Papers

Reasoning language models are trained to produce solutions, not to refuse them, and this bias persists when the problem they are handed is false. Asked to prove a corrupted theorem, a strong model will typically comply and produce a confident derivation of something untrue. We present Euston, an 8B mathematical claim-verification model trained to resist exactly this. Training data were generated with GraphSynth, a probabilistic factor-graph generator that couples attribute-level diversity to decode-time structural masking and span-synchronized verification, yielding 3{,}026 matched true/corrupted statement pairs (6,052 statements) drawn from arXiv papers spanning 2010–2025. We fine-tuned DeepSeek-R1-8B with GRPO under a rule-based, zero-API reward for 189 steps on four H100 GPUs. On a balanced 200-true/200-false held-out split, balanced accuracy rises from 29.50% to 63.75% and the discrimination gap—the difference between the rate of calling false statements false and the rate of calling true statements false moves from -0.5% (z=-0.1) to +27.5% (z=+6.0). Critically, the gain is not purchased with general mathematical ability: AIME 2026 accuracy under official semantics is 65.00% against a 69.17% base, a difference of -4.17% that is not statistically significant, whereas an earlier run of the same recipe on a smaller GraphSynth corpus collapsed to 40.00%. Median response length also falls from 19,217 to 18,296 tokens and the truncation rate from 25.8% to 8.3%, so the improvement does not come from thinking longer. We report the result together with the confounds that bound its interpretation, principally the all-false composition of the official evaluation sets and the low precision implied at realistic error prevalence.

Machine learning (ML) has emerged as a powerful tool for soil analysis using Laser-Induced Breakdown Spectroscopy (LIBS). However, traditional black-box models often lack interpretability, limiting their effectiveness in decision-making processes. This study introduced explainable AI (XAI) techniques to enhance both the interpretability and classification performance of Partial Least Squares Discriminant Analysis (PLS-DA) models for soil classification with LIBS. Local Interpretable Model-agnostic Explanations (LIME) was employed to identify the local spectral features associated with soil elements, providing explanations for their contributions to classification outcomes. To improve classification performance on unlabeled spectra, prediction uncertainty was quantified by sequentially removing the top local spectral features identified by LIME as critical to the classification. Higher uncertainty was associated with a smaller number of feature removals needed to change the label. Spectra for which a large number of features had to be removed before the label changed were treated as high-confidence predictions and admitted to a co-training process. Thresholds on this flip count were defined separately for spectrally ambiguous and stable classes to manage uncertainty identification effectively. To address the sensitivity of PLS-DA to class imbalances, equal proportions of pseudo-labels from each class were included in co-training. The proposed method was evaluated on the publicly available EMSLIBS dataset, achieving a test accuracy of 92.69%, competitive with the best-performing methods in the literature. The XAI results provided insights into the causes of misclassifications and identified the dominant spectral features critical for accurate predictions, advancing interpretable AI solutions for LIBS-based soil analysis.

An arrangement of $n$ lines in the plane defines cells, i.e., connected components of the complement of the arrangement. Answering a question of Volkmar Welker we show that, apart from two special cases, there is always a line $L$ in the arrangement such that one of the open halfplanes whose boundary is $L$ contains more than half of the bounded cells of the arrangement. We also consider some unusual discrepancy problems that are related to this question.

Let $(R,\mathfrak m)$ be a Noetherian local ring and let $\mathcal I^{(1)},\ldots,\mathcal I^{(s)}$ be graded $\mathfrak m$-primary families. We introduce weak asymptotic and strong homogeneous joint reductions and prove corresponding extensions of Rees's mixed multiplicity theorem relating joint reductions and mixed multiplicities. Actually, for weak asymptotic joint reductions, mixed multiplicities are realized as normalized limits of Hilbert–Samuel multiplicities, yielding an asymptotic Rees theorem. For multigraded admissible collections, a strong homogeneous joint reduction $\{x_{ij}\}$ of type $\mathbf d=(d_1,\ldots,d_s)$, with $x_{ij}\in I_{a_{ij}}^{(i)}$, satisfies the formula \[ e((x_{ij});R) = \left(\prod_{i,j}a_{ij}\right) e\!\left( \mathcal I^{(1)[d_1]},\ldots, \mathcal I^{(s)[d_s]} \right). \] We also prove a localized converse under formal equidimensionality, recovering the classical converse of Rees in the adic case. As an application, we derive a Böger-type theorem for graded families, whose adic specialization recovers Böger's classical theorem. In contrast, the converse to the weak asymptotic Rees theorem fails even for an adic family on a one-dimensional regular local ring.

Benchmark scores increasingly influence the development, marketing, and selection of large language models (LLMs). Yet an overall score is interpretable only in relation to the system tested, the questions included, and the conditions of evaluation. This perspective examines five connected limitations of general LLM rankings: differences between evaluated and publicly available systems; commercial incentives and dependencies in external evaluation; benchmark saturation, defective tests, and data contamination; models exploiting scoring procedures; and the limited relevance of general scores to users' tasks. Documented cases illustrate why these problems require different responses. I argue for evaluation procedures that disclose the tested configuration, validate questions and successful task completion, report performance alongside cost and execution time, and make the scope of generalization explicit. I then discuss Isotanta, a crowdsourced benchmarking platform, as a practical example of contributed questions and repeated evaluation. A larger question pool may improve task coverage, while repeated sampling can improve the stability of estimates on that pool; neither guarantees validity or personalization. The paper distinguishes the platform's current shared ranking from proposed task-specific and user-provided evaluations. Its central argument is that model selection requires evidence about performance on the intended work, not simply a high position on a general leaderboard.

Many modern systems involve the strategic interaction of multiple agents. In such settings, observed actions typically reflect equilibrium behavior under utilities that are only partially known. Recovering these hidden utilities from data - the central goal of inverse game theory - is key for prediction, counterfactual analysis, and mechanism design. However, existing approaches based on inverse variational inequalities are highly sensitive to noisy and inconsistent equilibrium observations, thus limiting their applicability. In this paper, we resolve this issue by introducing a game-theoretic suboptimality loss that measures the aggregate utility gain players could obtain by unilaterally deviating from an observed strategy profile. First, we show that this loss is convex and admits an efficient decomposition into player-wise best-responses. Second, we show this loss is sandwiched between the predictability loss and the inverse variational inequality loss, making it a tractable surrogate for equilibrium prediction. Third, we develop a mirror descent algorithm to minimize it and demonstrate on a heterogeneous networked Cournot competition that our approach remains accurate under noisy observations and inconsistent equilibrium data while inverse variational inequality methods produce degenerate estimates.

Fiber Bragg grating (FBG)-based sensing enables localized strain and temperature monitoring by tracking the phase changes of the light reflected from FBGs inserted along a fiber. A major source of disturbance in such systems is laser phase noise, and its influence is typically mitigated by means of additional hardware. In this article, we propose to mitigate the influence of laser phase noise by means of digital signal processing. We propose a practical estimator for coherent single-polarization spread-spectrum FBG-based sensing systems, which is motivated by linearizing the complex received signal and approximating the loss function to formulate a minimum mean square error (MMSE) estimation problem. Moreover, a Cramer-Rao lower bound for this FBG-based estimation problem is presented. Our simulation results demonstrate that the performance of our proposed estimator lies close to the Cramer-Rao lower bound, thus indicating that our estimator effectively compensates for phase noise in FBG-based sensing systems.

We construct a one-parameter family $(X_c)_{0<c<1}$ of real reflexive Banach spaces, isomorphic to $\ell_2$ and satisfying $d_{\mathrm{BM}}(X_c,\ell_2)\le c^{-1}$, such that $(X_c,X_c)$ fails the weak maximizing property while $(X_c^*,X_c^*)$ has it. The failure of the WMP for $X_c$ is witnessed by a diagonal operator which does not attain its norm but admits a non-weakly null maximizing sequence. On the dual side, a separated-block estimate yields, after dualization, a reverse Pythagorean inequality and a quantitative form of the Opial property; together with property $(M)$, this gives the weak maximizing property for $X_c^*$. We also show that the compact perturbation property is self-dual for reflexive pairs. Since the weak maximizing property implies the compact perturbation property, each $(X_c,X_c)$ has the compact perturbation property. Consequently, the compact perturbation property does not imply the weak maximizing property even arbitrarily close to Hilbert space, and the weak maximizing property is not stable under duality in the reflexive setting.

We study the Busy Machine Time with Preemption and Migration and One Resource Requirement problem, motivated by energy minimization in cloud data centers. Given unlimited identical-capacity machines and jobs with release times, deadlines, processing times, and resource requirements, we allow free preemption and migration at integer times and seek to minimize total machine busy time. The problem is NP-hard, and previous results consist of a 2-approximation, 2-competitive algorithm for the case of uniform heights. We obtain a 22/9 < 2.445-approximation algorithm and a 2.5-competitive online algorithm, both running in O(n^2 log n) time. Our methods are based on new non-asymptotic performance bounds for the First Fit Decreasing algorithm for Bin Packing, and a new generalization of Span Minimization, the Huge-Tiny Busy Time problem, for which we present an exact offline algorithm and an optimal (3/2)-competitive deterministic online algorithm.

In this work, we study the noisy truncated Hausdorff moment problem in the context of recovering parton distribution functions (PDFs) from their moments. We start by reviewing basics of the Hausdorff moment problem and analyze how the relation between the amount of moment data provided and the ability for $f(x)$ to be reconstructed varies across different classes of parton distribution functions; we then turn to using Bayesian methods centered around Gaussian Processes (GPs) to solve the moment problems. Standard aspects of Bayesian regression such as covariance kernel choice, analytical characterization of the posterior, hyperparameter sampling with Monte Carlo methods, and validation metrics are detailed. In addition to this, powerful novel tools, such as a method to correct for mean bias in posterior distributions, and a simple class of covariance kernels whose $x$ correlation length is learned during sampling are introduced. Finally, we test our framework on 5 datasets from valence, gluon, and sea quark phenomenological pion and nucleon PDF datasets, selected to reflect diversity in PDF behavior. We find that our GP framework robustly reconstructs PDFs given a moderate number of moments. Additionally, the novel tools developed in this work resolve persistent issues that would be difficult to address via conventional means. The presented framework can be readily applied to moments obtained via lattice Quantum Chromodynamics (LQCD) to reconstruct PDFs from theoretical first principles.

We construct boundary observables that retain memory for a quantified time window in quantum chains whose basis configurations carry a conserved ordered product of matrix labels. Under strong-irreducibility and proximality hypotheses on the label matrices, projective contraction of random matrix products localizes a conserved charge in the root-mean-square over uniform basis configurations. A finite-time inequality then converts readout overlap and reset leakage into a correlation bound: for a conserved reference observable $H$, a readout $F$, accumulated squared leakage $\mathcal B$, and the normalized Hilbert-Schmidt inner product, $\langle F,\Phi(F)\rangle\ge 2\langle H,F\rangle^2/(\|H\|_2^2+\mathcal B)-\|F\|_2^2$. Here $\Phi$ is a sequence of conserving channels and partial resets. The bound holds for each such circuit, without averaging its gates. It yields an exponential memory window in the distance from the noisy region, with quantitative corrections for spatially distributed noise and imperfect conservation. For a thirteen-state elementary-matrix model, exact polynomial certificates give root-mean-square localization error $e^{-r/1400}$ between the charge and its restriction to the last $r$ sites, and limiting variance at least $1/19$ for a rational charge. A related normalized-Gram charge gives an eight-site certificate retaining more than half the specified readout correlation through two boundary-reset rounds. Uniform depolarization imposes an inverse-noise-rate lifetime ceiling. A two-qubit IBM experiment illustrates the general reset inequality; it does not realize the matrix-product chain. We provide proofs, exact certificate programs, and an independent recount of the archived experimental outcomes.

Acoustic representation learning is crucial for speech processing, yet low-resource languages (LRLs) face severe data scarcity, limiting the effectiveness of traditional and self-supervised methods. As a promising alternative, in this work, we propose to enhance acoustic representation trough a cross-modal transfer knowledge approach, based on heterogeneous graph neural networks (HGNNs), where acoustic and linguistic entities are modeled as distinct node types within a unified graph. Through message-passing mechanisms, linguistic nodes explicitly transfer knowledge to acoustic nodes, enabling structured and interpretable cross-modal information flow. To highlight this knowledge transfer and its benefits, we measured standard clustering metrics as an intrinsic evaluation of acoustic representation, and to emphasize applicability, we performed isolated-word recognition tasks using an English benchmark and a Cameroonian language dataset in low resources settings . Results demonstrate that acoustic representations consistently benefit from linguistic knowledge propagated through the graph. To our knowledge, this is the first demonstration of explicit cross-modal knowledge transfer for acoustic representation learning using HGNNs, highlighting a promising direction for speech representation in low-resource settings.

As Large Language Model (LLM) APIs become increasingly integrated into privacy-sensitive workflows, ensuring inference-time privacy without compromising task utility remains a major challenge. Existing approaches preserve most of the original semantic content to maintain downstream performance, but this also leaves exploitable cues for reconstructing the original text. This work investigates semantic decoupling, which replaces original semantics with alternative content while preserving the structure needed for LLM reasoning. Based on this idea, we propose CROSS-MAP, a bidirectional framework that maps private inputs into a different semantic domain before inference and recovers the corresponding outputs afterward. Local models are trained with multi-objective optimization to maximize semantic divergence in the mapping stage while minimizing semantic inconsistency in the recovery stage. Experiments show that CROSS-MAP reduces reconstruction success across multiple attack settings while outperforming existing baselines in utility.

We derive the renormalized local equation of motion for the gravitational self-force on a compact object moving through matter in a black-hole spacetime. We integrate out the environment and metric perturbations on a Schwinger–Keldysh contour, obtaining a causal effective action given by a sum of curved-spacetime Feynman diagrams organized by powers of the mass ratio and environmental density. At leading order, an environmental wake gravitationally backreacts on the worldline. The corresponding diagram contains a logarithmic ultraviolet divergence that renormalizes the leading dissipative fluid–particle coupling. We isolate the divergence with a local large-momentum expansion, in which the curved-spacetime retarded Green's function reduces to its flat tangent-space form. We translate the resulting singularity into a Barack–Ori mode-sum scheme, deriving an analytic puncture and regularization parameters for an ideal-fluid environment. Mode subtraction fixes the divergent part but not the finite Wilson coefficient. For collisionless dust, we determine this coefficient by matching to an exact near-zone calculation for a black hole moving through the medium. This gives a complete renormalization prescription suitable for numerical self-force calculations.

Speech-text space alignment is a multimodal representation learning method consisting to map different speech and text into a shared representation space, leading to enrichment of the representation of each modality. Proposed architectures, such as SAMU-XLSR, typically follow a student/teacher framework, with the goal of fine-tuning an audio encoder to produce representations that closely match those of the text. In this way a speech representation is semantically enriched. However, such systems generally require large amounts of training data and considerable computational resource, making them difficult to apply to low resources languages under frugal constraints. The present work proposes a data-efficient space alignment method based on Heterogeneous Graph Neural Networks and link prediction. The core idea is to leverage message passing to explicitly transfer information from the text modality to the speech modality, thereby reducing the need for large training datasets and intrinsically enriching the acoustic representations, all in a more interpretable manner. Although thoroughly explored for high-resource languages, word-level tasks in speech remain relevant for certain low-resource languages. Therefore, we conducted experiments on speech-text alignment at the word level using the TIMIT (English) dataset and Yemba (a Cameroonian language). Our approach yields results comparable to those of SAMU-XLSR, a state-of-the-art method, and even surpasses it for the Yemba language in the task of word retrieval, while using far fewer resources, demonstrating its power, frugality, and efficiency.

Quantum-enabled semantic communication networks (QESCs) leverage quantum technologies to transmit data meaning efficiently, yet face challenges from costly resources and noise. This letter introduces Quantum Markov Blankets (QMBs) to QESCs, a novel framework to isolate essential quantum information for semantic transmission. We prove QMBs' validity using quantum conditional mutual information, showing that they shield semantic content from irrelevant subsystems. An implementation strategy optimises QMB detection, reducing resource use. Simulations suggest that QMB-based QESCs cut qubit consumption by 50%-75% while enhancing fidelity compared with non-optimised quantum semantic schemes. Unlike classical approaches, QMBs offer inherent security by limiting an eavesdropper's access to classical data outside the blanket. We outline future directions, including real-time QMB adaptation. This work bridges quantum information theory and semantic communication, advancing resource-efficient and secure quantum networks.

We prove that learning an unknown mixed fermionic Gaussian state on $m$ modes to trace distance $\epsilon$ requires $\Omega(m^3/\epsilon^2)$ copies when measurements act on one copy at a time, even with arbitrary POVMs, fresh ancillas and classical adaptivity, but without quantum memory between copies. The bound holds for $0<\epsilon\le1/3600$ and separates this model from the known collective rate $\Theta(m^2/\epsilon^2)$. It follows from a uniform single-copy Fisher-information budget and a dimension-independent comparison between trace distance and Gaussian parameters. On covariance matrices of operator norm at most $1-c$, we prove a Frobenius-to-trace-norm continuity bound with constant $[2c(2-c)]^{-1/2}$; matchgate shadows then attain $O(m^3/(c\epsilon^2))$ copies. This also gives explicit error certificates for thermal free-fermion states. For a class of mixed passive bosonic Gaussian states with total mean photon number at most one, a reduction to bounded-block qudit tomography gives a single-copy lower bound $\Omega(m^3/(\epsilon^2\sqrt{\log(m/\epsilon)}))$, versus collective complexity $\Theta(m^2/\epsilon^2)$. These separations answer the mixed-state measurement-resource question posed by Chen et al. A two-mode example has optimal two-copy Fisher trace $5$, versus the separable ceiling $4$. An IBM replication gave a pre-registered witness lower bound $4.12$ at one-sided $95\%$ shot-noise confidence; its interpretation assumes the prescribed preparations and a common measurement channel and does not bound preparation systematics.

Resilience is a system's capability to prepare for, resist, absorb, and recover from adverse events. By definition, resilience therefore encompasses multiple criteria that can conflict and may prescribe different decisions. Importantly, a system must also maintain its effectiveness during routine operations and appropriately scale its preparedness for adverse events. Although resilience is inherently multicriteria, existing models often focus on a single criterion and do not explicitly analyze potential conflicts, the associated trade-offs, and their implications for decision-making. We formulate rebound, resistance, loss, and maximum performance degradation as separate resilience criteria in a general two-stage multicriteria model of network flows over time that integrates preparedness, effectiveness, and response. We show that, in general, such multicriteria optimization models are intractable and develop an enclosure-based heuristic for approximating the nondominated set. Our computational results show that different preparedness instruments and activation timings are associated with different resilience criteria and that the corresponding trade-offs are strongly instance-specific. Thus, resilience should be approached from an explicit multicriteria perspective rather than through a universal, preference-independent scalar index.

We investigate the dynamics of charged particles in the dipolar electromagnetic field generated by a stationary current loop around a static black hole in the Randall–Sundrum braneworld model. The current loop is located at the innermost stable circular orbit (ISCO) of the tidal charged black hole, and the azimuthal electromagnetic four-potential is obtained as an exact analytical solution of the Maxwell equations in the curved background. Starting from the Hamilton–Jacobi equation, we derive the effective potential for charged particle motion in both the interior and exterior regions of the current loop, and analyze the dependence of the ISCO radius, angular momentum, energy, and orbital frequency on the tidal charge parameter $b$ and the magnetic coupling parameter $\omega$. We further compute three fundamental frequencies and show that the dipolar loop field revives a nonzero nodal precession frequency even though the background is static and non-rotating. Using these frequencies we construct five twin-peak QPO models (RP, WD, and ER2–ER4) and perform a Markov chain Monte Carlo (MCMC) analysis to constrain the braneworld parameters $(b,\omega)$ from the observed twin-peak QPO frequencies of six black hole sources spanning three mass regimes: GRO~J1655–40, XTE~J1550–564, GRS~1915$+$105, H~1743$+$322, M82~X-1, and Sgr~A$^{*}$. Adopting the epicyclic-resonance ER4 model as the representative framework, we find moderate, non-negligible tidal charges $b\simeq0.3$–$1.0$, while the magnetic coupling remains consistent with zero, $|\omega|\lesssim0.05$. Our results therefore place upper bounds on the tidal charge and on the magnetic coupling strength from astrophysical QPO data.

Side-channels are a promising approach for hardware trojan detection, as they can passively reveal malicious hardware activity without requiring additional circuitry or destructive analysis of the device under test. This work investigates the use of electromagnetic (EM) emanations for runtime detection of hardware trojan attacks. Using an open-source hardware trojan that implements an arbitrary memory-write primitive, we tamper with the kernel memory of a Linux system running on a RISC-V microarchitecture and perform a real-time baseline detection using the processor's EM emissions. Our results indicate that, under certain conditions, hardware trojans can be detected indirectly through the anomalous software behavior they enable.

Lossy compression of scientific simulation data increasingly relies on learned, latent-space architectures such as Residual Vector Quantization (RVQ), which iteratively quantize a base representation and its residuals to progressively reduce reconstruction error. While effective, RVQ performs this residual modeling entirely in latent space, leaving the pixel-space error structure of the reconstruction largely unaddressed. In this work, we propose a post-processing pipeline that augments an RVQ-based compressor with a U-Net trained to predict and correct pixel-space residuals between the original volume and its RVQ reconstruction. We show that these residuals are spatially structured rather than driven by local intensity or gradient features, motivating the need for a deep spatial model rather than simple statistical correction. The U-Net-corrected reconstruction is then passed through a Guaranteed Autoencoder (GAE) stage, which projects the remaining residual onto a per-block PCA basis to enforce a user-specified block-wise error bound. To the best of our knowledge, this is the first pipeline to combine latent-space RVQ, explicit pixel-space residual correction via a deep spatial post-processing network, and GAE-based error-bound guarantees within a single framework for scientific data compression. We evaluate our approach on S3D, JHTDB and E3SM datasets, demonstrating consistent improvements in NRMSE, compression ratio] over RVQ-only and standard residual-correction baselines, while maintaining strict error guarantees required for scientific data fidelity.

Embodied world models learn to predict future physical dynamics from visual observations and control signals, where physical knowledge is implicitly entangled within latent representations. We introduce CausalWM, a 16B embodied world model that performs explicit causal chain-of-thought reasoning before future video prediction. CausalWM organizes useful variables into a reasoning trajectory, allowing the model to progressively capture causal dependencies underlying physical evolution. To train CausalWM, we collect 31K hours embodied data and develop a three-stage paradigm consisting of large-scale video pre-training, causal CoT mid-training, and multi-objective RL post-training. Despite using only a limited set of supervised CoT variables, CausalWM exhibits emergent in-context learning capabilities, enabling contextual visual feature guidance and efficient few-step generation. CausalWM achieves state-of-the-art performance across language-conditioned, action-conditioned, single-view and multi-view benchmarks, including Top-1 performance on TriWorldBench leaderboard.

Inverse design of RF and electromagnetic (EM) circuits is challenging because the relationship between circuit layout and electrical response is non-unique, and full-wave simulation is computationally expensive. This paper presents K-TRAIL, a simulator-guided generative framework for automated EM/RF circuit synthesis. K-TRAIL combines diffusion-based layout generation with derivative-free ensemble Kalman guidance, allowing feedback from a black-box EM simulator to refine candidate layouts during generation without requiring adjoint sensitivities or differentiable solver models. The framework supports both synthesis from prescribed S-parameter responses and synthesis directly from RF performance constraints. Experiments on multi-layer RFIC structures show that simulator-guided generation improves agreement with target responses and can identify structurally distinct layouts that satisfy circuit-level design requirements. The proposed approach provides a practical path toward generative, verification-aware RF circuit design while retaining the flexibility to explore diverse layout topologies.

Feed-forward 3D Gaussian Splatting now reconstructs renderable scenes from unposed, uncalibrated images. Yet, most models supervise only photometric consistency and predict Gaussians pixel by pixel, which leaves global structure fragile and ties primitive count to image resolution and view count. To this end, GrapeSplat amalgamates multi-view cues into a voxel-aligned scene representation and decodes Gaussians directly from the learned grid, requiring no per-scene optimization or post-processing. An Atlas Encoder lifts all views into pixel-wise geometry-and-appearance features anchored at predicted 3D points. PEACH-Vox compands the unbounded scene into a bounded sparse grid through a smooth per-axis map with an exact closed-form inverse. The Sparse Decoder then consolidates the grid with sparse convolutions and decodes the full scene as multiple Gaussians per occupied cell. This amalgamated representation exploits sparse voxel occupancy, where the Gaussian count follows the occupied cells and saturates as views cover the scene, while grid resolution sets its ceiling. GrapeSplat turns unposed images into a renderable Gaussian scene in a single forward pass. Trained with 2D and 3D supervision on 8-view sequences, it generalizes zero-shot from 4 to 64 views across indoor and unbounded scenes. Code and trained weights are available at https://github.com/VAISR/GrapeSplat

The dynamics of interacting dipole skyrmion chains in a weak pinning landscape is studied through numerical solutions of the stochastic Thiele equation. Chains of different lengths with periodic boundary conditions are driven across quenched attractive pinning sites under different magnetic fields. A clear threshold spin current is identified as the critical depinning force. Three main results emerge: (i) for chains of 50 skyrmions or more, the depinning threshold is independent of chain length and remains close to one third of that of an isolated skyrmion. (ii) The transition rounding is only partly thermal: the width changes from w = 0.334 +/- 0.004 decades at T = 0 to 0.633 +/- 0.002 at 300 K, while the intrinsic Larkin correlation length remains about 2.6 bonds below kBT ~ V0/25. (iii) The width is nearly unchanged up to kBT ~ 0.14 V0, but increases almost fourfold by kBT ~ 0.23 V0, mainly through broadening of the creep regime. It is independent of chain length, ruling out finite-size rounding. Increasing the field from 30 to 40 mT changes the transition shape, widening its core by 26% while shortening the creep tails. For chains of about 200 skyrmions, depinning proceeds through a sequence of internal deformations - growth of the Larkin length and roughness, transient bond stretching, and subsequent recovery of mobility and Hall angle. These collective effects are relevant for skyrmion-based devices in which chains, rather than isolated textures, act as information carriers.

We benchmark classical optimization of a fixed low-depth Quantum Approximate Optimization Algorithm (QAOA) ansatz across four cost-Hamiltonian families at $N=12$, $p=3$, and $D=6$. Ten optimizers are compared over 25 independent runs under common ceilings of 10\,000 and 30\,000 function evaluations (FEs), first with exact statevector objectives and then with two additive observation-noise levels. Exact objectives favor multistart BFGS and multistart CMA-ES. Under noisy feedback, adaptive population methods become more competitive, but the ranking depends on whether performance is measured by the best exact point visited or by the point selected from noisy observations. A targeted extension over all three pre-screened instances per family confirms this regime change while showing that named adaptive-DE winners are instance dependent: jSO-lite leads low-noise oracle search, iL-SHADE high-noise oracle search, and L-SRTDE high-noise selected solutions in the equal-instance summaries. Bootstrap analysis quantifies a non-negligible high-noise search–selection gap, and a retrospective fixed-budget verification proxy shows that reserving a small measurement budget for final re-evaluation improves selected quality across all ten methods at 30\,000 FEs. A supplementary structure-aware study further shows that QAOA cross-depth restriction and continuous basin refinement are more useful in these conditions than standalone Monte Carlo tree-search selection. Overall, optimizer choice depends jointly on landscape structure, observation noise, and final-point identification.

For $k, r, n$ natural numbers let $\rho_{r,k}(K_n)$ be the number of $r$-edge-colorings of $K_n$ that do not contain a rainbow copy of a $K_k$, that is, a copy of $K_k$ in which all edges receive different colors. When $k=3$, the quantity $\rho_{r,3}(K_n)$ represents the number of Gallai Colorings. It was proved by Balogh and Li and independently by Bastos, Benevides and Han, that most of the Gallai colorings are 2-colorings, for $n$ large. A natural analogue conjecture would be that when $k=4$, $r\ge 5$ and $n$ large, most rainbow-$K_4$-free $r$-edge-colorings are $5$-colorings. We show that this is not true in general and identify an exact threshold for $r$ where this ceases to be true. For the range where the conjecture is false, we determine the exponential growth of $\rho_{r,4}(K_n)$ for every fixed $r$. More precisely, for \(6\le r\le24\), we prove that \(\rho_{r,4}(K_n)=(\binom{r}{5}+o(1))5^{\binom{n}{2}}\); and for each \(r\ge25\), the proportion using at most five colors tends to zero, and \(\rho_{r,4}(K_n)=r^{(n^2/4)+o(n^2)}\). A bipartite construction, with all edges within the two parts assigned one common color, achieves the latter exponential growth rate. The lower bounds can be easily generalized for every $k$. Those results are related to other recent results about counting colorings that avoid rainbow cliques or given rainbow patterns in general. Our proof combines hypergraph containers with the graph removal lemma, structural estimates for color palettes and a refined count of colorings close to a fixed five-color palette.

Language models are appealing tools for research on the past. But to trust the evidence a model provides, researchers need to know whether its responses fit the period represented. Validation is challenging, because this is not a task living people ordinarily perform, and because many questions have multiple correct answers. We use historical texts to develop a benchmark for a model's representation of English-language contexts 1831-1930, relying on pairwise comparisons to multiple ground truths and strong distractors to score the hardest questions in an appropriately graduated way. We find that generative tasks are harder than discriminative ones; in fact, reasoning models can typically discern the weakness of their own generated answers. While models pretrained exclusively on historical text lead the pack when evaluated by answer likelihood, they cannot compete with commercial models in free generation. None of the models we tested represent historical contexts in a fully persuasive way yet, but progress toward that goal is evident.

We extend the Obukhov-Corrsin theory of scalar turbulence to compressible flows with spatially variable, anisotropic diffusivity. Combining density and diffusivity into a single positive matrix field, a transport landscape, permits an exact scale-by-scale balance in which the sign-indefinite commutator between filtering and diffusion is eliminated rather than estimated. If the density-weighted third-order velocity and scalar increments scale as $\ell^\alpha$ and $\ell^\beta$, respectively, we prove that anomalous scalar dissipation is impossible when $\alpha+2\beta>1$. Remarkably, this threshold is independent of the anisotropy and spatial regularity of the diffusivity, provided it remains uniformly elliptic. Codimension-one shocks in both velocity and scalar have $\alpha=\beta=1/3$ and therefore lie exactly at the critical threshold. For statistically stationary turbulence we further obtain an exact density-weighted constant-flux relation, providing a compressible analogue of the relation underlying Yaglom's law. The results apply directly to passive-scalar transport in both gases and magnetized plasmas and provide testable diagnostics for simulations of compressible magnetohydrodynamic turbulence. Because the same operator governs anisotropic heat conduction, the results carry over to the electron temperature of a magnetized plasma, and they imply that gradient statistics in such flows must be contracted with the transport landscape rather than with the density.

This paper introduces the two-stage stochastic quadratic knapsack problem (TSSQKP) with uncertainty in profits and weights. To overcome the computational difficulties arising from the combined stochastic, binary, and quadratic structure, we propose a solution framework that integrates an adaptation of the progressive hedging algorithm with clustering-based scenario reduction. The enhanced progressive hedging algorithm (EPHA) incorporates a rounding procedure and a dynamic penalty update strategy driven by the detection of oscillation and stagnation patterns. In parallel, we propose a clustering framework based on opportunity-cost distances between scenarios, from which we derive the medoid lower bound (MLB), the cluster lower bound (CLB) and the cluster upper bound (CUB). To further improve computational efficiency, EPHA is also used to solve the cluster subproblems heuristically; in this case, the resulting upper bound is referred to as the estimated cluster upper bound (ECUB), and the corresponding gaps are interpreted as estimated optimality gaps. Computational experiments on 800 generated TSSQKP instances show that the proposed framework yields smaller gaps than CPLEX under comparable computational conditions. In the EPHA-based clustering framework, the average estimated gaps associated with the CLB, EPHA and MLB 1.65%, 1.88% and 2.41% respectively, compared with an average optimality gap of 35.86% for CPLEX. MLB is fastest to compute, with an average execution time of 420.88s, while EPHA provides a favourable compromise between solution quality and computational effort, reducing the average computational time associated with the cluster bounds by approximately 52.7%, while increasing the average estimated gap by only 0.23 percentage points.