Papers

Function-correcting codes are designed to protect the function values of a prescribed function against errors. Every error-correcting code that provides data protection inherently offers some degree of protection for functions defined on the data. In this work, we introduce a class of codes over $\mathbb{Z}_m$, termed function-correcting Lee metric codes with data protection (FCLMCs with data protection), which simultaneously provide error protection for both the data and the corresponding function values under the Lee metric. We consider codes that provide protection against a prescribed level of error for the function values that exceeds the level of protection guaranteed for the underlying data. We present a general construction of these codes and derive lower and upper bounds on the optimal redundancy, including a Plotkin-type lower bound. Furthermore, we derive explicit upper bounds on the redundancy of FCLMCs with data protection for several important classes of functions, including locally binary Lee functions, the Lee weight function, and the modular sum function. Finally, since the Lee metric coincides with the Hamming metric over $\mathbb{Z}_2$, all of our results remain valid over $\mathbb{Z}_2$ with respect to the Hamming metric.

This paper presents semi-automatic stride-independent patching (SSP) as an alternative to automatic stride-dependent patching techniques. SSP uses user or expert input to position predefined patches over one or more objects of interest. To evaluate its effectiveness, three patch-based datasets were created using SSP, overlapping patching (Overlap), and non-overlapping patching (Noverlap). DeepLabV3+ models with ResNet50, ResNet18, and MobileNetV2 backbones were trained sepa-rately on each dataset. Quantitative evaluations were performed on the respective test splits and a common external test set. SSP generally achieved higher segmentation scores on the test splits and required the shortest model training time across all three backbones. On the external test set, SSP achieved the highest average precision and F1-score across backbones, whereas Noverlap achieved the highest average recall. These preliminary results demonstrate that the potentially greater spatial coverage of Noverlap and Overlap did not generally translate into better segmentation perfor-mance and that SSP offers a favorable balance between segmentation performance and model training time.

Multiple imputation (MI) is widely used for handling missing data in medical research, with variance commonly estimated using Rubin's rules (RR). RR is simple to apply, but under uncongeniality between the imputation and analysis procedures, its variance estimate can be either too small or too large, leading to miscalibrated confidence intervals. Robins and Wang (RW) developed an estimating-equation variance estimator that does not require congeniality under the conditions of their parametric imputation framework. Practical use of RW, however, has been limited by the lack of accessible software and by the additional variance calculations required for modern imputation workflows. We develop an R package, rw, construct RW variance components for normal and logistic conditional imputation models fitted through mice, and propose an approximate RW variance procedure for predictive mean matching (PMM). The PMM procedure preserves the original imputations and selected donors. For the variance calculation, we define differentiable donor probabilities and use expected analysis scores to approximate the cross-moment between analysis and imputation scores. Analysis scores are summed by recorded donor to account for donor reuse. We evaluate the proposed methods in benchmark simulations based on the original RW setting and in validation-study simulations motivated by electronic health record data. RR coverage was up to approximately 23 percentage points below the nominal 95% level in some settings and above nominal in others. The proposed RW estimators generally produced coverage closer to the nominal level in larger samples under both parametric and PMM imputation, while retaining the same completed-data point estimates as RR.

Recent full-duplex spoken dialog models enable simultaneous listening and speaking, but fine-grained models still advance their backbone autoregressively at every interaction frame. We introduce DiffuPlex, a rolling masked diffusion framework that reduces this sequential computation by predicting multiple future user and assistant frames in a single backbone wake. DiffuPlex consumes only a confident prefix of each predicted future while interaction continues at the original frame rate. As user speech arrives, it checks the corresponding user predictions and, when the interaction diverges, preserves already played assistant content while revising only the unplayed future. We consider two inference policies over the same predictor: DiffuPlex-LISTEN consumes multiple future frames when they predict assistant silence, whereas DiffuPlex-SPEAK can also consume predicted assistant speech. Across full-duplex interaction and spoken-language evaluations, DiffuPlex substantially reduces sequential backbone computation while largely preserving interaction behavior and general capability. DiffuPlex-LISTEN and DiffuPlex-SPEAK achieve $1.46\times$ and $1.59\times$ deployment-path wall-clock speedups and $1.61\times$ and $1.80\times$ Core LM speedups, with all measured backbone invocations completing within the 80ms interaction interval. Human evaluation shows that LISTEN preserves speech naturalness and conversational quality, while SPEAK retains conversational quality with some degradation in speech naturalness.

Bayesian Optimization (BO) is a popular method for efficiently optimizing expensive black-box objectives. However, BO utilizing standard Gaussian Processes is ill-suited for doubly stochastic Cox Processes that are often used in spatio-temporal problem spaces. We introduce INLA-SPDE Spatio-Temporal Bayesian Optimization (ISBO): the first scalable BO framework for spatio-temporal data, that models the log-intensity with a Log-Gaussian Cox Process(LGCP) and performs inference via Integrated Nested Laplace Approximation and Stochastic Partial Differential Equations (INLA-SPDE) approach. Using a Matern field on meshes yields a sparse Gaussian Markov Random Field, where INLA provides fast and accurate posterior inference throughout sequential optimization. ISBO stably locates high-intensity regions and the peak of the latent intensity with minimal evaluations. A time-varying Upper Confidence Bound acquisition with masking avoids revisits, while penalized-complexity priors regularize early rounds. Experiments on synthetic and real-world spatio-temporal datasets show accurate peak discovery, intensity recovery, and substantial speedups over an RKHS-based baseline, positioning ISBO as a practical choice for BO with point-process data.

Bayesian neural network predictions are commonly approximated using a fixed number of Monte Carlo samples per input, without controlling the resulting error that comes from this finite sample. We propose the use of confidence sequences to dynamically determine how many samples are needed while maintaining statistical guarantees. We consider several ways in which predictive probabilities are used, including identifying the most likely class, approximating the full predictive distribution, and resolving probability-threshold decisions. Sampling stops once the corresponding decision can be made with the desired guarantee. Experiments show that the method allocates the computational budget efficiently, assigning more samples to ambiguous inputs than to easy inputs while preserving reliable decisions and reducing overall latency relative to a fixed Monte Carlo budget.

A verifier that accepts or rejects whole answers reveals little: under a flat prior over $k$-bit answers, zero error needs $2^k-1$ verifications. The usual remedy is to solve related source tasks, either all first, as a curriculum does, or interleaved with verification. We price this remedy in information and in calls. With an exact verifier, the least causal information that any interleaving of source calls and $n$ verifications needs to succeed with probability $s$ is a list rate-distortion function, attained by one observation before any verification. It lower-bounds the expected number of binary source calls, which designed sources meet within $1+\log_25$ calls for unique answers and within a logarithmic term in general, where no additive constant suffices. With an exact verifier and fixed sources, moving every call before the first verification preserves all hard caps on calls, although interleaving can save unboundedly many expected calls; under a noisy verifier, source-first protocols can lose unbounded factors in information and in error. For linear banks over $\mathbb{F}_2$, optimal accuracy has a closed form, and after a polynomial-time reduction the budget profile is computable in time $2^{O(h^2)}\operatorname{poly}(J,k+h)$ for $J$ sources and nuisance dimension $h$. In these banks, for zero error under a hard cap, the calls beyond the rounded-up information price are exactly those spent on nuisance. Every numbered result apart from two clauses about the planner is machine-checked in Lean 4, assuming two published results. Used as a ruler, the frontier shows a small transformer using all delivered bits at latent dimension $5$ and none at $11$ within fixed training budgets; in a test with predictions recorded before training, low XOR degree of the target bits did not suffice for their use.

This note gives direct proofs that, under an effective isometric $T^2$ action, Einstein metrics on smooth homotopy four-spheres are round and complete Ricci-flat metrics on smooth manifolds homeomorphic to $\mathbb R^4$ are Euclidean or positive one-center Taub–NUT, up to isometry, scaling, and orientation reversal.

Quantum networking represents the future of secure communication, enabling fundamentally new capabilities through quantum information exchange. However, these networks require secure, high-fidelity quantum communication channels, and they require every participating node to be a genuine quantum device. Currently, there is no reliable method to verify whether clients entering a quantum network truly possess quantum computational capability and are connecting over robust channels. In this work, we introduce a client-validation protocol that functions as a proof-of-quantum-capability handshake. Our protocol secures a quantum network against classical spoofers, noisy quantum computers, and genuine quantum devices connecting with the network over noisy or insecure channels. We validate the efficacy of this protocol through numerical simulations under erasure, dephasing, and depolarizing noise models.

We present a combined analysis of the latest publicly available atmospheric neutrino data from Super-Kamiokande including all data-taking stages previous to the gadolinium phase, IceCube-DeepCore, and the six-detection-unit configuration of KM3NeT/ORCA. Our fit uses all event samples simultaneously and treats the systematic uncertainties shared among experiments as fully correlated, while detector-response uncertainties are modeled independently for each experiment. The combined data constrain the atmospheric oscillation parameters to $\Delta m^2_{31} = 2.44^{+0.06}_{-0.04} \times 10^{-3}\,\mathrm{eV}^2$ and $\sin^2\theta_{23} = 0.52^{+0.03}_{-0.04}$, with a precision of $2.2\%$ and $6.1\%$, respectively, which is competitive with current accelerator-based measurements, and independently constrain the $CP$-violating phase to $\delta_{CP} = 1.30^{+0.24}_{-0.28}~\pi$. Finally, comparing the orderings of the neutrino mass spectrum, we find a preference for the normal ordering with $\Delta\chi^2 = 11.0$; further calibrated with pseudoexperiments, we exclude the inverted ordering at $99.95\%$ confidence level ($3.3\sigma$). In a joint fit including 207 days of JUNO data, we further exclude the inverted ordering at $\Delta \chi^2 = 15.1$, corresponding to $3.9 \sigma$.

Pre-trained transformer models are increasingly being used to study scientific and technological progress. Encoders tuned to paper or patent text outperform general-purpose models on downstream classification, regression, and proximity tasks within science and technology. However, the applicability of these models for studying time-dependent or archival properties of science, technology, and their interface is limited due to lookahead and domain biases inherent to these pre-trained models. These limitations arise from training on corpora with unconstrained chronological and text source distributions. We introduce SciTBERT: a family of chronologically consistent BERT-derived language models trained on text from scientific papers, patents, and high-quality educational web text with training data cutoff dates spanning each year between 2013 and 2025. We also post-train these models in a chronologically-consistent manner using paper and patent citations, creating SciTBERT-CI model family. We find that these models generally outperform predecessor domain-specific encoder models even when training data is limited by early year restrictions in the corpus. To further investigate the extent to which this class of models can learn representations that bridge science and technology, we introduce the PatRepEval benchmark, a suite of patent-related text embedding tasks at the science-technology interface. Performance in a variety of classification, regression, and retrieval tasks spanning papers and patents highlights the importance of aligning encoder model representations with the domain distributions of their downstream tasks, and chronologically consistent encoders can match or exceed models trained without temporal constraints.

We prove a single measurement uniqueness result for interior sound-soft obstacles in the planar Schrödinger equation with an unknown surrounding potential. For any two configurations with different obstacles, we construct a boundary datum for which the corresponding Neumann measurements differ. The full Dirichlet-to-Neumann map uniquely determines both the obstacle and the potential. The obstacles may have several connected components, and no convexity or analyticity assumptions are imposed. Neither potential is required to be known near the measurement boundary.

GW231123 is the most massive binary black hole merger observed to date and one of the most intriguing hierarchical merger candidates in the pair-instability mass gap. Its exceptionally large inferred component spins and remarkably short in-band duration make the source highly sensitive to waveform physics near merger. Here we show that GW231123 is better described as an eccentric binary black-hole merger. We analyse data over 11–448 Hz using the eccentric, spin-precessing effective-one-body waveform model TEOBResumS–Dalí, accounting for detector calibration uncertainty. We measure $e_{5.5\,\mathrm{Hz}}=0.34^{+0.12}_{-0.23}$ at 90% credibility and obtain a Bayes factor of 10.2 in favour of the eccentric model over its quasi-circular counterpart. GW231123-like injection–recovery studies further show that analyses starting at 20 Hz, as in previous studies, can obscure this eccentricity. Including eccentricity substantially changes the spin inference, weakening the preference for a near-extremal secondary spin and lowering its posterior median to $a_2\simeq0.7$, close to the characteristic spin expected for a black-hole merger remnant. These results provide a coherent dynamical interpretation of GW231123, in which residual eccentricity, a mass-gap black hole, and a remnant-like spin arise naturally from a hierarchical merger channel in a dense environment.

A second-price auction must determine its price but need not learn how far losing values lie below it. We show that protecting this information from the seller conflicts with auction credibility. In deterministic protocols with private communication, lower-tail privacy forces the first informative question to reveal whether a bidder has the highest possible value. The seller can then manipulate the winner's payment without any bidder detecting the deviation, increasing revenue at some valuation profiles and never reducing it. A descending protocol conceals losing values below the price but permits manipulation; with mandatory sale, a credible ascending protocol reveals them.

For $s>0$, and $z\in\mathbb H=\{z=x+iy:y>0\}$, define $\theta(s;z)=\sum_{m,n\in\mathbb Z}e^{-\pi s\big(m^2y+\frac{(mx-n)^2}{y}\big)}$ and $ J(z;a,b)=\sum_{m,n\in\mathbb Z}e^{-\pi \big(m^2y+\frac{(mx-n)^2}{y}\big)} \cos\bigl(2\pi(ma+nb)\bigr)$ for the classical and shifted theta functions (Gaussian lattice sums), respectively. We prove that, up to the modular group, there exist three thresholds $0<\alpha_a<\alpha_b<\alpha_c<1$ such that \begin{equation}\aligned\nonumber \Minima_{z\in\mathbb H,\,(a,b)\in\mathbb R^2}\Big(\theta(1;z)+\alpha J(z;a,b)\Big)= \begin{cases} \;\big(e^{i{\pi}/{3}};1/3,1/3\big), &\hbox{if}\;\; \alpha\in[0,\alpha_a),\\ \;\big(e^{i{\pi}/{3}};1/3,1/3\big)\;\hbox{or}\;\big(e^{i{\varphi_{\alpha_a}}};1/2,1/2\big), &\hbox{if}\;\; \alpha=\alpha_a,\\ \;\big(e^{i{\varphi_\alpha}};1/2,1/2\big),\;\varphi_\alpha\in(\varphi_{\alpha_a},\frac{\pi}{2}),\;\; &\hbox{if}\;\; \alpha\in(\alpha_a,\alpha_b),\\ \;\big(i;1/2,1/2\big),\; &\hbox{if}\;\; \alpha\in[\alpha_b,\alpha_c],\\ \;\big(iy_\alpha;1/2,1/2\big),\; y_\alpha\in(1,\sqrt3],\;\;y_1=\sqrt3,\;\;&\hbox{if}\;\; \alpha\in(\alpha_c,1], \end{cases} \endaligned\end{equation} where the complex variable $z$ and vector $(a,b)$, represent the total vortex shapes and relative positions of the two-component Bose gas, respectively. Consequently, this completely proves the conjecture of Mueller and Ho~\cite{Mue2002} (2002) arising in Bose–Einstein condensates.

Autonomous Surface Vehicles (ASVs) operating in dynamic marine environments require robust control policies for tasks such as path following and station keeping, making reinforcement learning (RL) a promising alternative to classical controllers. However, existing ASV simulators rarely support parallel environments for RL training. Such existing simulators require accurate hydrodynamic modeling from computational fluid dynamics solvers or towing tank tests for setting hydrodynamic parameters to address the sim-to-real gap. To address these challenges, we present an ASV simulator and accompanying pipeline that enables training policies starting from unknown vehicle dynamics. Our framework uses only a CAD model and brief set of open-water field trajectories for approximating and refining both hydrodynamic and thruster parameters. Real-world deployments on a BlueBoat ASV demonstrate successful zero-shot sim-to-real transfer in path following and station-keeping tasks without prior hydrodynamic and propeller information.

Full-duplex speech models can listen and speak simultaneously, enabling natural interaction, but become increasingly difficult to control as the conversation history grows. When used as user simulators, this lack of control can cause them to deviate from prescribed scenarios and produce unreliable evaluation outcomes. We introduce SimIF-Bench (Simulator Instruction-Following Benchmark), which evaluates whether a conversational model stays within a prescribed scenario and completes multiple goals in the required order. The benchmark reveals that current open-source full-duplex models struggle to follow such constraints. We then introduce a Group Reward-Decoupled Normalization Policy Optimization (GDPO)-based training recipe that enables a full-duplex model to follow textual instructions during an ongoing conversation while maintaining its turn-taking ability. By connecting the resulting SteerablePlex to an asynchronous backend language model that monitors the conversation and provides instructions when needed, we build a more controllable full-duplex user simulator that follows multi-stage constraints more reliably than existing open-source models and GPT-Realtime.

Classical CUSUM relies on the log-likelihood ratio of the underlying distributions, which cannot generally be computed from finite pre- and post-change samples alone. We propose diffusion-integrated score CUSUM (DI-SCUSUM), a training-free detector. We add Gaussian noise to the samples to form two smooth density estimates and calculate their Hyvärinen scores exactly, without training a score network. For each incoming observation, we sample a diffusion time, perturb the observation, and use the importance-weighted score difference as an increment in the DI-SCUSUM recursion. Under the assumption that observations follow the fixed empirical distributions, the post-change mean increment is proportional to the Kullback-Leibler (KL) divergence from the smoothed post-change to the smoothed pre-change empirical distribution. We establish exponential false-alarm scaling and a first-order delay bound that, for a fixed threshold and increment scaling, is inversely proportional to the KL divergence. In the calibrated anisotropic Gaussian simulation, DI-SCUSUM nearly matches likelihood-ratio CUSUM and reduces the measured detection delay by about 91% relative to score-based CUSUM. On MNIST and Oxford-IIIT Pet, DI-SCUSUM also has lower empirical conditional detection delay than SCUSUM at comparable false-alarm levels.

Autocorrelation in black hole movies encodes the time delays and angular separations between gravitationally lensed images, offering a means of testing the spacetime geometry. Using an orbiting hot spot in the parametrized Johannsen-Psaltis metric with a single deformation parameter, we investigate the ability of lensing-induced correlations to distinguish departures from Kerr. From ray-traced movies, we extract the slope (k) and intercept (b) of an approximately linear secondary ridge in the time-angle autocorrelation map as potential future observables. Variations in the spin and the metric deformation parameter produce distinctive trajectories in the (k,b) plane, allowing the two observables to jointly constrain both parameters when the orbital radius, observer inclination, and orbital angular velocity are specified. By varying the orbital angular velocity, we construct a Kerr reference region in the (k,b) plane, and we find that, for some low-spin configurations with negative deformation parameters, the measured slope-intercept pairs of the secondary peaks lie outside this reference region. This feature appears for sub-Keplerian, Keplerian, and super-Keplerian motion, indicating that secondary-ridge measurements from black hole flare movies have the potential to distinguish non-Kerr signatures.

Maximum likelihood expectation maximization (MLEM) is a common approach for Poisson image reconstruction, but accurate recovery requires many iterations and is sensitive to mismatch in the assumed acquisition model. We propose a deep-unfolded penalized MLEM framework that maps a prescribed small number of iterations into trainable layers while retaining the analytical forward/backward projections and the multiplicative structure of MLEM. The unfolded architecture learns layer-dependent regularization and Poisson-model parameters, together with a data-dependent correction of the sensitivity normalization to mitigate model mismatch. We numerically show that our method improves reconstruction resolution at a fixed iteration budget and attains reconstruction quality comparable to long MLEM runs and direct data-driven models.

Multiparameter complex processes, based on the Costa-Farber model, provide a common framework for growing random simplicial complexes, including the Linial-Meshulam and random flag complex processes. We establish laws of large numbers for persistent Betti numbers of these processes and prove that, after a deterministic time change and normalization, their persistence diagrams converge weakly in probability to a deterministic finite measure. Its quadrant masses are determined by universal limits of normalized persistent Betti numbers, characterized by an explicit finite-dimensional optimization problem. We extend the diagram convergence to integrals of continuous functions with polynomial growth in the death coordinate and controlled singularities at the diagonal. These results yield convergence of additive and multiplicative lifetime measures and total persistence. We further deduce convergence in optimal transport distance. The proofs combine local weak convergence of simplicial pairs, spectral analysis of compressed Laplacians accounting for dependence through shared faces, and quantitative estimates for large death coordinates and short lifetimes.

Autonomous racing requires accurate trajectory tracking near the handling limits of a vehicle while maintaining low computational latency. Geometric controllers are computationally efficient, but the Ackermann steering geometry becomes invalid under limit-handling conditions. Model- and Acceleration-based Pursuit (MAP) preserves the simplicity of geometric approaches while leveraging tire dynamics. Yet MAP remains fundamentally a geometric controller that relies on Ackermann steering geometry, and its tire model may not fully capture the vehicle's actual dynamic response. This paper presents MAP2, a model-based pursuit controller that combines a curvature-based kinematic MPC and a Sparse Gaussian Process (SGP) residual correction. The proposed algorithm uses MPC to optimize kinematic control inputs over a prediction horizon and maps them to steering commands through a tire dynamics model augmented with SGP residual correction. Real-world vehicle experiments demonstrate substantial reductions in lateral tracking error and lap time. Compared with MAP and Pure Pursuit (PP), MAP2 reduces the average lateral tracking error by 37.99% and 44.65%, respectively, while reducing average lap time by at least 1.5%.

We study vehicle routing with vehicles of different speeds on a complete undirected graph whose vertex set consists of a depot and a set of clients, where the distances satisfy the triangle inequality. Each vehicle has a specified speed, and if the total length traveled by a vehicle of speed $s$ is $L$, its completion time is $L/s$. In the heterogeneous traveling salesman problem (HetTSP), each vehicle executes one tour starting and ending at the depot, and the tours collectively visit all clients. The objective is to minimize the maximum completion time among the vehicles. We give a $6$-approximation algorithm for HetTSP, improving the previous $90(1+\delta)$-approximation for any fixed $\delta>0$. We also consider two versions of the heterogeneous capacitated vehicle routing problem (HetCVRP). Each client has a demand, and the vehicles have identical capacities. A vehicle may execute several tours, each starting and ending at the depot, and reload at the depot between consecutive tours; the total demand delivered on each tour cannot exceed the vehicle capacity. In the split-delivery version of HetCVRP, the demand of a client may be divided among multiple visits, possibly by different vehicles. We give a $\frac92+2\sqrt3<7.965$-approximation algorithm for this problem. In the unsplit-delivery version of HetCVRP, the entire demand of each client must be delivered in a single visit. We give a $\frac{11}{2}+3\sqrt2<9.743$-approximation algorithm, improving the previous $450(1+\delta)$-approximation for any fixed $\delta>0$.

World modeling has emerged as an effective co-training objective for robot policies, giving rise to World Action Models (WAMs) that jointly predict actions and future states. However, most WAMs predict future states in the native representation space of pretrained visual backbones, resulting in high-dimensional targets with substantial training cost. We introduce MiniWAM, which instead predicts compact future representations learned from privileged current-future transitions. To construct these targets, we propose Predictive Representations via Inverse Spatiotemporal Modeling (PRISM), which combines inverse-dynamics supervision with feature reconstruction to emphasize control-relevant transition information while preserving useful future-state information. With the learned PRISM encoder frozen, MiniWAM is trained to jointly predict the resulting targets and robot actions from current observations. With 65$\times$ fewer native future feature tokens, MiniWAM consistently outperforms native future-feature prediction with both DINOv3 and WAN2.1 VAE features, while achieving up to an 8$\times$ speedup in world-action training. At 0.25B parameters, MiniWAM is already competitive with substantially larger WAMs on LIBERO, LIBERO-Plus, and RoboTwin 2.0 simulation benchmarks. Representation analyses further show that PRISM contributes behavioral structure beyond feature reconstruction alone. These results demonstrate that effective world-action modeling does not require predicting native visual futures, and that compact predictive representations provide a strong and substantially more efficient target for policy learning. The project page is available at: https://j1dan.github.io/MiniWAM.

A band that is exactly flat at zero magnetic field has zero velocity, a divergent effective mass, and no Fermi surface, so the standard theory of orbital magnetism does not apply. We show that the magnetic field generates an effective dispersion. In the expansion organized by the Moyal algebra of the noncommutative kinetic momenta, the band energy acquires a first-order shift $B\,\mathcal{M}(\mathbf k)$, set by the orbital moment of the Bloch state, and a second-order shift $\tfrac12\mathcal{X}(\mathbf k)B^{2}$, whose gauge-invariant coefficient we obtain in closed form. These two functions, together with the Berry curvature $\Omega$, fix the entire orbital response. The susceptibility is purely geometric, and for a generic isolated flat band it reproduces the established gauge-invariant response formula. With the chemical potential pinned to the flat band, the $\mathcal{M}=0$ contour becomes an emergent Fermi surface, and bosonizing excitations in its vicinity yields a modified Lifshitz–Kosevich formula with level spacing quadratic in $B$. The phase shift of the oscillations is given jointly by the Berry phase around the emergent Fermi surface and $\mathcal{X}$. When the band is narrow rather than exactly flat, the oscillation frequency crosses over, with a parameter-free profile, from the zero-field Fermi-surface area to the area of the $\mathcal{M}=0$ contour. We verify our analytical findings numerically by exactly diagonalizing a flattened Chern lattice model.

We study arrangements of conics and lines in the complex projective plane from the viewpoint of 4-manifolds. We introduce combinatorial conic-line arrangements, the conic-line counterpart of rank-3 matroids, together with their topological and smooth realisations, and we ask which restrictions on a complex arrangement survive when its components are replaced by locally-flat spheres in the same homology classes with the same local singularity models. For an ADE combinatorial conic-line arrangement of even total degree admitting a topological realisation we prove a Hirzebruch-type inequality; the proof uses only branched covers and the local topology of rational double points. In the complex-algebraic category we show that equality holds exactly when the arrangement is a maximising curve, hence free with prescribed exponents. We then introduce divisible and odd combinatorial conic-line arrangements and obtain inequalities and congruences for the multiplicity sequence of their resolutions, via cyclic branched covers, the G-signature theorem, spin structures, and Furuta's 10/8-theorem.

To a polycube $\mathcal P$ in $\mathbb R^n$, we associate an ideal $I_{\mathcal P}$ generated by the join–meet relations of vertices that are corners of a cuboid of $\mathcal P$. For $n=2$ these are the polyomino ideals. In contrast with the planar case, we show that for $n\geq 3$ the ideal $I_{\mathcal P}$ is prime if and only if $\mathcal P$ is a cuboid. For convex polycubes in $\mathbb R^3$ of uniform thickness whose vertex set is a sublattice of $\mathbb N^3$, the defining relations form a quadratic Gröbner basis, and we characterize the Cohen–Macaulay ones in terms of a poset on the vertices of $\mathcal P$; in this case the order complex of the poset is vertex decomposable. Finally, as an application, we show that the polycube algebra of a thickened $L$-convex polyomino is Koszul, and we characterize when it is Cohen–Macaulay.

As claims about recursive self-improvement (RSI) and artificial general intelligence (AGI) proliferate, we ask a simple question: do frontier AI models have a sense of data, i.e., can they reliably select the right data for training? We introduce DataSense-Bench to study this capability through the fundamental problem of data selection and performance forecasting in machine learning. We ask AI agents to select and rank candidate training subsets that can be used to fine-tune a small LLM model. Agents are allowed to inspect the data, write and execute analysis code, and run model forward passes, but can not train the model or access the actual evaluation tasks. We then fine-tune the base model on each selected subset and evaluate its post-training performance under a standardized protocol. We instantiate the benchmark in terminal problem solving and tool use, selecting trajectories from OpenThoughts-Agent and EnvScaler and evaluating on TBLite and BFCL, respectively. We then evaluate the agents along two complementary dimensions: the post-training performance of the top-ranked subset, reflecting the ability to identify high-value training data, and ranking accuracy, reflecting the ability to predict the relative performance of the selected subsets. In our experiments, selection gains over random selection are limited; agents do not reliably rank their selected groups, and ranking ability does not hold consistently across tasks: Astra identifies the best group in all three tool-use runs but in only one of three terminal runs. Analysis of execution traces on both tasks shows that agents often use similar data signals while interpreting their training value differently.

Generative diffusion models are well-suited for probabilistic precipitation nowcasting, but existing approaches often rely on separately trained compression or deterministic forecasting components and remain costly at inference due to iterative denoising. We introduce Just Weather Scoring (JWS), a single-stage, end-to-end diffusion model which addresses both issues by forecasting directly in radar space and enabling few-step generation. Radar-space modeling greatly simplifies training and inference and eliminates uncertainty arising from lossy compression. JWS combines Masked Asynchronous Diffusion, a timestep-sampling scheme that preserves clean context while adapting diffusion training to high-dimensional spatio-temporal data, with a simple scoring-rule objective that aligns training with probabilistic forecasting and unlocks few-step generation. On the SEVIR and MeteoNet benchmarks, JWS achieves state-of-the-art probabilistic forecasting performance at reduced training and inference cost. Even our smallest model remains competitive using substantially fewer parameters and more than 17x faster inference.

Let $\Rn$ be the variety of rings satisfying $x^n\eqid x$, where $n\geq2$, and let $\W$ be a variety of idempotent semirings with commutative addition. The equality $\Rn\circ\W=\Rn\vee\W$ holds, and this variety has subvariety lattice $L(\Rn)\times L(\W)$. Its subdirectly irreducible members that are not additively idempotent have exactly one nontrivial ring component, which is a finite field. Such a member is determined by this field and an idempotent semiring with a multiplicative identity; a separation condition on unary polynomial functions of the latter characterizes subdirect irreducibility. Every subvariety has a finite identity basis. A four-element semiring generates a variety with subdirectly irreducible members of unbounded cardinality. The results extend the Mal'cev product theorem of Wang and Shao from the absorption subvariety to arbitrary $\W\leq\Slp$.