Papers

NuSTAR and XMM-Newton have observed the James Webb Space Telescope (JWST) North Ecliptic Pole (NEP) Time-Domain Field (TDF) for almost five contiguous years starting in 2019. In that time, the NEP X-ray survey has accumulated 3.5 Ms and 228 ks of quasi-simultaneous NuSTAR and XMM-Newton observations, respectively. This paper presents variability results for the 112 NuSTAR and 453 XMM-Newton sources detected in this field, based solely on the X-ray photometric data. Four NuSTAR sources and 11 XMM-Newton sources varied in at least one band at >=99% confidence. The sources with redshift measurements show a relationship between luminosity and variability with 74% of variable sources brighter than 5x the sensitivity limit of the survey. This is supported by about 1/3 of sources with more than 400 counts detected being variable and only 4 sources with fewer counts showing variability. Variability timescales are not well determined, but variability amplitude tends to be larger on longer timescales.

We establish a spectral weak-to-strong stability criterion and a sharp Sobolev dichotomy for Maxwell–Ohm evolution with prescribed velocity on $\T^d$, $d=2,3$. Uniform spatial spectral tightness, together with weak convergence of each fixed spatial Fourier mode and strong convergence of the electromagnetic initial states, yields strong convergence of the electromagnetic fields, weak convergence of the currents, and distributional convergence of the Lorentz forces. In particular, weak convergence of the velocity coefficients in $L^2_tH^s_x$ suffices when $s>d/2$. At the critical index $s=d/2$, this conclusion fails sharply. We construct smooth divergence-free velocities converging strongly to zero in the critical Sobolev space, together with electromagnetic initial states converging strongly to zero, while the corresponding terminal fields remain of order one and the currents stay bounded. In two dimensions the construction is based on a moving logarithmic core, whereas in three dimensions it uses a Fourier-capacity core built from Leray-projected lattice modes and a polarized six-component Maxwell packet with exact magnetic divergence constraint. In both dimensions, the Lorentz forces converge to an explicit nonzero measure supported on a single ray with fixed unit direction.

The $12\%$ rule relates hadronic decays of the $J/\psi$ and $\psi(2S)$ through the ratio of their wave functions at the origin, but is strongly violated in several vector–pseudoscalar ($VP$) channels, most prominently in the $\rho\pi$ one. We study these decays within an effective chiral framework including strong and electromagnetic interactions, with the latter implemented through vector meson dominance. The $\psi(2S)\to VP$ data are described well by a relatively minimal model with three free parameters, yielding $\chi^2_{\rm red}\simeq 6.71/(9-3)=1.12$. In contrast, the corresponding description of the $J/\psi$ decays is insufficient ($\chi^2{\rm _{red}}\simeq 132/(11-3)=16.5$) and requires additional $\mathrm{SU}(3)$ flavor breaking and electromagnetic contributions for a fair agreement with data: $\chi^2_{\rm red}\simeq 9.87/(11-6)= 1.97$. In the past, a small mixing of $J/\psi$ with an invisible vector glueball was considered as a way to describe the decay patterns. However, we will show that our extended fits are `de facto' equivalent to those where a vector glueball mixes with the $J/\psi$, so that we cannot distinguish whether or not the vector glueball is present. Our results suggest that an important part of the $\rho\pi$ puzzle may arise from additional contributions to the $J/\psi\to VP$ amplitudes rather than from a suppression mechanism specific to the $\psi(2S)$.

We construct global finite-energy weak solutions for a 1D barotropic Navier–Stokes–Maxwell system with displacement current and the algebraic Ohm law. The result holds for every \(\gamma>1\) and arbitrary finite-energy initial data, allowing vacuum and requiring only \(L^2\) initial electromagnetic fields. A key ingredient is a weak-to-strong compactness principle for the Maxwell–Ohm subsystem: weak convergence of the velocity coefficients in \(L^2_tH^1_x\), together with strong convergence of the initial fields, yields strong electromagnetic trajectories in \(C_tL^2_x\). This permits identification of the weak current and the distributional Lorentz force without strong convergence of the velocity. The electromagnetic closure is combined with the classical artificial-viscosity and artificial-pressure construction for compressible flow. A density-primitive effective-flux argument identifies the physical pressure and eliminates the physical and artificial pressure-concentration defects.

The magnon Kerr effect is a nonlinear phenomenon that occurs universally in any ferromagnet with finite magnetic anisotropy. It manifests itself as a magnon population-dependent change in the magnon dispersion relation. Here, we derive the Hamiltonian for the magnon Kerr effect for a thin film with uniaxial anisotropy. We consider the external field, parallel, perpendicular, and at an intermediate angle to the anisotropy axis, and determine the Kerr coefficient in each case. We show how the nonlinearity scales for different magnetic materials as a function of magnon frequency and magnetic sample volume. Moreover, we derive the equations of motion for a hybrid cavity-magnon system with such thin-film magnon Kerr nonlinearity, to obtain populations of photons and magnons, and scattering matrix terms for the microwave transmission of the cavity, relevant for experimental observations.

Let $\mathbf{C}=\partial E\subset\mathbb{R}^{n+1}$ be an area-minimizing hypercone. The cone may have nonisolated singularities. We prove that there is a constant $c_{\mathbf{C}}>0$ such that \[ \frac{\operatorname{Per}(F;B_R)-\operatorname{Per}(E;B_R)}{R^n} \geq c_{\mathbf{C}} \left(\frac{|F\triangle E|}{R^{n+1}}\right)^2 \] for every $R>0$ and every set $F$ of locally finite perimeter with $F\triangle E\Subset B_R$. This extends the unweighted quantitative inequality from regular area-minimizing hypercones to general area-minimizing hypercones. We follow the calibration argument in the author's earlier work on regular cones. The main change is the construction of the vector fields. The pointwise asymptotic estimates for positive Jacobi fields used in the regular case do not directly apply here. We use the minimal foliations constructed by Zhihan Wang on the two sides of the cone. On each leaf, we integrate projection kernels with a positive Jacobi field as the weight. The kernel construction gives the required divergence bound. Wang's weak Harnack inequality and growth estimates give the integral bounds needed to prove linear growth of the vector fields.

Skew-symmetric matrix Schubert varieties are determinantal varieties obtained by intersecting matrix Schubert varieties with the space of skew-symmetric matrices. They are closely related to the orbit closures of the symplectic group action on the flag variety, and their torus-equivariant K-classes are the symplectic Grothendieck polynomials. We compute the Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties by giving a combinatorial formula for the degree of symplectic Grothendieck polynomials. In addition, we characterize the highest-degree homogeneous component of a symplectic Grothendieck polynomial and compute the maximal Castelnuovo-Mumford regularity of skew-symmetric matrix Schubert varieties.

This work addresses the construction of local interaction vertices in the holomorphic zero-form sector obtained from Vasiliev equations. We focus on a requirement on zero-form vertices, previously proposed in a less restrictive form in arXiv:2208.02004, which, together with spinor spin-locality, guarantees space-time spin-locality. Necessary and sufficient conditions on the holomorphic one-form sector vertices are derived that ensure the existence of holomorphic zero-form vertices satisfying this requirement. As a concrete demonstration, the proposed scheme is applied to compute the spin-local holomorphic $\eta^2$ zero-form sector vertex, a result that goes beyond previous work where only spinor spin-locality was established. These findings lay the groundwork for a systematic all-order construction of local vertices in higher-spin theory.

Visual instructions for physical tasks are typically authored in one context and followed in another, requiring users to translate demonstrated tools, materials, and spatial relationships into their own environment. We introduce Generative Tutorial, a conceptual framework for live visual instruction that depicts intended outcomes and actions within the user's environment and task flow. A formative evaluation of state-of-the-art image and video generation identifies failures and potential benefits across 15 physical tasks. Drawing on these findings, we build an augmented-reality prototype system that proactively generates goal images and demonstration videos using observed workspace context and predicted visual outcomes of preceding actions. A 24-participant lab study found higher task performance quality, greater perceived workspace correspondence, and shorter step-confirmation intervals with the system than with pre-authored guidance. Qualitative findings highlighted how contextual resemblance shapes trust, how generation errors affect interpretation, and how guidance delivery should adapt to users' needs, informing future designs.

Pharmaceutical process characterization is central to Quality by Design because it defines how variations in process parameters affect the ability to meet product quality specifications, thereby supporting proven acceptable ranges and robust manufacturing. In practice, however, characterization still relies largely on factorial design of experiments (DOE) approaches, which are inefficient for resolving multivariate pass/fail boundaries in higher-dimensional spaces. While Bayesian optimization has transformed process optimization, adaptive methods for multi-objective process characterization remain lacking. Here, we introduce JAREX (Joint Acceptable Region EXploration), a Bayesian active-learning acquisition function for multi-objective process characterization. JAREX formulates characterization as a joint boundary-learning problem and adaptively selects experiments to recover the joint pass region defined by simultaneous satisfaction of threshold criteria across multiple objectives. JAREX combines an optimistic joint-feasibility mask with a multi-objective extension of randomized straddle, focusing sampling on the joint edge of failure. Our benchmark study suggests that JAREX provides more accurate and sample-efficient recovery of the joint pass region than factorial DOE, space-filling designs, and greedy objective-wise strategies over the full experimental budget range. For batched experimentation, it reduces the number of iterative process characterization experiments by more than half while preserving high accuracy for the boundary-identification task. Implemented in the open-source obsidian package, JAREX provides a modular framework for adaptive, data-efficient multi-objective algorithmic process characterization, supporting sample-efficient range finding in high-dimensional spaces.

We establish quantitative entropy contraction bounds for finite-dimensional quantum channels beyond detailed balance. For channels compatible with a faithful conditional expectation, we show that GNS (Gelfand–Naimark–Segal) norm contraction yields relative entropy contraction with only a logarithmic loss in the dimensional constant. For quantum Markov semigroups with a faithful asymptotic conditional expectation, this gives a lower bound on the complete modified logarithmic Sobolev constant in terms of the GNS spectral gap. The bounds allow initial entanglement with an external environment and are independent of its system size. Applications to alternating reservoir pulses and continuously coupled energy ladders give bounds with optimal size dependence.

Autonomous navigation on Mars requires vehicles to distinguish between traversable terrains across diverse and visually challenging environments. However, progress in learning-based navigation for off-world environments has been limited by the lack of large-scale datasets. Since landing in Jezero Crater, the Mars 2020 Perseverance rover has traversed terrain ranging from sandy dunes, rocky patches, and flat bedrocks. As a result, this paper presents a dataset spanning 500 sols and 45km of trajectories driven by both human operators and the onboard planner, ENav. Our dataset contains grayscale stereo image pairs, poses, accelerometer readings, rocker-bogie angles, and estimates of tilt and wheel slip. Building on this dataset, we introduce an uncertainty-aware traversability-estimation framework that learns terrain representations from multimodal driving experience. We compare our proposed method against existing approaches on the Mars 2020 dataset and show that our method achieves an AUROC of 0.874 and an F1 score of 0.758, outperforming the strongest baseline by 0.058 and 0.156, respectively, while also achieving the highest average precision and recall. Finally, we show that the visual representations can be integrated into path planners, such as ENav, on a physical rover test bed. Videos, code, and the M2020 dataset will be available at https://darren-chiu.github.io/learning-to-drive-on-mars.

We study fixed point theorems for actions of lattices of semisimple groups. They are deduced from vanishing results for the group cohomology of $L^p$-representations. We show that for lattices in simple groups of higher rank, the cohomology with $L^p$-coefficients vanishes below the rank whenever there are no invariant vectors. As a corollary of the vanishing for $L^1$-coefficients, we obtain that every action on an acyclic simplicial complex of dimension lower than the rank has a finite orbit. This in particular proves a conjecture by Farb. The $L^p$-vanishing below the rank proves a conjecture by Gromov regarding $L^p$-cohomology of symmetric spaces.

A search for a new top-philic vector boson ($Z'$) produced in association with a top-quark or a pair of top quarks, and decaying into a top quark pair is presented. The search uses $pp$ collision data collected by the ATLAS detector at the Large Hadron Collider at centre-of-mass energies of $\sqrt{s} =$ 13 TeV and 13.6 TeV, corresponding to integrated luminosities of 140 fb$^{-1}$ and 56 fb$^{-1}$, respectively. Events containing exactly two same-sign leptons or at least three leptons (electrons or muons) are selected. A transformer-based classifier parameterised as a function of the $Z'$ mass is used to optimise the signal-to-background discrimination. The results are interpreted in a simplified model with a colour-singlet vector boson coupled to top quarks with coupling strength $c_t$ and chirality angle $\theta$. No significant excess is observed above the expected Standard Model background. A $Z'$ boson with mass below 1150 GeV is excluded at 95% confidence level for a benchmark scenario with $c_t = 1$ and $\theta = 0$, with an expected limit of 1250 GeV.

Binary classification trees select subgroups using the same outcomes later used to assess their differences. We develop finite-sample conditional tests of a common success probability within a parent selected by deterministic Gini CART. The construction retains all eligible cutpoints and conditions on the selected split, its ancestor path, the parent success total, and outside outcomes. The resulting uniform label fiber gives an exact count distribution, while a reversible parallel Monte Carlo construction yields super-uniform inclusive and exactly uniform tie-randomized p-values for any prespecified finite run budget. Within a two-child constant-risk model, the selected count law is an exponential family with information equal to its conditional count variance. We separate information loss from computational limitations and exhibit a selected fiber disconnected under single-label swaps. Simulations with 200 or 400 observations, ten independent or correlated predictors, and trees of depth three show conservative inclusive tests and nontrivial power for large risk differences. At 400 observations and a generating risk difference of 0.4, randomized rejection conditional on reaching the prespecified third-level target is 51–71%, while selection followed by rejection occurs in 11–21% of datasets. Smaller signals remain difficult to detect, and a representative fivefold increase in computation gives little power improvement. The guarantee concerns parent homogeneity, or equality of two constant child risks, and does not cover equality of heterogeneous regional averages.

The effects of weak gravitational lensing induced by clusters of galaxies makes it possible to constrain their dark matter distribution. In general mass estimates from weak lensing are made by compressing the two-dimensional shear-field into one-dimension. In this work we build a forward model of the two-dimensional reduced-shear field around a galaxy cluster, including the non-Gaussian correlated large-scale structure from N-body simulations, the uncorrelated line-of-sight structure, cluster miscentering and ellipticity. We then use simulation-based inference to obtain posteriors on the cluster mass, concentration, miscentering and ellipticity from the full field. The two-dimensional approach leads to improvements on cluster mass constraints by up to 20%. We show that this is due to a better treatment of the spatially correlated noise across the shear field. There is also significant improvements on the cluster concentration and miscentering. Whilst improvements are also made to the estimation of cluster ellipticity, the constraints are still prior dependent for these individual cluster constraints. We also quantify the impact of the line-of-sight structure on the constraints. Neglecting it underestimates the mass uncertainty by up to a factor of $2$ for the most massive clusters.

Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependence on labeled data, yet their optimization can be basin-fragile: when the governing residual admits multiple solutions, a PINN trained from scratch may converge to a physically incorrect state despite achieving a small residual. We show that these failure modes can be addressed jointly: an imperfect NO provides the structural prior needed to place a PINN in the correct solution basin, while the PDE residual refines the solution beyond the operator's accuracy. We introduce a three-stage framework that freezes the spatial basis of a physics-informed NO, extrapolates its solution branch to an out-of-distribution parameter using a polynomial continuation prior, and distills the resulting field into a fresh PINN. The NO need not be accurate at the target; it transfers solution-branch information, while PDE residual minimization in the PINN governs convergence. We evaluate the framework on three nonlinear PDEs: 1D viscous Burgers, 2D steady Allen-Cahn near a pitchfork bifurcation, and 2D steady lid-driven cavity flow. For Allen-Cahn, where the trivial solution satisfies the PDE residual exactly, a standard PINN collapses to the trivial zero branch, whereas distillation from the crude extrapolated operator recovers the non-trivial branch that matches the finite-difference reference. For the lid-driven cavity, extrapolating to a Reynolds number of Re = 3200 accelerates convergence to the correct physical state, achieving competitive accuracy using fewer parameters and optimization steps than recent literature baselines. These results establish a simple principle: an NO need not accurately predict the solution to be useful; it only needs to identify the correct basin from which PINN optimization can recover it.

We present Merlin, a simulation-based inference (SBI) pipeline to perform cosmological analyses of 3x2pt summary statistics: cosmic shear, galaxy clustering and the cross-correlation power spectra. Our approach combines Marginal Neural Ratio Estimation (MNRE) with 3x2pt angular power spectra predictions from the cloelib library, although the pipeline is readily extensible to other cosmology libraries. We demonstrate this pipeline on a realistic setting representative of a Stage-IV photometric survey, with a 50-dimensional parameter space describing cosmology and a wide range of systematic effects. We find posteriors that are in excellent agreement with the nested sampler Nautilus, while reducing the number of required CPU-hours by two orders of magnitude. Because the generation of training data and the training of inference networks are decoupled processes, a single simulation bank can be reused to perform inference under different analysis choices, further improving the simulator-efficiency. We illustrate this flexibility by applying scale cuts, varying the survey area, and removing cosmic shear from the data vector (2x2pt), all at zero extra model evaluations, whereas sampling-based methods need costly re-runs for each case. The Merlin code is publicly available on GitHub.

Ultra-high-dimensional data, with p far exceeding n, are common in genomics and biomedical research. Marginal screening can miss active predictors with weak marginal signals, especially under strong predictor correlation. We develop Structured Screen-and-Select Variable Selection (S3VS), an iterative framework that combines outcome-based screening with correlation-based local predictor sets. At each iteration, S3VS identifies leading variables, forms local sets through predictor associations, applies a model-specific selector, aggregates selected and nonselected variables, and updates the candidate set and, when appropriate, the outcome representation. The framework allows flexible leading-variable, local-set, and aggregation rules, with implementations for linear, generalized linear, accelerated failure-time, and Cox models. For a specified one-step linear configuration, we establish sure screening under conditions on proxy coverage, correlation separation, within-set retention, and active-preserving aggregation. Simulations compare full and first-iteration S3VS with one-pass SIS procedures in linear, logistic, and Cox settings. S3VS can improve variable recovery or prediction when correlated predictors provide useful proxy information, although gains depend on predictor structure and selector choice. In ovarian-cancer data, full S3VS with clinical variables showed the strongest internal discrimination and early prediction, whereas SIS–Cox–LASSO with clinical variables showed the strongest external discrimination. Neither molecular approach consistently reduced prediction error, and no gene was selected in all five outer folds. S3VS provides a flexible framework for exploiting predictor dependence before model-specific selection. The method is implemented in the CRAN R package S3VS.

The prize-collecting traveling salesperson problem is a variant of the metric traveling salesperson problem in which vertices may be left unvisited by paying their associated penalties. The objective is to minimize the length of the tour plus the total penalty of the unvisited vertices. Blauth, Klein, and Nägele gave the previously best-known LP-relative $1.599$-approximation. Their algorithm constructs tours by applying a splitting-off preprocessing to an LP solution, decomposing the resulting solution into trees, pruning them, and performing parity correction. We improve the LP-relative approximation ratio to $1.55576$. Our main contribution is a new bound on the cost of parity correction that exploits parity information revealed by further pruning in the analysis. This bound makes the splitting-off preprocessing unnecessary, so the improvement is achieved by a simpler version of their algorithm. The stated factor follows from a numerical parameter search with exact verification, while an elementary analysis already yields an LP-relative $1.56$-approximation.

Multiparameter eigenvalue problems arise in boundary value problems, stability analysis, and delay-differential equations. Despite their importance, existing methods either require solving extremely large global problems or rely on local iterative techniques that only recover a few eigenvalues at a time. In this work we develop the first contour method for analytic multiparameter eigenvalue problems. The key theoretical ingredient is a new residue formula for multivariate matrix-valued analytic functions, extending Beyn's Keldysh-based residue theorem for meromorphic operator functions to several complex variables. Using this, we derive a multidimensional analogue of Beyn's contour method that computes all the eigenvalues of a multiparameter eigenvalue problem contained in a prescribed region of $\mathbb{C}^d$. The resulting algorithm targets eigenvalues in a region without constructing preposterously large matrices and is embarrassingly parallelizable. Numerical experiments demonstrate that we can now successfully solve large multiparameter problems arising in applications where existing approaches struggle.

A model generalizes outside its training distribution only when it computes a representation structurally equivalent to the generating mechanism, not an approximation fitted to it. Such equivalence is necessary for exactness in and out of distribution, and extrapolation is governed by this exactness at inference, whatever its realization. Tensor Logic shows this: a zero-temperature contraction is equivalent to discrete logic, deducing in place with no artefact extracted, its tensors Boolean, its embeddings orthonormal, only its arithmetic continuous. Lacking infinite recursion it reaches Datalog, not Prolog, and though exact over closed domains it needs external memory to bind a novel entity. The criterion needs neither a discrete representation nor an extracted expression, and constrains inference, not training: an exact marginal in $[0,1]$ passes, a Neural Network thresholded to a hard label does not. Logic Tensor Networks fail it, while differentiable ILP and Tensor Logic at $T=0$ pass. Piecewise-affine extrapolation divergence and an inability to bind novel entities are two faces of a shortfall in exact representability. For hybrid architectures, a propagation rule follows: the output inherits the bounds of every fitted estimator on its path, explaining which axes fail in equivariant models and the ARC-AGI induction/transduction split. Only an exact hypothesis class certifies what the training data leave underdetermined: on a law-derived partition it finds the $56.3\%$ of distant queries that are answerable, which ensembles meet with false confidence and distance metrics rank backwards. Common inductive biases, from symmetries to memory, reach exactness only because humans inject them, an argument for inducing exact representations rather than fitting surrogates whose residuals, even at the arithmetic floor in training, diverge outside the data and compound under composition.

Heralded multipartite entanglement distribution is a key requirement for device-independent conference key agreement (DI-CKA) over lossy quantum networks. Although locally equivalent in the absence of loss, different single-rail photon-number encodings of Greenberger–Horne–Zeilinger (GHZ) states respond differently to photon loss. Here, we investigate the critical detection efficiencies for detection-loophole-free parity–CHSH violations of computational-basis GHZ states—a coherent superposition of the vacuum and an $n$-photon component—and of fixed-photon-number GHZ states, deriving exact analytical conditions for both. We show that for states that are not permutation symmetric, such as the latter, the assignment of measurement roles to physical modes affects loss tolerance. We introduce a star-network protocol employing heterogeneous sources to directly herald the loss-tolerant vacuum-$n$-photon GHZ states while retaining the favourable long-distance scaling $O(\eta_{\text{c}}^{n/2})$, where $\eta_{\text{c}}$ is the channel transmittance. For four users, we characterize the heralded state under photon loss and show that tunable source parameters allow genuine multipartite entanglement to persist at any finite channel distance. With ideal Pauli and displacement-based measurements, our protocol achieves positive DI-CKA key rates at lower detection efficiencies than previous schemes, while retaining comparable or greater rates and communication distances at high efficiency. Overall, our work improves the loss tolerance of heralded photonic GHZ states for DI-CKA both by directly heralding a more loss-tolerant encoding and by optimizing existing schemes. These results identify photon-number encoding, source architecture, and measurement-role assignment as key design parameters for loss-resilient multipartite quantum networks, offering a practical route toward near-term DI-CKA.

Connecting nuclear experiments to neutron star composition requires controlling the extrapolation of experimental information beyond the densities probed in the laboratory. We combine a broad set of nuclear structure observables and INDRA-FAZIA isospin-transport data within a Bayesian inference of the dense matter equation of state (EoS). To limit uncontrolled extrapolation to high density, we employ a flexible asymptotically causal metamodel whose neutron star posteriors are comparable to those obtained with agnostic EoS models. The nuclear structure information is propagated through its full multidimensional distribution of correlated nuclear matter parameters, while the density-dependent INDRA-FAZIA likelihood is evaluated directly along each sampled metamodel symmetry energy curve. These two sources of laboratory information give compatible constraints on the symmetry energy, and their combination preserves agreement with finite nuclear observables. When combined with ab initio chiral effective field theory calculations and astrophysical observations, all these constraints substantially improve the determination of central proton fractions in low-mass neutron stars, while leaving larger uncertainties for massive stars. Within the adopted nucleonic metamodel, the reduced probability of large proton fractions strongly disfavors electronic direct-Urca onset at or below $1.4\,M_\odot$: its posterior probability falls from $\sim20\%$ with chiral and astrophysical constraints alone to below $1\%$ when the laboratory information is included.

We obtain the action for the chiral Carroll string moving in a curved string-Carroll target spacetime from a Carroll expansion, in powers of the speed of light $c$, of the action for the relativistic closed bosonic string. Applying this setup to a classical closed bosonic string approaching the $4$-dimensional Schwarzschild black hole, we study the dynamics of the string when it behaves as a chiral Carroll string with the near-horizon string-Carroll expanded geometry as the target spacetime. We find that the chiral Carroll string can have either left-moving or right-moving fluctuations on the horizon, while exhibiting a non-trivial motion in the Rindler spacetime which depends on these horizon fluctuations.

We show that for any number field $K$ and any rational map $f$ in $K(x)$ of degree at least $2$ that is not conjugate to a power, (signed) Chebyshev or CM Lattès map, $K^{\mathrm{ab}}$ has the strong Bogomolov property for the canonical height of $f$. Combined with former results of Amoroso-Zannier, Pottmeyer and Ratazzi, this implies that $K^{\mathrm{ab}}$ has the Bogomolov property for canonical heights of any rational map of degree at least $2$. We also classify the pairs $(f,\alpha)$ whose backward orbit contains infinitely many abelian points. This settles the Andrews–Petsche conjecture in the greater generality of rational maps over a number field and infinite abelian subsets of backward orbits. The authors were led to the main idea of the proof in conversation with Astra. The key insight consists of applying Yuan's equidistribution results, followed by a classification of $(f,f)$-preperiodic curves due to Pakovich and Beaumont followed by an additional application of equidistribution on a parametrized preperiodic curve.

Bone overlap can obscure abnormalities in chest radiographs, while scarce paired training data limit supervised bone suppression. We address this challenge with a digitally reconstructed radiograph (DRR) framework that converts chest computed tomography (CT) into paired supervision for component suppression. A novel bone segmentation algorithm enables CT decomposition into bone, non-lung soft-tissue, and lung components, which are projected separately. Their weighted combination yields synthetic radiographs with pixel-registered component images that sum exactly to the full DRR. Models trained on these data suppress bone or lung components by predicting the target component and recovering the remainder by subtraction, transferring to real radiographs without real paired training data. As an extension, their outputs on real radiographs provide target domains for unpaired, component-wise DRR translation, reducing the appearance gap while retaining anatomical details. Across multiple public datasets, downstream detection experiments demonstrate the utility of bone suppression, with gains concentrated on abnormalities with substantial bone overlap. Compared with open-source DRR engines applied to the same CTs, our unmodified DRRs achieve comparable realism and preservation of label-relevant anatomy, while translated DRRs achieve the best Fréchet inception distance (FID), lung-field sharpness, and agreement with source-CT anatomy among the evaluated methods. Models and inference code: https://huggingface.co/qureaiorg/bone-suppression ; Translated projections: https://huggingface.co/datasets/qureaiorg/ct2xr-projections.

In the one-round discrete Voronoi game a multiset $V$ of $n$ voters on a line is given; player P places $k$ facilities, player Q then places $\ell$, and each voter is won by the nearer facility, ties going to P. P wins if it keeps at least $n/2$ voters. In the vocabulary of competitive location this is the absolute $(\ell|k)$-centroid problem on a path with unit demands, and the responder's problem is the $(\ell|X_k)$-medianoid, whose closed form on a path – the sum of the $\ell$ largest of at most $2k$ explicit marginals – is due to Spoerhase and Wirth. We record this structure, with complete proofs, and draw two consequences that we believe are new. First, we compute the value of the game against a single responding facility, $\Gamma_{k,1}(V)$, together with an optimal strategy for P, in $O(n\log n)$ time for arbitrary positive real demands and every $k$. This improves the $O(kn\log^2 n)$ bound of Lazar and Tamir for the absolute $(1|k)$-centroid on a path. Second, we study the facility advantage $k^*(\ell)$, the least $k$ for which P wins every instance against $\ell$ facilities. We prove $k^*(\ell)\le 2\ell-1$, exhibit instances proving $k^*(\ell)\ge\ell+1$ for $2\le\ell\le6$ (an exact, computer-assisted proof resting on a half-integer discretisation), determine $k^*(1)=1$ and $k^*(2)=3$, and show that on uniform instances $k=\ell$ already suffices, so the extremal instances are weighted and Q wins them by a single voter. We conjecture $k^*(\ell)=\ell+1$ for all $\ell\ge2$.

We prove a formula for Reidemeister numbers of virtually polycyclic groups that generalises known formulas for finite groups and torsion-free virtually polycyclic groups. Based on this formula, we introduce a new invariant which we call the tamed Reidemeister number, and prove that its associated zeta functions are rational on virtually polycyclic groups. We also show that this implies rationality of (ordinary) Reidemeister zeta functions, as well as rationality of Nielsen zeta functions on compact infra-solvmanifolds.

LLM benchmarks function as evaluation instruments, informing decisions that affect education, labor, and public services worldwide. Drawing on Hood, Kirkhart, and Hopson's culturally responsive evaluation (CRE) frameworks, this paper applies a six-dimension CR rubric to audit OpenAI's SimpleQA (N = 4,326 items) and the LMSYS Chatbot Arena (N = 600 conversations). Every SimpleQA question requires English-language archival verification as its evidentiary basis. A single rater's preoccupation with Colombian founding dates accounts for 2.70% of items, inflating the appearance of Global South coverage. English-language prompts constitute 76.3% of Arena conversations, against an International Telecommunication Union (ITU)-estimated 25.9% share of global internet users. A 50-item counter-benchmark scored a mean CR deficit nearly three times lower than SimpleQA (Cohen's d = 1.01). The paper proposes a practical CR evaluation framework. These are structural validity failures, not incidental measurement problems, with direct consequences for communities whose knowledge traditions these instruments were not built to see.