Papers

We establish the global well-posedness for the energy-subcritical defocusing cubic nonlinear Schrödinger equation (NLS) on the three-dimensional Friedlander model domain \( \Omega=\{x\in\mathbb{R}:x\geq0\}\times\mathbb{R}^2_{y,z}, \) subject to homogeneous Dirichlet boundary conditions, for arbitrarily large initial data in the coercive energy space $H_0^1(\Omega)$. The phase-space geometry of this configuration features a strictly convex boundary that admits a non-empty glancing set, trapping high-frequency wave packets within a boundary layer via generalized whispering-gallery caustics. These concentration phenomena induce an intrinsic derivative loss in the sharp linear Strichartz estimates, establishing a major microlocal obstruction to closing the nonlinear Duhamel iteration directly at the energy level via classical perturbative frameworks. To bridge the regularity deficit between the conservation laws and the linear theory, we construct a boundary-adapted family of continuous–discrete Bourgain–Strichartz restriction spaces $X^{s,b}$ built from the spectral decomposition of the Dirichlet realization of the model Friedlander operator \( \Delta_g=\partial_x^2+(1+x)\partial_y^2+\partial_z^2. \) The normal variable is resolved through discrete Airy spectral modes, while the tangential variables are continuously Fourier analyzed. Within this functional framework, we implement a refined high–low frequency decomposition to formulate a perturbed nonlinear equation for the high-frequency remainder in the sub-energy space $H_0^s(\Omega)$ for \( \frac{1}{2}<s<1. \) The initial high-frequency datum satisfies a quantitative sub-energy decay estimate of the form \( \|P_{>\lambda}u_0\|_{H_0^s(\Omega)} \label{eq:abs_decay} \lesssim \lambda^{s-1}\|u_0\|_{H_0^1(\Omega)}, \) providing a small parameter to counteract the derivative loss.

Shallit's law of leap years in Pierce expansions gives, for Lebesgue-almost every $x\in[0,1]$, the upper and lower limits of a normalized difference between $Nx$ and the number of leap years up to the year $N$ determined by the Pierce expansion digits of $x$. In this paper, we show that, for every $x\in[0,1]$, both limits are determined by the lower limit of a normalized logarithm of the product of the first $n$ digits of $x$. In particular, the upper and lower limits always have the same absolute value. As applications, we characterize the sets of points with prescribed upper and lower limits, and show that each of these sets, if non-empty, is dense in $[0,1]$ and its intersection with any non-empty open subset of $[0,1]$ has full Hausdorff dimension. We also compare these sets with the sets defined by the growth rate of the digits, and show that, for each finite parameter, their difference has full Hausdorff dimension.

Robust counterfactual explanations promise recourse that still works after the model behind it changes. Whether they keep that promise depends on what the change is. A small perturbation of the parameters, retraining on new data, and a new architecture are different events, and each existing method is evaluated against the one it was built for. Reported robustness scores, therefore, answer different questions and cannot be compared. We propose a unified cross-family evaluation protocol that holds factual instances and generated counterfactuals fixed while testing every method against the same eight types of model change. The benchmark compares six robust methods and two standard baselines on four tabular datasets. It characterizes every changed classifier through its outputs and reports empirical robustness together with coverage, base validity, and proximity. We find that relative performance and failure modes vary across change families. Bounded parameter perturbations change 0.95% of test predictions on average, compared with 4.9% for bootstrap retraining. Methods with guarantees for these perturbations do not necessarily transfer to other changes. RobX transfers most consistently in our experiments, although greater stability can require larger interventions. We argue that robust CFE methods should be evaluated through a common protocol that specifies the model changes, measures their realized behavioral magnitude, and keeps generation performance separate from robustness.

In very-high-energy gamma-ray astronomy, signals must be separated from the residual background which arises from misidentified cosmic-ray protons. Building on previous work, we introduce an ensemble of variational autoencoders that aims to perform automatic signal-background separation with minimal assumptions that include separability of the spatial and energy distributions in both the signal and background, with no prior specification of the number of components or the point-like/diffuse nature of the signal itself. In addition, we do not assume knowledge of which region of the coordinate space is background-dominated or where the signal is supposed to be located in the field of view. We test the model on an analytic point-source mixture scenario, a realistic simulation of dark matter annihilation in the Galactic centre, and real observations of the Crab nebula and MSH 15-52 from the public H.E.S.S data release. The model proves capable of completely reconstructing the signal and background at a pixel by pixel level in all scenarios, whilst also denoising the inputs. Stable performance and reasonable error estimates are obtained even for low signal-to-background ratios.

The discovery of the twist-bend nematic phase in liquid crystals composed of bent-core and dimeric molecules has revealed an unexpected mechanism for the spontaneous formation of nanoscale periodic structures in soft condensed matter. Unlike conventional liquid-crystalline phases, the twist-bend phase exhibits a nanoscale heliconical modulation despite the absence of molecular chirality. In this note, dedicated to the late R. Meyer, we discuss a Landau phenomenological interpretation of this phenomenon. The central idea is that a short-range orientational order parameter undergoes condensation, giving rise to a heliconical structure characterized by a finite wave vector. We emphasize that the conventional nematic order is already long-ranged, whereas the additional order parameter describes local orientational correlations hidden within the nematic state. The resulting phase transition bears a close analogy to the de Gennes theory of the nematic–smectic-A transition. Fluctuation effects are expected to drive the transition weakly first order. The theory also predicts a new Goldstone mode associated with the spontaneously broken continuous symmetry of the heliconical state

Warm Jupiters (gas giant planets with orbital periods of P$\sim$8-200 d) are thought to be largely unaffected by the tidal interactions that can erase information about the dynamical histories of hot Jupiters. Their orbital eccentricities ($e$) and stellar obliquities are therefore expected to be preserved, making them valuable probes of giant-planet formation and migration. Our aim is to identify and characterise transiting warm Jupiters in order to expand the sample of well-characterised systems and enable further studies of giant-planet formation and migration. We analyse TESS transit photometry together with ground-based radial velocity measurements and perform a joint fit of the photometric and spectroscopic data from the TS23 and FIES spectrographs to determine the planetary and orbital parameters. We report on the discovery and characterisation of two new, transiting warm Jupiters; TOI-5120 b ($M_p = 1.23\pm0.05$ M$_{\rm Jup}$, $R_p = 0.969\pm0.017$ R$_{\rm Jup}$, $P = 24.91645\pm0.00002$ d, $e = 0.10\pm0.02$) and TOI-5699 b ($M_p = 0.25\pm0.03$ M$_{\rm Jup}$, $R_p = 0.996\pm0.015$ R$_{\rm Jup}$, $P = 22.01850\pm0.00004$ d, $e = 0.30^{+0.09}_{-0.08}$). We also refine the parameters of the known warm Jupiter TOI-2158 b ($M_p = 0.87\pm0.04$ M$_{\rm Jup}$, $R_p = 0.899\pm0.015$ R$_{\rm Jup}$, $P = 8.60079^{+0.00002}_{-0.00001}$ d, $e = 0.028^{+0.013}_{-0.014}$). In addition, we detect an outer planetary companion, TOI-2158 c ($M_p \sin i = 1.62\pm0.13$ M$_{\rm Jup}$, $P = 414.5^{+1.5}_{-1.6}$ d, $e = 0.54\pm0.04$), and identify a long-term radial velocity trend that may indicate another planetary companion on a wide orbit. The diverse architectures of these systems, in particular the presence and absence of outer companions, highlight the range of dynamical pathways leading to warm Jupiters.

Quantum-inspired algorithms emulate quantum mechanical principles, such as, superposition, interference, and probabilistic amplitude evolution, on classical hardware by representing candidate solutions as qubit vectors and evolving them through rotation-gate operators. This approach offers higher optimization performance without physical qubits, and has been shown to achieve order-of-magnitude speedups (10–80$\times$) over traditional solvers on combinatorial, high-dimensional NP-hard problems. A critical barrier to adoption, however, is the lack of a unified execution framework that delivers both algorithmic performance and hardware portability. We present Cross-Backend Quantum Inspired Evolutionary Optimizer (QIEO), the runtime core of BQP's BQPhy solver, which addresses this gap through a single-source-of-truth architecture. One C++ implementation of the QIEO algorithm is compiled once per hardware target and exposed to multiple high-level languages via thin binding layers. The framework dispatches to CPU (sequential), OpenMP~5 (multi-core), CUDA (NVIDIA), and HIP (AMD) backends at runtime, adapting kernels to each device's memory hierarchy and warp/wavefront execution model. The framework's real-world utility is validated through binding demonstrations that share the identical C++ runtime. BQPhy's Python library is demonstrated on a neural network hyperparameter optimisation achieving 88.60% test accuracy on MNIST. BQPhy's MATLAB's Toolkit is tested on wind farm layout optimisation attaining $365\,399 \pm 4\,552$~MWh/yr, which is statistically indistinguishable from particle swarm optimisation and $+7.6\%$ above genetic algorithms on a 32-variable constrained engineering problem. The Julia package tackles the Lotka–Volterra parameter estimation where BQPhy replaces native Julia solvers on the same residual, cutting mean SSE by $2.1\times$.

Vision-language-action (VLA) policies can execute many tasks from standard initial states, yet a new instruction may fail after another task has altered the robot's physical state. We study instruction switching, where a new task is issued during or after the execution of a different one. We observe that a target task that is reliably completed from its standard initial states can become inaccessible from states produced by a preceding task. We call such states task islands. We propose Causeway, a training-free inference-time intervention. Given the current state and a re-entry pose for the target task, Causeway back-propagates through the frozen decoding computation and applies a state-directed write within the action-stream representation. The VLA decodes the return motion itself, without parameter updates, a new action head, or external action generation. Across 71 cross-object pairs, three switch timings, and three VLA architectures on LIBERO-Goal, Causeway raises bare-switch success from 3-26% to 47-65% and increases the rate of reaching the handoff neighborhood by 42-72 percentage points across models. Additional experiments on LIBERO-Object and a real xArm platform show that the recovery extends beyond the main LIBERO-Goal setting, both in simulation and on a robot.

Music source separation (MSS) methods aim to extract stems from music mixtures, which is important, for example, in karaoke, music remixing, and pedagogical applications. While earlier research on MSS systems has been dominated by models targeting narrow sets of general stems, there have recently been attempts to support broader source definitions. One of these methods uses audio queries to provide direct and descriptive control over the desired separation targets based on the sound itself. However, query-based separation remains cumbersome due to the need to provide audio examples with features matching the sources contained within mixtures. This paper proposes Music Source Separation via Stem Discovery (MuS3D), a query-based source separation framework that iteratively discovers active sources from the mixture. On correctly detected sources, our model matches manually queried baselines and surpasses state-of-the-art text-based models. Subjective evaluation indicates encoding artifacts as the limiting factor in current generative separation. The findings suggest that audio-based query representations offer an effective and automatable interface for source separation.

In the present work, the Light Induced White Emission (LIWE) was investigated as one of the sources of laser loss in transparent Cr:YAG ceramics. We have found that transparent Cr:YAG ceramics is capable of generating bright LIWE at excitation powers above a certain threshold. Intensity of LIWE strongly depends on the excitation power and ambient pressure. The host temperature estimated from Cr3+ luminescence was found to be below 600{\deg}C, while the most intense white emission was found between 50-400{\deg}C. The mechanism of the laser induced white emission was discussed in terms of Intervalence Charge Transfer (IVCT) in chromium mixed valence pair.

Error-correction records can reveal noise yet supply the information needed for control too slowly. In a surface code under Gaussian dephasing, encoded calibration learns a correlation that reverses the preferred control mainly through rare events. A product probe exposes it more often through the same checks, reducing ideal-record sample complexity from inverse-square to inverse-linear in phase variance. Counting both calibration and execution costs, we show that this gain can repay probe overhead and enable protected tasks within budgets that exclude encoded calibration.

Machine unlearning aims to remove target influence while preserving other capabilities. This survey compares methods, benchmarks, and evidence across large language models and systems using retrieval, memory, tools, and interacting agents. A five-layer framework connects removal requests, system boundaries, target locations, interventions, and supported claims. A seven-stage lifecycle and six evidence dimensions guide comparison. The review shows that target construction, retained data, and recovery tests affect reported outcomes. Evidence from model evaluations remains insufficient to establish removal across external state and subsequent updates, motivating evaluation that tracks dependencies and tests whether target influence returns.

Prediction models can perform poorly when the deployment population differs from the training population. Data from the target population would help, but individual-level target data may be inaccessible because of access restrictions or reporting conventions. We consider a multi-resolution setting in which individual-level data are available from a source population, while the target population is observed only through subgroup summaries. We propose SAGE, a one-step estimator that updates a source-trained predictor using a gradient estimated from these summaries. Motivated by diagnostics consistent with the random distribution shift model, we choose SAGE's step-size to account for both sampling and distributional uncertainty. Under this model, SAGE reduces mean asymptotic target excess risk relative to the source-trained predictor. We also show that, under the model, entropy-balancing weighted empirical risk minimization (EB), which reweights source observations to match the target summaries, is asymptotically equivalent to a full-step SAGE update. SAGE with the optimal step-size has asymptotic mean squared error no larger than that of EB. Across real-world datasets, SAGE generally improves on the source-trained predictor and one-step updates that ignore distribution shift, including when the random shift model only partially captures the observed shifts. Compared to EB, SAGE improves prediction more consistently across the sample size and shift settings studied.

Laser-induced white (light) emission was observed from transparent Cr:YAG ceramics irradiated with a focused continuous wave beam of light from an infrared laser diode. The laser-induced white emission is detected only on the surface of the sample and is not observed in volume. It is found that the intensity of the emission increases exponentially with the laser power density above the threshold. The impact of broadband emission on the power of the transmitted laser beam through the sample was measured. The disappearance of broadband emission due to displacement of the laser beam or an increase in ambient pressure leads to a decrease in the power of transmitted laser beam. Origins of the laser-induced white light emission along with its characteristic features are discussed in terms of multiphoton absorption, intervalence charge transfer and ionic space charge models.

Large language models (LLMs) excel at natural language processing but struggle to interact with external environments. Tool learning provides a promising way to extend LLMs into actionable agents, where tool selection is a critical prerequisite for successful tool use. Existing work often assumes a small or predefined set of tools, leaving large-scale tool selection underexplored. Real-world repositories contain a vast and diverse array of tools, making it difficult for LLMs to effectively search, distinguish, and compose tools under context-length constraints. We identify large-scale tool selection as a new challenge for agentic reinforcement learning, highlighting that existing RL methods for knowledge-based question answering are inadequate for selecting tools while considering compatibility. To address this challenge, we propose ToolSearcher, a novel RL framework for effective multi-turn search and fine-grained optimization in large-scale tool selection. Specifically, we introduce category-constrained tool discrimination to improve the model's ability to distinguish functionally similar tools, event-level search modeling to explicitly optimize the discovery of target tools during multi-turn search, and trajectory-aligned credit allocation to provide fine-grained reward signals for different stages of the search-selection process. Extensive experiments on large-scale tool selection benchmarks demonstrate that ToolSearcher consistently outperforms a set of strong baselines in challenging settings involving iterative search and complex tool composition.

Network analysis has become a standard way of representing consultation, sourcing, media use, attention, and influence in communication research. This review examines 31 applications across communication subfields and asks of each what communication problem it addresses, which explanatory resource it invokes, and what its research practice makes observable. The three dimensions form a comparison framework and yield three propositions with stated scope and refutation conditions: resource relevance is task- and criterion-dependent; commonality at one level of aggregation does not imply commonality at another; and influence estimates are conditional on relationship type, group stage, and time. A short bibliometric section describes how the literature's cited references are organised: method references are paired with one another more often than year-specific margins predict (ratio 1.36) and with theoretical references less often (0.82), a pattern consistent with a methodological toolkit that circulates apart from the commitments that license its use. The review closes with designs that would test each proposition.

Passage reranking plays a crucial role in information retrieval by refining the ordering of candidate passages to better reflect relevance. Existing listwise LLM rerankers with Chain-of-Thought (CoT) reasoning can handle complex queries effectively, but they suffer from substantial redundancy and high latency due to sliding-window strategies, which repeatedly generate highly similar CoTs. To address this, we propose QReason, a decoupled framework that separates query-focused reasoning from window-specific passage relevance assessment. Specifically, QReason introduces a dedicated rewriter that generates a ranking-oriented reasoning query once, capturing the query's core intent while avoiding redundant reasoning, and then reuses it across all windows with a non-reasoning reranker. The rewriter is trained via a two-stage process that first uses supervised fine-tuning with relevant-passage guidance through semantic evidence to produce deeply grounded, query-focused CoTs. It then applies reinforcement learning to align CoT generation with both the inference-time setting and the reranking objective, optimizing listwise metrics and passage-level discrimination to produce reusable reasoning chains for reranking. Experiments on the BRIGHT benchmark demonstrate that QReason significantly reduces redundant reasoning, achieves ranking performance comparable to or better than strong reasoning-based rerankers, and outperforms existing query rewriting models.

I present a discrete-element approach developed to study the collisional and gravitational evolution of small self-gravitating granular aggregates. Each body is represented as a composite of cohesively bonded spherical grains, so that fragmentation and reaccumulation emerge from the microscopic competition between short-range dissipative contact forces, an irreversible bond-breaking criterion, and pairwise Newtonian self-gravity summed over every particle pair, including those internal to a single body. A numerical experiment is described: a random-sequential packing procedure that generates two bonded spherical aggregates, a controlled two-body encounter with tunable approach speed and impact parameter, and a systematic parameter sweep designed to map the conditions under which two bodies launched from rest under their mutual gravity alone either merge into a single remnant or fail to settle after a low-speed encounter. Of the 125 simulated collisions, 56.8% result in the formation of a single residue. The cohesive network remains intact for $\Pi_\sigma\lesssim0.036$, is partially damaged with dispersion determined by the contact damping ratio, and breaks completely for $\Pi_\sigma\approx3.59$

We consider the large time asymptotic behavior of solutions to the initial value problem for the incompressible Navier-Stokes equations in the whole space $\mathbb{R}^d$ ($d\ge 2$). When the initial velocity belongs to $L^1(\mathbb{R}^d)$, it is well-known that its spatial integral vanishes as a consequence of the divergence-free compatibility condition. Taking this property into account, Carpio (1996) and Fujigaki-Miyakawa (2001) derived higher-order asymptotic formulas for the strong solutions. In this paper, we investigate the large time behavior of solutions when the initial velocity belongs to the Fourier-Herz space $\widehat{L}^1(\mathbb{R}^d)$, which provides a broader framework than $L^1(\mathbb{R}^d)$ and imposes an additional condition in the low-frequency region. In particular, in the two-dimensional case, we show that an asymptotic profile different from those obtained by Carpio and Fujigaki-Miyakawa arises.

Thorium-229 possesses the only known low-energy nuclear transition suitable for spectroscopy with narrowband VUV lasers. While previous experiments have focused on application as a nuclear clock, this transition also offers a route to high-accuracy magnetometry. Experimental observations of magnetic fields generated by phonons carrying angular momentum remain inconclusive, highlighting the need for quantitative tests of the underlying physical mechanisms. In this article, we propose doping thorium-229 into a solid-state host to probe phonomagnetic fields in situ. We identify Na$_2$ThF$_6$, a chiral stoichiometric thorium compound, as a promising host material and evaluate its spectroscopic sensitivity to magnetic interactions under two excitation schemes: driving degenerate phonon modes with a circularly polarized laser, and applying a temperature gradient. Density functional theory simulations combined with quantitative estimates suggest that the temperature-gradient scheme yields a magnetic signal that appears too weak to be measurable, while a circularly polarized, high-intensity THz/VUV pump-probe driven phonomagnetic response may approach the shot-noise-limited detection threshold. While experimental challenges remain, the unique suitability of thorium-229 provides a testable pathway toward detecting phonomagnetic fields in a solid-state platform.

Odd Cycle Transversal is a classic $\mathsf{NP}$-hard graph optimization problem asking for a minimum-weight set of vertices whose deletion makes the input graph bipartite, or equivalently, a maximum-weight induced bipartite subgraph. We show that Odd Cycle Transversal is quasi-polynomial-time solvable on $kP_4$-free graphs, for every fixed $k \in \mathbb{N}$. In fact, we provide an $n^{O_k(\log n)}$-time algorithm for the more general \textsc{Max-Weight List $2$-Colorable Induced Subgraph}, where the notation $O_{k}(\cdot)$ hides factors depending on $k$. Paired with known results from the literature, this allows us to obtain a complete complexity dichotomy for these two problems on $H$-free graphs into cases solvable in quasi-polynomial time and cases which are $\mathsf{NP}$-hard, in particular resolving an open problem of Agrawal, Lima, Lokshtanov, Saurabh, and Sharma [SODA 2024]. Our algorithms are based on a new structural tool that may be of independent interest. We introduce the notion of $H$-amiable family and show that, for every fixed graph $H$ without isolated vertices and every fixed $k\ge2$, every $kH$-free graph admits an $H$-amiable family of quasi-polynomial size that can be constructed in quasi-polynomial time. Besides yielding the aforementioned algorithms, this result gives, for every fixed connected graph $H$ and every fixed $k\ge2$, a reduction from Max-Weight Independent Set on $kH$-free graphs to the same problem on $H$-free graphs with $n^{O_{H,k}(\log n)}$ overhead. In this setting, it improves the $n^{O_{H,k}(\log^3 n)}$ overhead obtained by specializing the general reduction of Gartland and Lokshtanov [FOCS 2020].

Quantum sensing increasingly demands materials combining room-temperature optical spin addressability and coherent control with rapid, accessible fabrication. Yet semiconductor platforms require costly materials and specialized processing, while molecular systems often depend on bespoke synthesis or involved crystal growth. Here we apply microspacing in-air sublimation (MAS) to rapidly fabricate quantum-sensing materials within minutes. Microgram quantities of commercially available precursors crystallize on glass, in air and without vacuum or inert-gas handling. Monitored in situ, growth yields optically clear, stoichiometric single crystals of excellent quality, including plates and needles with intrinsic optical waveguiding. Donor-acceptor charge-transfer co-crystals pairing anthracene or biphenyl with tetracyanobenzene, together with localized-exciton pentacene:pentacenequinone (P:PQ), exhibit room-temperature optically detected magnetic resonance (ODMR). Charge-transfer ODMR resonances reach linewidths below $4\mathrm{MHz}$, consistent with motional narrowing of mobile triplet excitons, while P:PQ supports coherent ensemble spin control with $T_2=0.56\mu\mathrm{s}$. Functionality across chemically and electronically distinct pairs establishes MAS as an accessible screen for molecular quantum-sensing materials, connecting molecular crystal engineering with low-cost, chemically tunable thin triplet-spin layers and waveguiding sensor geometries for quantum sensing and microscopy.

In this paper, we consider bilevel variational inequality problems, where the feasible set is the solution set of another variational inequality. We propose a Bregman inertial regularized extragradient method for solving these problems. By performing the inertial extrapolation in the dual space, the proposed method aligns the inertial step with the structure of the Bregman three-point identity. We also derive explicit non-asymptotic bounds for the generalized gap function. More precisely, using diminishing regularization, we establish convergence rates of $\mathcal{O}(1/k^{1-b})$ for the optimality gap and $\mathcal{O}(1/k^b)$ for the feasibility gap with $ 0 < b< 1$. For constant regularization parameter $\eta>0$, we establish an $\mathcal{O}(1/k)$ rate for the optimality gap and an $\mathcal{O}(1/k)+\mathcal{O}(\eta)$ bound for the feasibility gap. Furthermore, numerical experiments on traffic networks and multi-portfolio Nash equilibrium problems demonstrate the practical effectiveness of the proposed framework.

How should we evaluate language models when more than one interpretation can be right? Cultural benchmarks often test factual knowledge, agreement with survey responses, or recognition of a predefined meaning. These tasks leave open whether a model can explain how a cultural reference works in a particular text, support a reading with evidence, or revise it after criticism. This is a question of interpretive depth, complementary to the breadth of cultural coverage. We argue that literary interpretation offers a useful setting for studying these capabilities. We focus on cultural referencing and reuse: how texts invoke, repeat, and transform earlier expressions across historical and linguistic contexts. Our central claim is that literary scholars can disagree about an interpretation while recognizing the quality of its support. We propose linking evidence-centered benchmarks, evaluation that preserves scholarly disagreement, and model-development experiments on literary data, contextual resources, and scholarly feedback. Danish literature provides a concrete starting point, with implications for other languages and domains. The aim is to develop alternative evaluation strategies that go beyond conventional benchmark metrics and guide model development toward cultural robustness in AI systems.

A key aspect of culture is a society's norms about everyday behavior. How accurately do large language models (LLMs) represent cultural differences in such norms? To answer this question we used the recent Global Study of Everyday Norms (GSEN), which collected ratings of 150 scenarios in 90 societies, as the human benchmark. We prompted GPT-5 to estimate each society's average rating for every scenario, and later repeated the benchmark in three other LLMs: GPT-5.4, Claude Opus 4.6, and Gemini 3.1 Pro. Compared to GSEN estimates, all four LLMs misrepresented cultural variation in two ways. First, they greatly underestimated its magnitude, estimating differences between societies to be, on average, less than half their measured size. Second, for many scenarios the LLMs poorly identified the pattern of variation, that is, which societies judged the behavior less acceptable and which societies judged it more acceptable. The pattern of variation was identified better for scenarios that elicit concerns about vulgarity, especially scenarios involving kissing and flirting. We also found that norms in more developed societies tended to be estimated somewhat more accurately, and that prompting in local survey languages rather than English produced only a modest improvement in accuracy. Local-language prompting also reduced, but did not remove, the underestimation of between-society differences. Cultural differences in everyday norms are only weakly and unevenly represented by LLMs.

Let $\mathbb{P}(x\prec y)$ be the probability that $x$ precedes $y$ in a uniformly random linear extension of an $n$-element poset $P$, and define the balancing coefficient to be $\delta(x,y)=\min(\mathbb{P}(x\prec y),\mathbb{P}(y\prec x))$ with $\delta(P)=\max_{x,y}\delta(x,y)$. We prove (Theorem 1) that sufficiently large width forces $\delta(P)$ to be arbitrarily close to $1/2$, answering a long-standing conjecture of Kahn and Saks. In fact, we prove the stronger result (Theorem 2) that large width forces one of two configurations in our poset: either a nearly uniform order on $k$ vertices, or an almost fixed order on $t$ vertices with one further vertex inserted uniformly among the $t+1$ slots. We also show that, for fixed $k$, the first possibility must occur within any antichain $X$ of size $\Omega(n^{2/3})$.

We introduce Acacia, a graph foundation model, trained on the web graph. Acacia (i) supports arbitrary feature dimensionalities and semantics without additional training, (ii) supports a wide range of tasks, including node classification, link prediction, node clustering, and graph generation, without additional training, (iii) has in-context learning capabilities, and (iv) does not rely on pretrained LLMs. In particular, existing graph foundation models often require training additional classification heads or feature projectors to accommodate new graphs or new labels, whereas Acacia does not. Moreover, existing graph foundation models often gain their capabilities by being stitched together with pretrained LLMs, whereas Acacia is trained from scratch using only the Common Crawl web graph. This is also an important result because it provides evidence that graph models can acquire emergent capabilities from scratch like LLMs.

We combine two coloring aspects that work in opposite directions. One can 2-color the vertices of a cubic graph such that each monochromatic component is very small. One can also 2-color the vertices of a cubic graph such that each monochromatic component has degree at least 1. As an intended tool for solving a special case of Wegner's conjecture, Thomassen formulated a conjecture that combined the two previous properties. This led to the concept of a crumby coloring. However it turned out that there are cubic graphs without such coloring. Here we try to see what natural relaxations of the original concept might hold for each cubic graph. We show there exists a constant $c$ such that every cubic graph has a vertex 2-coloring such that every monochromatic component has at least 2 and at most $c$ vertices. We also prove an unbalanced version, which is the natural relaxation of the crumby coloring.

Given a family of genus $g$ curves $f:\Psi\to S$ and a relative degree $d$ line bundle $L$ on $\Psi$ such that $f_*L$ is a vector bundle, the projectivization $\mathbb{P}(f_*L)$ is stratified by relative de Jonquières loci, which parameterize sections of $L$ with prescribed vanishing orders. We give universal formulas for the classes of these loci in terms of the relative $O(1)$ on $\mathbb{P}(f_*L)$ and tautological classes pulled back from the universal Picard stack $\mathrm{Pic}_g^d$. When $f$ is the family of lines in $\mathbb{P}^r$, we use the universal polynomials to compute $\mathrm{GL}_{r+1}$-equivariant classes of loci of hypersurfaces and complete intersections admitting lines with prescribed contact orders.

Semantic communication (SemCom) and integrated sensing and communication (ISAC) are promising technologies for future 6G wireless networks. Existing studies have applied semantic technology to either the communication module or the sensing module of ISAC. In this work, we propose SemISAC, which performs both SemCom and semantic sensing within a single dual-function waveform. SemISAC uses a joint semantic encoder that extracts task-specific information for both communication and sensing. We evaluate SemISAC in a vehicular scenario in which vehicles share pixel-wise segmentation of the road environment and, through sensing, classify surrounding objects and estimate their ranges. On the transmitter side, a deep learning encoder converts the input road-scene image into semantic symbols and places them on the data cells of an OFDM grid, while the remaining cells serve as pilots for channel state information estimation and sensing. The pilot configuration is adaptively optimized based on the channel conditions to balance communication and sensing requirements. At the receiver, a deep learning model reconstructs the segmentation from the received waveform, while the transmitting vehicle captures the reflected waveforms from surrounding objects and uses task-specific deep learning decoders for target recognition and range estimation. Simulation results show that SemISAC achieves a segmentation accuracy close to that of the dedicated SemCom module while outperforming both conventional and semantic baselines in target recognition and range estimation.