditional growth in characterizing the low-degree region of the degree distribution and the issues regarding the universality of linear preferential attachment. Results indicate that our model describes real-world networks more comprehensively and faithfully, and is highly interpretable. Its performance on diverse empirical datasets is several times better than traditional methods. Related mechanisms and conclusions are substantiated through ablation experiments and statistical analysis. Notably, it achieves a unified interpretation of previously isolated classical network characteristics. This work not only provides a higher-quality universal network generation method, but also bridges the boundaries between traditional concepts, thereby promoting substantive progress in the "world model" of networks.

Recent causal inference literature has introduced causal effect decompositions to quantify sources of observed inequalities or disparities in outcomes, but these approaches are typically limited to pairwise comparisons. In healthcare delivery settings, both the exposure of interest-hospital or healthcare unit-and sociodemographic group membership may be polytomous, making pairwise contrasts inadequate. We therefore take the observed variance in care delivery outcomes as the quantity of interest and develop a new causal variance decomposition framework for this setting. The proposed framework attributes the observed variation to eight components, including novel terms characterizing modification of hospital effects by sociodemographic group membership, hospital access or selection, and the correlation between these two sources of heterogeneity. We discuss the causal interpretation of these components, propose both parametric and nonparametric model-based estimators, and study their performance through simulation. Finally, we illustrate the method using data from the SEER program in an application to cervical cancer care delivery.

The $O_k$ null test can not only assess whether the cosmic curvature is zero, therefore if true reducing degeneracies between cosmic curvature and other cosmological parameters, but also provide a model-independent check of compatibility between different data sets. However, traditional implementations often require absolute distance data from Type Ia supernovae (SNe Ia) or baryon acoustic oscillation (BAO) measurements, limiting their applicability because such absolute distance data usually are not accessible. The BAO Alcock Paczynski (AP) parameter $F_{AP}$ is a measurement of a distance ratio, making the Dark Energy Spectroscopic Instrument (DESI) AP measurements particularly well suited for the $O_k$ null test because no absolute distance measurements are required. We propose a novel null test of cosmic curvature tailored to DESI BAO data that combines $F_{AP}$ with ratios such as $D_V'/D_V$ or $D_M'/D_M$. Crucially, this construction eliminates the need for absolute distance measurements. We further develop multi-task Gaussian processes to perform the null test. This approach can also be applied to a joint DESI BAO and SNe Ia dataset, and we find that DESI BAO and SNe Ia data are compatible. Although there is $\sim 2σ$ evidence of nonzero curvature at low redshift $z\lesssim 0.5$, this result is not conclusive largely due to the lack of observational data in the corresponding redshift range.

A much-cited 2022 paper by Pekar et al. claimed that Bayesian analysis of the molecular phylogeny of early SARS-CoV-2 cases indicated that it was more likely that two successful introductions to humans had occurred than that just one had. Here I show that after correcting a fundamental error in Bayesian reasoning the results in that paper give larger likelihood for a single introduction than for two.

We study the problem of modelling high-dimensional, heavy-tailed time series data via a factor-adjusted vector autoregressive (VAR) model, which simultaneously accounts for pervasive co-movements of the variables by a handful of factors, as well as their remaining interconnectedness using a sparse VAR model. To handle heavy tails, we propose an element-wise data truncation step followed by a two-stage estimation procedure for estimating the latent factors and the VAR parameter matrices. Assuming the existence of the $(2 + 2ε)$-th moment only for some $ε\in (0, 1)$, we derive the rates of estimation which, making explicit the effect of heavy tails through $ε$, are comparable to the rates attainable in light-tailed settings as $ε\to 1$. Numerically, we demonstrate the competitive performance of the proposed estimators on simulated datasets and in an application to forecasting macroeconomics indicators.

We investigate the formation of toponium in the single-leptonic final state at the LHC. Our study builds on our recently proposed framework that incorporates the associated non-perturbative effects into Monte Carlo simulations through the Green's function of the non-relativistic QCD Hamiltonian and the re-weighting of hard-scattering matrix elements. This allows us to perform a phenomenological analysis that demonstrates that a statistically significant excess from toponium formation could already be accessible in Run~2 data. Moreover, our results highlight observables that provide handles for signal characterisation and establish the single-leptonic channel as a competitive and complementary avenue for the ongoing exploration of toponium signatures at colliders.

Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised learning with genomic data remains insufficiently explored. Conventional clustering methods assign a singular identity to each cell, potentially obscuring transitional states during differentiation or mutation. This study introduces a variational Bayesian framework for clustering and analysing single-cell genomic data, employing a Bayesian Gaussian mixture model to estimate the probabilistic association of cells with distinct clusters. This approach captures cellular transitions, yielding biologically coherent insights into neurogenesis and breast cancer progression. The inferred clustering probabilities enable further analyses, including Differential Expression Analysis and pseudotime analysis. Furthermore, we propose utilising the misclustering rate and Area Under the Curve in clustering scRNA-seq data as an innovative metric to quantitatively evaluate overall clustering performance. This methodological advancement enhances the resolution of single-cell data analysis, enabling a more nuanced characterisation of dynamic cellular identities in development and disease.

Spin- and orbital-resolved access to the electronic bands is necessary to establish key properties of quantum materials such as the quantum-geometric tensor. Despite recent revival on magnetic Kagome compounds, no spectroscopic access to their magnetic properties has been available so far due to small domain sizes and lack of appropriate techniques. Furthermore, their real space magnetic texture is often complex and temperature-dependent. We investigate the magnetic Kagome metal DyMn$_6$Sn$_6$ using high-resolution micro-focused circular-dichroic angle-resolved photoemission ($μ$-CD-ARPES) to probe its magnetic and electronic properties. By tuning the kinetic energy to various features of the Dy $4f$ multiplet, we resolve magnetic domains in samples cryo-cooled down to 20 K. Smaller, but clear signatures are detected in the Mn $3p$ levels. The behavior of both Dy $4f$ and Mn $3p$ features are in remarkable agreement with our modeling based on the Hartree-Fock method, revealing ferrimagnetic alignment of Dy and Mn local moments, and further strengthening our interpretation. Adjusting the energy to the Mn $3d$-dominated valence bands reveals signatures which we relate to the orbital magnetization through a comparison to {\it ab initio} electronic structure calculations. Our study establishes the spectroscopic access to a single magnetic domain in a Kagome metal, paving the way for further research into imaging magnetic phases of novel magnetic materials using $μ$-CD-ARPES.

Let $q$ be a power of $2$ and let $\mathbb{F}_q$ be the finite field with $q$ elements. For a positive integer $n$, the polynomial $X^n-1\in\mathbb{F}_q[X]$ is called $3$-sparse over $\mathbb{F}_q$ if every monic irreducible factor of $X^n-1$ over $\mathbb{F}_q$ has at most three nonzero terms. This corrected version gives the characteristic-two classification. Writing $n=2^λm$ with $m$ odd, $X^n-1$ is $3$-sparse over $\mathbb{F}_q$ if and only if either $\rad(m)\mid q^2-1$, or $q=2^e$, $3\nmid e$, and $m$ lies in the exceptional $7$-family \[ m=7^A s_0, \quad A\ge1, \quad (s_0,7)=1, \quad \rad(s_0)\mid q-1, \quad 3\nmid s_0/\gcd(s_0,q-1), \] with the additional maximal $7$-adic orbit condition $\ord_{7^a}(q)=3\cdot7^{a-1}$ for $1\le a\le A$. The latter condition is equivalent to $A=1$ or $7\nmid e$. This condition is necessary; for example, $X^{49}-1$ is not $3$-sparse over $\mathbb{F}_{128}$.

In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.

Build scripts automate the process of compiling source code, managing dependencies, running tests, and packaging software into deployable artifacts. These scripts are ubiquitous in modern software development pipelines for streamlining testing and delivery. While developing build scripts, practitioners may inadvertently introduce code smells, which are recurring patterns of poor coding practices that may lead to build failures or increase risk and technical debt. The goal of this study is to aid practitioners in avoiding code smells in build scripts through an empirical study of build scripts and issues on GitHub.We employed a mixed-methods approach, combining qualitative and quantitative analysis. First, we conducted a qualitative analysis of 2000 build-script-related GitHub issues to understand recurring smells. Next, we developed a static analysis tool, Sniffer, to automatically detect code smells in 5882 build scripts of Maven, Gradle, CMake, and Make files, collected from 4877 open-source GitHub repositories. To assess Sniffer's performance, we conducted a user study, where Sniffer achieved higher precision, recall, and F-score. We identified 13 code smell categories, with a total of 10,895 smell occurrences, where 3184 were in Maven, 1214 in Gradle, 337 in CMake, and 6160 in Makefiles. Our analysis revealed that Insecure URLs were the most prevalent code smell in Maven build scripts, while HardcodedPaths/URLs were commonly observed in both Gradle and CMake scripts. Wildcard Usage emerged as the most frequent smell in Makefiles. The co-occurrence analysis revealed strong associations between specific smell pairs of Hardcoded Paths/URLs with Duplicates, and Inconsistent Dependency Management with Empty or Incomplete Tags, which indicate potential underlying issues in the build script structure and maintenance practices.

Fe3GaTe2 (FGaT), a two-dimensional (2D) layered ferromagnetic metal, exhibits a high Curie temperature (TC) ~ 360 K along with strong perpendicular magnetic anisotropy (PMA), making it a promising material candidate for next-generation energy-efficient magnetic devices. However, the vast majority of studies on FGaT to date have been limited to millimeter-sized bulk crystals and exfoliated flakes, which are unsuitable for practical applications and integration into device processing. Also, its combination with other 2D materials to form van der Waals heterostructures has only been achieved by flake stacking. Consequently, the controlled large-scale growth of FGaT and related heterostructures remains largely unexplored. In this work, we demonstrate a breakthrough in the high-quality, large-scale growth of epitaxial FGaT thin films on single-crystalline graphene/SiC templates using molecular beam epitaxy. Structural characterization confirms the high crystalline quality of the continuous FGaT/graphene van der Waals heterostructures. Temperature-dependent magnetization and anomalous Hall measurements reveal robust PMA with an enhanced TC well above room temperature, reaching up to 400 K. Furthermore, X-ray absorption and X-ray magnetic circular dichroism spectra provide insight into the spin and orbital magnetic moment contributions, further validating the high TC and robust PMA. These findings are highly significant for the future development of high-performance spintronic devices based on 2D heterostructures, with potential applications in next-generation data storage, logic processing and quantum technologies.

We numerically investigate the telltale signs of pair-density-wave order (PDW) in the Kondo-Heisenberg chain by focusing on the momentum resolved spectrum in different parameter regimes. Density matrix renormalization group calculations reveal that this phase is characterized by a dispersion with two minima and four Fermi points, indicating the emergence of an effective next-nearest-neighbor hopping that arises as a second-order effect to avoid magnetic frustration. The pairs appear in the spectrum as in-gap bound states with weight concentrated in the hole pockets. The low-energy physics can be understood by means of a generalized t-J model with next-nearest-neighbor hopping. Our results offer a guide for searching for experimental signatures, and for other models that can realize PDW physics.

We visualize the topological ladder and band inversions in PtTe$_2$ using spin-polarized photoemission spectroscopy augmented by three-dimensional momentum imaging. This approach enables the detection of spin polarization in dispersive bands and provides access to topological properties beyond the reach of conventional methods. Extensive mapping of spin-momentum space reveals distinct topological surface states, including a surface Dirac cone at the binding energy $E_B \sim 2.3$ eV and additional states at $E_B \sim 1.6$ eV, $E_B \sim 1.0$ eV, and near the Fermi level. The electronic structure analysis demonstrates strong hybridization between Pt and Te atomic orbitals, confirming the nontrivial topology of these surface states. Furthermore, by comparison to one-step model photoemission calculations, we identify a robust correlation between the initial-state and measured spin polarizations while revealing asymmetries in specific experimental spin textures. These asymmetries, absent in the initial states due to symmetry constraints, arise from the breaking of time-reversal symmetry during the photoemission process, emphasizing the crucial influence of symmetries on experimental signatures of topology.

In this paper, we investigate noncommutative resolutions of (generalized) AS-Gorenstein isolated singularities. Noncommutative resolutions in graded case are achieved as the graded endomorphism rings of some finitely generated graded modules, which are seldom $\mathbb{N}$-graded algebras but bounded-below $\mathbb{Z}$-graded algebras. So, the paper works on locally finite bounded-below $\mathbb{Z}$-graded algebras. We first define and study noncommutative projective schemes after Artin-Zhang, and define noncommutative quasi-projective spaces as the base spaces of noncommutative projective schemes. The equivalences between noncommutative quasi-projective spaces are proved to be induced by so-called modulo-torsion-invertible bimodules, which is in fact a Morita-like theory at the quotient category level. Based on the equivalences, we propose a definition of noncommutative resolutions of generalized AS-Gorenstein isolated singularities, and prove that such noncommutative resolutions are generalized AS regular algebras. The center of any noncommutative resolution is isomorphic to the center of the original generalized AS-Gorenstein isolated singularity. In the final part we prove that a noncommutative resolution of an AS-Gorenstein isolated singularity of dimension $d$ is given by an MCM generator $M$ if and only if $M$ is a $(d-1)$-cluster tilting module. A noncommutative version of the Bondal-Orlov conjecture is also proved to be true in dimension 2 and 3.

The symbiosis of strong interactions, flat bands, topology and symmetry has led to the discovery of exotic phases of matter, including fractional Chern insulators, correlated moiré topological superconductors, and Dirac and Weyl semimetals. Correlated metals, such as those present in Kondo lattices, rely on the screening of local moments by a sea of non-magnetic conduction electrons. Here, we report on a unique topological Kondo lattice compound, CeCo2P2, where the Kondo effect - whose existence under the magnetic Co phase is protected by PT symmetry - coexists with antiferromagnetic order emerging from the flat bands associated with the Co atoms. Remarkably, this is the only known Kondo lattice compound where magnetic order occurs in non-heavy electrons, and puzzlingly, at a temperature significantly higher than that of the Kondo effect. Furthermore, at low temperatures, the emergence of the Kondo effect, in conjunction with a glide-mirror-z symmetry, results in a nodal line protected by bulk topology near the Fermi energy. These unusual properties, arising from the interplay between itinerant and correlated electrons from different constituent elements, lead to novel quantum phases beyond the celebrated topological Kondo insulators and Weyl Kondo semimetals. CeCo2P2 thus provides an ideal platform for investigating narrow bands, topology, magnetism, and the Kondo effect in strongly correlated electron systems.

Recent years have witnessed a steady progress towards blending 2D quantum materials into technology, with future applications often rooted in the electronic structure. Since crossings and inversions of electronic bands with different orbital characters determine intrinsic quantum transport properties, knowledge of the orbital character is essential. Here, we benchmark angle-resolved photoelectron emission spectroscopy (ARPES) as a tool to experimentally derive orbital characters. For this purpose we study the valence electronic structure of two technologically relevant quantum materials, graphene and WSe$_2$, and focus on circular dichroism that is believed to provide sensitivity to the orbital angular momentum. We analyze the contributions related to angular atomic photoionization profiles, interatomic interference, and multiple scattering. Regimes in which initial-state properties could be disentangled from the ARPES maps are critically discussed and the potential of using circular-dichroic ARPES as a tool to investigate the spin polarization of initial bands is explored. For the purpose of generalization, results from two additional materials, GdMn$_6$Sn$_6$ and PtTe$_2$ are presented in addition. This research demonstrates rich complexity of the underlying physics of circular-dichroic ARPES, providing new insights that will shape the interpretation of both past and future circular-dichroic ARPES studies.

Identifying dependency between two random variables is a fundamental problem. The clear interpretability and ability of a procedure to provide information on the form of possible dependence is particularly important when exploring dependencies. In this paper, we introduce a novel method that employs a new estimator of the quantile dependence function and pertinent local acceptance regions. This leads to an insightful visualisation and a rigorous evaluation of the underlying dependence structure. We also propose a test of independence of two random variables, pertinent to this new estimator. Our procedures are based on ranks, and we derive a finite-sample theory that guarantees the inferential validity of our solutions at any given sample size. The procedures are simple to implement and computationally efficient. The large sample consistency of the proposed test is also proved. We show that, in terms of power, the new test is one of the best statistics for independence testing when considering a wide range of alternative models. Finally, we demonstrate the use of our approach to visualise dependence structure and to detect local departures from independence through analysing some real-world datasets.

Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise the problem is generally intractable. Search-based methods, like simulated annealing, empirically generate low resource cost approximate implementations of general multi-qubit unitaries so long as low precision (Hilbert-Schmidt distances of e>10^-2) can be tolerated. These algorithms build up circuits that directly invert target unitaries. We instead leverage search-based methods to first approximately diagonalize a unitary, then perform the inversion analytically. This lets difficult continuous rotations be bypassed and handled in a post-processing step. Our approach improves both the implementation precision and run time of synthesis algorithms by orders of magnitude when evaluated on unitaries from real quantum algorithms. On benchmarks previously synthesizable only with analytical techniques like the Quantum Shannon Decomposition, diagonalization uses an average of 95% fewer non-Clifford gates.

We theoretically propose a possibility of realizing high $T_c$ superconductivity having $s\pm$-wave symmetry in the heavily hole-doped infinite layer nickelates La$_{1-x}$Sr$_x$NiO$_2$. We consider situations where the original $P4/mmm$ symmetry of LaNiO$_2$ is maintained even for a significant amount of Sr substitution by growing thin films on substrates having tetragonal symmetry. Considering such cases is indeed justified by our phonon calculations. For electron configurations somewhat close to $d^8$, the interaction between the $d_{x^2-y^2}$ band and the other $3d$ bands that lie just below the Fermi level results in an enhancement of superconductivity where the sign of the gap function is reversed between the former and the latter bands. The strong enhancement of superconductivity can be attributed to the large energy level offset between $d_{x^2-y^2}$ and other orbitals due to the absence of the apical oxygens, as has been pointed out in previous studies.

In a continuous-time economy, this paper formulates the Epstein-Zin preference for discounted dividends received by an investor as an Epstein-Zin singular control utility. We introduce a backward stochastic differential equation with an aggregator integrated with respect to a singular control, prove its well-posedness, and show that it coincides with the Epstein-Zin singular control utility. We then establish that this formulation is equivalent to a robust dividend policy chosen by the firm's executive under the Maenhout's ambiguity-averse preference. In particular, the robust dividend policy takes the form of a threshold strategy on the firm's surplus process, where the threshold level is characterized as the free boundary of a Hamilton-Jacobi-Bellman variational inequality. Therefore, dividend-caring investors can choose firms that match their preferences by examining stock's dividend policies and financial statements, whereas executives can make use of dividend to signal their confidence, in the form of ambiguity aversion, on realizing the earnings implied by their financial statements.

We present a unified and concise method for establishing L^p Hardy and Rellich inequalities for a broad class of subelliptic operators of divergence type. The approach, based on a fundamental algebraic identity, provides explicit control on maximizing sequences and yields sharp constants in several significant cases. It applies beyond the Euclidean framework, covering the Heisenberg and Carnot group settings, and extends to a variety of subelliptic operators such as the Heisenberg-Greiner and Baouendi-Grushin operators.

We consider the problem of operating a battery in a home connected to the grid to minimize electricity cost, which combines an energy charge and a tiered peak power charge based on the average of the $N$ largest daily peak powers in each billing month. With perfect foresight of loads and prices, the minimum cost is the solution of a mixed-integer linear program (MILP), which provides a lower bound on the cost of any implementable policy. We propose a model predictive control (MPC) policy that uses simple forecasts of loads and prices and solves a small MILP at each time step. Numerical experiments on one year of data from a home in Trondheim, Norway, show that the MPC policy attains a cost within $1.7\%$ of the prescient bound, and saves close to three times as much as the best rule-based policy we consider.

We have investigated, both analytically and numerically, accreting supermassive black hole binaries as they inspiral due to gravitational radiation to elucidate the decoupling of binaries from their disks and inform future multi-messenger observations of these systems. Our numerical studies evolve equal-mass binaries from initial separations of $100 GM/c^2$ until merger, resolving scales as small as $\sim0.04 GM/c^2$, where $M$ is the total binary mass. Our simulations accurately capture the point at which the orbital evolution of each binary decouples from that of their circumbinary disk, and precisely resolve the flow of gas throughout the inspiral. We demonstrate analytically and numerically that timescale-based predictions overestimate the binary separations at which decoupling occurs by factors of $\sim3$, and illustrate the utility of a velocity-based decoupling criterion. High-viscosity ($ν\gtrsim0.03 GM/c$) circumbinary systems decouple late ($a_b\lesssim 15 GM/c^2$) and have qualitatively similar morphologies near merger to circumbinary systems with constant binary separations. Lower-viscosity circumbinary disks decouple earlier and exhibit qualitatively different accretion flows, which lead to precipitously decreasing accretion onto the binary. If detected, such a decrease may unambiguously identify the host galaxy of an ongoing event within a LISA error volume. We illustrate how accretion amplitude and variability evolve as binaries gradually decouple from their circumbinary disks, and where decoupling occurs over the course of binary inspirals in the LISA band. We show that, even when dynamically negligible, gas may leave a detectable imprint on the phase of gravitational waves.

We address the problem of magnetic-field-induced corner states in quantum spin Hall insulators (QSHIs) beyond the particle-hole-symmetric limit. Starting from a realistic low-energy model for zinc-blende semiconductor quantum wells (QWs), we derive the effective edge Hamiltonian in the form of a Dirac Hamiltonian with two magnetic-field-dependent mass terms, whose structure depends on the crystallographic orientation of the edge and of the magnetic-field orientation. Our \emph{analytical} results show that magnetic-field-induced corner states are most naturally understood as in-gap bound states of the effective edge theory, controlled by the relative configuration of the edge mass vectors rather than, in general, as higher-order topological corner modes protected by a stable bulk invariant. We demonstrate that, although mirror-graded winding numbers can be defined and quantized for certain crystallographic configurations, the existence of magnetic-field-induced corner states is not restricted to regimes in which these bulk invariants are well defined. Finally, we argue that even without higher-order topological protection these corner states may remain spectrally robust under weak perturbations as isolated in-gap quasiparticle excitations.

I generalize a theorem of Predd, et al.~(2009) on domination and strictly proper scoring rules to the case of non-additive scoring rules.

Despite growing concerns about the risks of Generative AI (GenAI), there is limited understanding of public perceptions of these risks and their associated failure modes -- defined as recurring patterns of sociotechnical breakdown across the GenAI lifecycle that contribute to risks of real-world harm. To address this gap, we present a survey instrument, validated with eight subject matter experts and deployed on a sample of 960 U.S.-based participants, to assess awareness and perceptions of GenAI's failure modes, their associated risks, and stakeholder responsibilities to address them. To support realism and content validity, our instrument is structured around scenarios grounded in publicly reported incidents and a taxonomy of GenAI's failure modes. Findings suggest that our instrument is (1) effective for assessing risk awareness and perceptions in a way that is grounded in people's current contexts of use, yet is extensible to new contexts that will inevitably arise; and (2) potentially useful for informing the design of AI literacy tools and interventions. We argue for AI literacy and governance approaches that align with how people encounter and reason about GenAI in everyday life.