Papers

Predicting cellular responses to perturbations is a central problem in cellular biology, with broad applications in systems biology and drug discovery. This task is challenging because cellular responses can be complex and cell-state dependent, intrinsic cell-to-cell variability can be confounded with perturbation effects, and destructive single-cell RNA sequencing precludes paired measurements of the same cell before and after treatment. Flow matching transports control cells to perturbed states flexibly, but acting on the full cell state can confound perturbation effects with pre-existing cell-to-cell variability. Disentangled approaches separate responsive from invariant components, but model perturbations through prescribed mechanisms, such as latent shifts or graph edits, limiting their flexibility. We address both limitations in a unified framework. A variational encoder disentangles each cell into an invariant block, capturing state unaffected by the perturbation, and a responsive block, capturing state it changes, through conditional priors and an information-theoretic invariance constraint. Conditional flow matching transports only the responsive block, conditioned on the perturbation and invariant state, yielding a flexible, data-driven model of perturbation effects without confounding pre-existing variability. Across several benchmarks, our method outperforms the strongest published method in settings involving combinatorial and unseen perturbation prediction.

To calculate transmission coefficients, current Hauser-Feshbach reaction codes assume a one-dimensional fission path that is both independent of excitation energy and universal across different fission channels. In contrast, microscopic fission studies typically explore multiple collective variables. Predicting observable fission quantities such as cross sections based on microscopic input thus requires a way to reduce the dimensionality of the latter. For spontaneous fission, the least action path (LAP) – which minimizes the semiclassical action and maximizes the transmission coefficient – is the solution. We demonstrate that the LAP does not generalize to other fission modes such as neutron-induced or $\beta$-delayed fission: at finite excitation energy, the LAP generally does not maximize the transmission. A microscopic PES can have multiple coexisting stationary-action paths. We show that these (i) can switch their action ordering as a function of excitation energy and (ii) yield different neutron-induced fission cross sections predictions, yet match known spontaneous fission lifetimes equally well. For the BSkG3 Skyrme-type energy density functional model, the transition from the axially symmetric LAP at zero excitation energy to a path exploiting the triaxial degree of freedom occurs at an excitation energy that is smaller than the neutron separation energy for essentially all actinides and the majority of unknown exotic nuclei.

Many real systems can be represented as growing networks where new nodes and links gradually emerge. The Barabási-Albert model for growing networks, and many models inspired by it, are based on the idea that nodes compete for links. However, the strength and the very presence of this competition have not been tested. We propose a robust statistical approach to quantify how strongly nodes compete for links, and apply it to data from various real systems—commenting on online news and cinema attendance data. We find a range of possible behaviors, from the perfectly elastic case, where new entrants shape network growth in a way that leaves the rest of the system unaffected, to an intermediate case where new entrants measurably affect the rest. Perfect competition is never observed. These findings have direct implications for complex systems modeling and e-commerce applications.

We consider Brownian last passage percolation (BLPP) in which the Brownian increment process on each unit horizontal interval is independently resampled at rate one. By combining strong passage-time stability estimates with a multiscale analysis of static near-optimal paths, we show that, for every $\varepsilon>0$, the union of all geodesics between two KPZ-scale rectangles of transverse width of order $n^{2/3}$ and longitudinal length of order $n$, separated by a distance of order $n$, visits at most $n^{1+\varepsilon}$ unit horizontal cells in the bulk during the critical time interval $[0,n^{-1/3}]$, both in expectation and with stretched-exponentially high probability. We also obtain the quantitative bound $n\exp\{C(\log\log n)^2\}$ on the expected hitset size, with a corresponding failure probability at most $Ce^{-c(\log n)^2}$. Using this, we establish that the set of times admitting a non-trivial bigeodesic has almost surely zero Hausdorff measure for the subpolynomially decaying gauge $H(r)=\exp\{-L(r)^2\log L(r)\}$, where $L(r)=\log\log(1/r)$, as $r\downarrow0$. In particular, this set almost surely has Hausdorff dimension zero. For each fixed deterministic non-axial direction, we further show that almost surely no time admits a bigeodesic in that direction.

We study the hard-core model on recursively defined sequences $(G_n)_{n\geq0}$ of graphs with a fixed number $k\geq 1$ of labeled vertices in each graph. The next graph in the sequence is constructed by taking a fixed number $m\geq 2$ of copies of the previous graph, connecting these copies by identifying some labeled vertices according to a fixed rule, and afterward choosing $k$ labeled vertices in the resulting graph, again in accordance with a fixed rule. Examples of such sequences include the Sierpiński gasket graphs, hierarchical lattices, and many more. We prove that, when the vertex degrees of the graphs $G_n$ are uniformly bounded and the distances between the labeled vertices in $G_n$ diverge, the complex zeros of the univariate independence polynomials $Z_{G_n}(\lambda)$ avoid a neighborhood of the non-negative real axis. By the Lee–Yang theory this implies that no phase transitions occur for the hard-core model on these recursive sequences of graphs, independently of the starting graph $G_0$. The proof relies on the study of the dynamical properties of a one-parameter family of rational maps $F_\lambda$ on the $(2^k-1)$-dimensional complex projective space induced by the graph recursion operator. The dynamical framework developed in this paper can be naturally extended to other classical models in statistical mechanics (such as the Ising or Potts models) and to more general notions of graph recursions.

Decoded quantum interferometry (DQI) and its Hamiltonian extension (HDQI) prepare states whose amplitudes are low-degree polynomials of an objective, using Fourier transforms and coherent decoding. We recast and generalize this approach as quantum state transduction through algebra homomorphisms. We transfer an efficiently preparable operator state of a degree-$D$ polynomial in a source Hamiltonian $H_A$ to the corresponding polynomial state of a target Hamiltonian $H_B=\pi(H_A)$, where $\pi$ is a unital $*$-homomorphism between the finite-dimensional source and target $C^*$-algebras. The transduction uses operator Fourier transforms and relative decoding to recover source operators rather than individual term-selection labels. The relative distance $d_{\mathrm{rel}}$ is the first degree at which source and target traces disagree. We prove that $2D<d_{\mathrm{rel}}$ is equivalent to preserving all inner products between degree-$D$ polynomials. Moreover, $d_{\mathrm{rel}}\ge d_{\mathrm{ord}}$, where $d_{\mathrm{ord}}$ is the ordinary distance used in (H)DQI, and we give families with $d_{\mathrm{ord}}=O(1)$ but $d_{\mathrm{rel}}=\Theta(n)$ and efficient decoders. Our framework replaces the complicated pilot state preparation by the more modular task of preparing a source polynomial state. DQI and HDQI arise as relation-free special cases. The framework accommodates nonuniform coefficients and noncommuting interactions and extends to fermionic and qudit systems, with applications to approximate optimization and Gibbs sampling. As evidence of advantages, for a nonlinear pairwise variant of optimal polynomial intersection where constant $d_{\mathrm{ord}}$ limits DQI-style preparations, relative decoding yields an ideal quantum score of 0.643 versus 0.606 for the best tested classical heuristic, a gap exceeding 3 percentage points.

Building on recent advances in coronal spectropolarimetry, seismology, and magnetic-field inferences of Z. Yang et al. (2024) and A. R. Paraschiv (2026), we present the first application of the CLEDB IQUD inversion methodology to Mauna Loa Solar Observatory CoMP and UCoMP observations. Using spectropolarimetric IQU measurements together with coronal seismology derived magnetic field BPOS constraints, we recover vector magnetic field solutions across the off-limb solar corona accessible to the observations, demonstrating the feasibility of routine large-scale coronal vector magnetometry without the need for Stokes V observations.

We present e3j, a fast Euclid-equivariance backend for geometric deep learning applications with JAX bindings for GPU and TPU. Leveraging both optimized CUDA and Pallas kernels and algorithmic improvements, the library achieves state-of-the-art throughput and runtime on both forward and backward paths. On a machine learning interatomic potential (MLIP) use case, it outperforms established backends, measuring up to 34% speed-up over cuEquivariance on water box NPT simulation using MACE, while remaining fully open source. E3j achieves over 80% efficiency over the H100 maximum memory bandwidth on tensor product operations, and in many cases more than doubles throughput of message passing convolutions forward compared to previously available backends. In addition, with the release of dedicated Pallas TPU kernel, e3j opens the possibility of large scale equivariant deep learning workloads on TPU architectures, which has so far been difficult to achieve. Our benchmarks show that e3j also achieves over 80% of a TPUv6e memory bandwidth, up to one order of magnitude more than e3nn-jax. The library is available on GitHub, PyPI and is released under an open source Apache 2.0 license.

The Solar Wind Charge Exchange (SWCX) mechanism, where X-rays can be generated through interactions between heavy, highly charged solar wind ions and neutral atoms, offers an opportunity to observe the large-scale transfers of energy and momentum through the Sun-Earth system. In this study, we simulate SWCX signatures from Earth's outer boundaries using Gorgon global magnetohydrodynamic (MHD) simulations combined with kinetic particle-based simulations which we call the X-ray Imaging of the Magnetosphere (XIM) framework. The XIM-predicted emissivities agree with the predictions of the MHD model, producing enhanced emissions from the magnetosheath and cusp regions, but several differences are apparent. Compared with MHD, XIM shows enhanced structuring in the magnetosheath and notable enhanced emissions along the magnetopause associated with betatron acceleration. The results also evidence species-specific spatial variations, which are shown to vary compared to anticipated relative abundances in the solar wind and ion-specific properties. These simulations provide new insights into the underlying dynamics of SWCX at the Earth's outer boundaries, which can be used to understand what might be observed using X-ray observatories in space, such as the recently launched SMILE mission.

Spiking neural networks (SNNs) offer an energy-efficient paradigm for time-series forecasting through spike-driven computation. However, recent SNN forecasters often pursue higher accuracy through increasingly complex attention mechanisms, or specialized neuronal dynamics, weakening the lightweight motivation of SNNs. We introduce SpikeLite, a spiking forecasting framework built around two modules: a Frequency-Selective Spiking Encoder (FSSE) for frequency-sensitive temporal encoding and a Sparse Spiking Channel Attention (SSCA) module for selective cross-channel interaction. FSSE exploits the low-pass filtering behavior of LIF dynamics to reorganize each input sequence into frequency-sensitive components while collectively preserving the input at the decomposition stage. SSCA then learns a binary mask from encoded channel representations and uses it to selectively exchange information within spike-driven self-attention, retaining informative cross-channel interactions while suppressing redundant ones. When explicit channel interaction is unnecessary, SpikeLite uses the lighter FSSE-only channel-independent path. Experiments under the SeqSNN and SpikF protocols cover four standard multivariate and eight long-term forecasting benchmarks. SpikeLite achieves the best aggregate performance under both protocols, with an average $R^2$ of 0.790 and RSE of 0.440, and lowest average MSE/MAE of 0.343/0.345 in long-term forecasting. Moreover, evaluation on the ECL dataset shows that SpikeLite achieves the lowest reported energy consumption, further demonstrating its potential for energy-efficient time-series forecasting.

Deepfake detection methods have become increasingly effective yet most provide limited insight into the evidence behind their predictions. However, in forensic settings users also need to know which manipulation cues support the decision and where they appear. Existing explainability methods only partially address this need since localization-based approaches lack semantic descriptions while language-based explanation methods are only weakly grounded in visual evidence. In this work, we propose DF-CBM, a region-aware concept bottleneck model for explainable deepfake detection. DF-CBM builds a compact vocabulary of manipulation-related concepts from textual artifact annotations and links each concept to plausible facial and boundary regions. It then predicts these concepts from visual features using a concept-specific masked attention mechanism guided by parsed facial masks and the final real/fake decision is made from the predicted concept bottleneck. Our experiments show that DF-CBM outperforms concept-based baselines in concept prediction and deepfake classification while remaining competitive with state-of-the-art black-box detectors. Finally, qualitative results and intervention analyses demonstrate that DF-CBM provides spatially grounded concept evidence and enables counterfactual explanations of how individual manipulation concepts influence the final prediction. Our code is available at: https://github.com/GeorgeTsoumplekas/DF-CBM.

This paper studies stochastic algorithms for minimizing paraconvex functions, a function class that generalizes weakly convex functions and includes, for instance, Hölder smooth functions and compositions of convex functions with Hölder smooth maps. We first establish the convergence of the stochastic subgradient method and the stochastic proximal subgradient method for unconstrained and composite paraconvex optimization, respectively. The analysis is then extended to a broad family of algorithms that access the objective through stochastic models satisfying certain approximation-quality and continuity assumptions. The main principle that underlies the convergence analysis is that the algorithms under consideration can be interpreted as perturbed descent methods on the generalized Moreau envelope of the original paraconvex problem.

Uncrewed aerial manipulators (UAMs) integrate robotic arms with aerial platforms for three-dimensional physical interaction. However, enlarging the workspace increases arm-induced disturbances, while existing geometric representations face a trade-off between geometric fidelity and computational efficiency in close-proximity interaction. This paper presents QuadHand, a compact quadrotor aerial manipulator with a 3-DoF arm, gripper, and battery-assisted passive CoG compensation module to reduce dominant arm-induced disturbances. We further propose MRC-SDF, a Multi-articulated Robot-Centric Signed Distance Field that preserves fine geometric detail with tractable computation, and a spatiotemporal whole-body trajectory optimization framework that jointly optimizes the quadrotor and manipulator for safe and executable trajectory generation. Simulations and real-world experiments demonstrate safe and executable aerial manipulation in complex environments.

Context. Supernova remnants (SNRs) are renewed sources of non-thermal particles and the main contributors of Galactic cosmic rays (CRs). Recent ultra-high energy (UHE) gamma-ray data from middle-aged SNRs, such as IC 443 and W51 C, highlight the key role of these systems for particle acceleration. Understanding SNR contribution to PeV CRs requires a detailed modelling about how accelerated particles escape their shocks and are released inside the Galaxy. Aims. We aim at critically assessing the SNR paradigm for the origin of Galactic CRs by investigating the expected secondary radiation produced by hadronic collisions of confined and escaping protons in SNRs, and compare these to recent UHE observations. Methods. Through a time-dependent analytical model describing particle acceleration at the SNR forward shock, we investigate particle escape from the shock expanding into uniform environment and diffusing inside and outside the SNR. Results. Our results support the interpretation that the gamma-ray emission from W51 C and IC 443 is due to hadronic emission from both confined and escaping protons, allowing us to derive robust constraints on the particle maximum energy, the magnetic field amplification process, and the CR acceleration efficiency in these systems. Conclusions. We find that the acceleration efficiency is in the range 1 - 10% (2 - 12%) when the spectrum of accelerated particles is proportional to p^-4 (p^-4.3) and the in-situ diffusion coefficient is suppressed by a factor of 3-10 compared to the average Galactic value. On the other hand, the particle maximum energy ever achieved falls, by a factor of a few, below the PeV energy required to explain the CR knee in the context of SNRs only.

We study the multifractal analysis of self-affine measures supported on planar carpets of type Gatzouras–Lalley. We work primarily with Olsen's Hausdorff-dimensional variant of the $L^q$ spectrum, which we denote by $\vartheta(q)$. We prove a variational formula for $\vartheta$, from which it follows that multifractal formalism holds at all values $q$ for which $\vartheta(q)$ is differentiable. However, in general, $\vartheta$ need not be differentiable and the multifractal formalism may fail. In fact, the multifractal spectrum may be non-differentiable and have jump discontinuities in the interior of its support, and there may be multiple phase transitions at both negative and positive values of $q$.

Achieving high-quality superconducting thin films at low temperatures is a central challenge for scalable quantum device integration and Complementary Metal-Oxide-Semiconductor (CMOS)-compatible fabrication. Here, we demonstrate a room-temperature magnetron sputtering approach for synthesizing niobium nitride (NbN) thin films using a novel energy-selective ion source that enables independent control of ion energy and ion flux. This capability provides a powerful route to precisely tailor surface kinetics and crystallization pathways, overcoming longstanding limitations in stabilizing high-quality NbN at reduced temperatures. The resulting films were characterized by superconducting transport measurements, X-ray diffraction, X-ray photoelectron spectroscopy, and transmission electron microscopy. Compared with conventional reactive sputtering, ion beam-assisted growth yields a substantial narrowing of the transition width at the superconducting temperature, indicating improved phase purity and electronic homogeneity. Furthermore, this work introduces energy-selective ion control as a general, non-equilibrium route to stabilize metastable superconducting phases at low temperatures, offering a new design paradigm for thin-film quantum materials.

Video-text pretraining has achieved remarkable progress through the scaling of models and datasets, yet the quality of language supervision remains underexplored. Existing web-scale datasets often provide only a single sparse caption per video that fails to capture rich spatiotemporal semantics, while directly using captioning models can generate noisy descriptions. We propose a large-scale multimodal large language model-based supervision generation framework that improves supervision diversity, fidelity, and semantic coverage. Starting from 10 million videos, our approach generates multi-view captions (MVC) through complementary summary and detailed captions, reasoning-based refinement, and semantic positive caption generation. To effectively exploit supervision at different granularities, we further introduce a granularity-aware text representation with separate CLS tokens for summary and detailed views. We pretrain video-text models using the resulting supervision corpus and evaluate them across standard, fine-grained and detailed text-to-video retrieval benchmarks. Our approach consistently improves both zero-shot and fine-tuned performance while using smaller pretraining corpora than existing methods, demonstrating the importance of rich and complementary textual supervision for video-text pretraining. Project page: https://rvandeghen.github.io/mvc/

Meta-analysis is the synthesis of information from multiple sources to arrive at an overarching conclusion. There is a large need for meta-analysis in agricultural research to synthesize what is known and analyze overarching patterns. Extracting data from published literature is, however, labor-intensive, time-consuming, and tedious, and is impeded by a lack of standardization in research design, units of measurement, and terminology. These challenges are particularly evident in the domain of crop species mixtures, also called intercropping. With the growing capabilities of LLMs, many recent attempts have focused on building systems and tools to automate data collection, yet rigorous assessment against human-labeled ground truth is often missing. In this research, we evaluate three LLM-based approaches—direct zero-shot prompting, a staged workflow, and a multi-agent system—with six open-weight models to extract data from the intercropping literature. The results are evaluated against the manually curated ground truth and through a downstream statistical analysis. Overall, direct zero-shot prompting is the strongest and most consistent approach, achieving the highest mean similarity-adjusted F1 of 0.577, although none of the approaches is close to fully accurate. In the downstream analysis, most model–approach combinations recover the direction of the relationship between the predictor and outcome variables, but do not estimate its magnitude accurately.

Tool-enabled agents form calls from model-visible interfaces, while hosts later select their implementation. Standard dispatch omits the descriptor-handler relation. An unchanged and schema-valid call can therefore acquire a different security effect during rollout, reconnect, or delayed approval. We call this failure schema-epoch drift. We present formation-consistent dispatch (FCD), which connects implementation analysis to execution authority. Reviewed profiles produce provenance-bound over-approximations of declared in-scope effects from official source. Under a closed-target approval policy, a verifier applies each formed call to a summary and captures a successor only when its effects fit the call's security contract. Atomic admission and a final-hop fence preserve this decision to the effect. The exact source retains priority, and the captured successor becomes eligible only after source retirement. Stock releases and deployment changes reproduced the failure. Four profiles covered 32 official releases: 29 required no release-specific change and three escalated. A frozen 16-release expansion matched a separate source oracle. In a preregistered stock comparison, FCD completed all three pending calls whose effect remained private and blocked all three whose omission became public. Exact pinning and release-wide denial stopped all six calls, while release-wide approval completed all six but produced three public effects. A separate lifecycle experiment carried a formation-captured certificate across source retirement. The same safe certificate installed later governed new formations without expanding the pending call's authority.

We study the loss of observability for a class of strongly coupled parabolic systems as the coupling parameter tends to zero. The system is observed through a fixed matrix $B$ on a measurable subset of space-time with positive measure. Under the Kalman rank condition, we determine the exact blow-up rates of the optimal observability cost. Different components of the state, as well as different combinations of them, may have different blow-up rates, and these rates are determined by the algebraic structure of the pair $(B,K)$. The full-state observability cost is determined by the largest of these rates. We also show that the worst-case minimum $L^\infty$-norm of null controls has the same asymptotic behavior.

In this work, we study portfolio optimization under the stochastic discount factor (SDF) framework by learning market state representations that capture the underlying risk structures of financial data. This is challenging due to several factors: financial markets exhibit non-stationary dynamics with shifting regimes, multimodal inputs such as price and news data often contain stochastic noise, and existing diffusion-based approaches, while effective for modeling stochastic dynamics, rely on assumptions such as isotropic Gaussian noise that fail to capture the state-dependent nature of financial uncertainty. To address these challenges, we introduce RADAR, a retrieval-augmented diffusion framework that learns market representations by conditioning on similar historical regimes. RADAR leverages retrieval to construct context-dependent noise distributions, applies conditional diffusion to denoise multimodal representations, and initializes the diffusion process using empirical statistics to reflect state-dependent uncertainty. Experiments show that RADAR achieves state-of-the-art performance on key risk-adjusted metrics while producing economically meaningful signals on asset returns and correlations.

Motivated by biological systems and my previous studies of quorum sensing with density-enhanced motility, I study a model of density-enhanced size and motility, in which both particle size and motility increase when the local density (over a distance larger than particle diameter) exceeds the global density. The emergent structures along different size ratios are spots, holes, bands and labyrinths controlled by several distinct observations. First, the characteristic pattern length scale is controlled by the sensing radius and remains approximately independent of the size ratio. Second, the total area occupied by the particles decreases with increasing size ratio. Third, the active fraction barely depends on the size ratio. These results demonstrate how both particle size and motility can couple microscopic regulation to large-scale pattern formation. I conclude by discussing possible extensions of the model.

Group-based reinforcement learning (RL) has advanced large language models (LLMs) and is increasingly extending to agentic tasks, where sparse terminal rewards make step-level credit assignment essential. Existing methods assign credit from what follows an action in sampled rollouts, but do not explicitly capture its retrospective relation to the realized outcome. Hindsight credit assignment (HCA) instead attributes credit through the ratio of hindsight to behavior-policy probabilities, but estimating the hindsight distribution requires an auxiliary model or an extra pass. To address this estimation bottleneck, we propose GraphHCA, a model-free realization of HCA that eliminates explicit hindsight-distribution estimation. For terminal-goal tasks with deterministic transitions, Bayes' rule reduces the hindsight ratio to a ratio of behavior-policy success probabilities at consecutive states. Taking logs yields a state-wise success potential, whose increment across a transition provides step-level credit. GraphHCA estimates this potential from pooled rollouts through a discounted recursion on the induced transition graph, which admits a unique fixed point on any directed graph. The resulting step-level signal is combined with the trajectory-level advantage, requiring neither a learned hindsight model nor an extra forward pass and recovering GRPO when the step-level weight is zero. Among all compared baselines, GraphHCA achieves state-of-the-art results on ALFWorld and WebShop at both LLM scales, and on Sokoban with a vision-language agent. For example, on ALFWorld it improves overall success rate by up to 24.6 points over GRPO and by up to 4.7 points over the strongest step-level baseline.

Biological machine learning was long bottlenecked by the ability to synthesize designed DNA. Variational synthesis models control chemical reactions to physically manufacture quadrillions of designed sequences in DNA. However, training these generative models is challenging: constraints on chemical synthesis can force many parameters into a discrete space, limiting the ability to pre-train and fine-tune. In this article we train “free” variational synthesis models using stochastic gradient descent in continuous space, and then discretize with post-training quantization to impose hardware and wetware constraints. This enables variational synthesis models to satisfy stringent reward criteria, while still synthesizing diverse designs, achieving a strictly dominating quality-diversity Pareto frontier. We demonstrate by training variational synthesis models of enzymes, peptides, antibody CDRH3s, and regulatory DNA elements. In silico performance is maintained in vitro.

Group-based reinforcement learning such as GRPO trains LLM agents by comparing rollouts sampled for each task, without a learned critic. In long-horizon settings, these rollouts revisit shared anchor states, offering cross-rollout evidence for step-level credit. Ideally, step-level credit should incorporate evidence beyond the realized suffixes observed at an anchor while aggregating alternative continuations according to their empirical frequencies. Visit-local averaging pools realized suffix returns at shared anchors and respects observed frequencies, but does not recursively propagate evidence across rollouts, whereas shortest-path estimators have global reach but allow a rarely observed route to dominate an anchor's value. We introduce Cross-Rollout Bellman Closure (CRBC), which merges each rollout group into a finite empirical process with absorbing success and failure boundaries and evaluates its behavior-policy Bellman fixed point with one linear solve. This fixed point uses the same empirical action and transition frequencies to propagate evidence through shared anchors and aggregate alternative continuations. Backing up the resulting state values through observed transitions yields action values, whose gain over the corresponding state value provides step-level credit. A corresponding finite-depth family recovers visit-local return averaging at zero depth and converges to the exact closure as depth increases. The normalized closure credit is combined with the trajectory-level group advantage for policy optimization, without additional environment rollouts. Across ALFWorld, WebShop, and Sokoban benchmarks with multiple model scales, CRBC consistently improves final performance and learning efficiency. For example, CRBC outperforms the strongest evaluated baseline by 5.59 percentage points on ALFWorld with Qwen2.5-1.5B-Instruct.

A fundamental issue with first principles electronic structure calculation is the requirement for magnetic initialisations, which are usually derived from experimental results. In this paper, we present a new and computationally inexpensive method to predict magnetic structures from first principles, based upon symmetry analysis and a non-magnetic band structure only. We demonstrate that this method of creating initialisations successfully reproduces the known magnetic ground state for a wide class of magnetic materials, including ferromagnetic BCC Fe, antiferromagnetic L1$_0$ PtMn, and frustrated antiferromagnetic L1$_2$ IrMn$_3$, while also predicting non-magnetic materials to remain non-magnetic.

We study post-hoc refinement of frozen node classifiers: given only the graph $G$ and class distributions $Q$ predicted by a frozen model, can we improve accuracy without access to node features, model parameters, or gradients? APPNP answers this by propagating logits with a restart towards the initial predictions, minimizing the anchored Dirichlet energy. Instead, we consider the Potts energy, and decompose it into a Dirichlet term, which penalizes disagreement between neighbouring nodes, and a Gini term, which penalizes indecision within each node. This decomposition motivates Propagate, Then Sharpen (PtS), which alternates between propagation of class probabilities and node-wise, mass-preserving sharpening, with only one additional hyperparameter selected using labelled validation nodes. Across nine homophilic graphs, with a frozen MLP backbone, PtS improves mean test accuracy over independently tuned APPNP by $1.71$ percentage points on clean inputs and $3.90$ under severe Gaussian feature corruption. Gains over APPNP become smaller, but remain positive with frozen GCN and GraphSAGE backbones. Sharpening also removes most of the accuracy loss of deep propagation: on clean inputs without restart, accuracy falls by $2.2$ points between $2$ and $100$ propagation steps under PtS, compared with $33.8$ for APPNP.

The set-coloring Ramsey number $R(k;r,s)$ is the least $N$ such that every assignment of an $s$-element subset of $[r]$ to each edge of $K_N$ yields a copy of $K_k$ whose edges share a common color. For every fixed prime power $q$, we construct infinitely many positive integer triples $(r,j,s)$ with $j\sim(q-1)^{-2/3}r^{1/3}$ and $s=(1-1/q)(r-j)$ such that $R(q+1;r,s)=\Theta_q(r^{4/3})$. For $q=3$, this answers in the affirmative a question of Conlon, Fox, Pham and Zhao, showing that polynomially superlinear growth for $R(4;r,2(r-j)/3)$ already occurs at the scale \(j=\Theta(r^{1/3})\). Moreover, along the same sequence, the maximum size of a $q$-ary code of length $r$ and minimum Hamming distance at least $s$ is $(1+o(1))(q-1)^{4/3}r^{4/3}$.

Vision-Language-Action (VLA) models for autonomous driving rely heavily on successful expert demonstrations, leaving model-specific failures underexploited. Learning from these failures is hindered by unreliable diagnoses, poorly matched correction targets, and coarse rewards. We propose RefineDrive, a failure-guided post-training framework that learns from self-generated failures through targeted supervision and safety-aware reinforcement learning. Reliable Diagnosis derives structured, verifiable feedback on collisions and drivable-area violations directly from simulator states. Minimum-Correction Target Retrieval searches a clustered human trajectory bank for nearby corrections that satisfy hard-safety constraints in the current scene, prioritizing preservation of the failed prediction's motion pattern. Conditioned on the driving context and failed trajectory, Correction SFT learns to generate the diagnosis followed by the retrieved correction as a training-only auxiliary task. We then apply GRPO with a Safety-Layered Reward that strictly prioritizes hard-safe trajectories, retains continuous safety feedback for both unsafe and hard-safe trajectories, and rewards driving progress only after hard safety is satisfied. At inference, the policy directly predicts trajectories from the driving context without an explicit diagnosis or repair stage. On NAVSIM v1, RefineDrive improves the 4B base SFT policy from 87.7 to 91.7 PDMS. Using the same checkpoint without additional training, RefineDrive achieves 89.4 EPDMS on the original NAVTEST scenes evaluated with NAVSIM v2 extended metrics. Controlled ablations support the benefits of structured diagnosis supervision, retrieved corrections, and safety-layered optimization for direct planning.

Production large language models retrieve and cite web pages alongside generated answers, yet the page-level features that predict citation frequency remain poorly characterised. We present an observational study of approximately 2 million LLM citations from four commercial engines (ChatGPT, Claude, Google AI, Gemini) over six months, joined to 10,000 crawled pages from nineteen B2B SaaS workspaces. Sixty-plus features are tested using a nine-method consensus framework combining mixed-effects regression with domain fixed effects, FDR correction, stability-selection Lasso, double machine learning, generalised additive models, and temporal hold-out replication. Four findings survive all checks. First, prompt-content alignment (Jaccard overlap between page tokens and the full workspace prompt corpus, including non-citing prompts) is the dominant page-level predictor (beta = +0.37, 95% CI [+0.33, +0.41], q ~ 10^-73). Second, the standard AEO checklist (FAQ blocks, structured data, Core Web Vitals) shows positive effects in pooled data that reverse or collapse to zero once domain fixed effects are applied: Simpson's paradox with practical consequences for the AEO literature. Third, domain-level AI authority exceeds the strongest non-alignment page-level feature by a factor of six in mean absolute SHAP value. We release the analytic pipeline as a methodological contribution.