Papers

We extend the quark mean-field (QMF) model to finite temperature and systematically investigate the thermodynamic properties of uniform nuclear matter, using the relativistic mean-field (RMF) model as a reference. For each model, we consider two parameter sets calibrated to the same selected nuclear-matter saturation properties but with different nucleon Dirac effective-mass ratios at saturation. We examine the effective nucleon mass and the composition of $\beta$-equilibrium matter, together with the free energy, energy density, pressure, entropy, and heat capacities of symmetric nuclear matter, pure neutron matter, and $\beta$-equilibrium matter. The QMF and RMF models exhibit similar qualitative trends, but their predictions increasingly differ at high density, where the effective masses have distinct density dependences. These differences are particularly evident in the thermal pressure and thermal index. For the two parameter sets considered in this work, we further provide compact analytical representations of the thermal index, $\Gamma_{\rm th}(\rho_{\rm b},T,\beta)$ over baryon densities of 0.08-1.0 $\rm fm^{-3}$, temperatures of 5-100 MeV, and isospin asymmetries of 0-1. The fits reproduce the numerical results with an accuracy better than $2\%$ and can be directly implemented in binary neutron-star merger simulations. This study establishes a finite-temperature extension of the QMF framework and provides a basis for future assessments of how a quark-structure-based description of nuclear matter affects thermal support and post-merger dynamics in binary neutron-star mergers.

This paper examines the stability analysis of two-dimensional incompressible fluids in $L^2_{uloc}$ spaces. Extending the classical stability framework for Euler equations in Yudovich-type settings, we establish the convergence of Navier-Stokes solutions toward Euler solutions as viscosity $\nu \to 0$, under the weakened assumptions $u^\nu_0 \in L^\infty$ and $\omega^\nu_0 \in L^\infty$ without imposing decay conditions at infinity. We first derive a priori estimates for the Navier-Stokes equations in $L^\infty$ spaces. Then, using harmonic analysis tools including Littlewood-Paley decomposition and Bony's paraproduct calculus, we prove the $L^\infty$-convergence of the velocity field and $L^2_{uloc}$-convergence of the vorticity as $\nu \to 0$.

We introduce a strict monoidal groupoid associated with a given commutative ring $K$. It acts on the Clifford extension systems of $K$-central algebras which are graded by a group $G$, as well as on the generalized collective characters, both of type $\phi \in$ Hom$(G,$ Aut$(K))$. These actions partition the two sets above with respect to graded Morita equivalence. By that we establish a seven term exact sequence of type $\phi$, which boils down to the celebrated Chase-Harrison-Rosenberg sequence when $\phi$ is Galois.

The growing availability of quantum-mechanical (QM) datasets offers new opportunities to investigate structure-property and property-property relationships in drug-like molecules using data-driven methods. However, interactive tools that integrate molecular visualization, statistical analysis of QM properties, clustering, and machine learning (ML) remain limited, despite their value in facilitating dataset exploration and interpretation. To address this gap, we introduce QUPEX (QUantum Property EXplorer), an open-source Streamlit-based framework for the interactive exploration of QM property spaces in molecular systems. As a demonstration, we apply QUPEX to a subset of the QM7-X dataset comprising 41,537 equilibrium molecular structures containing up to seven non-hydrogen atoms (C, N, O, S, and Cl) and their 24 associated QM properties. In addition to property-space analysis, QUPEX incorporates an XGBoost regression pipeline for predicting PBE0 dipole moments from tight-binding-derived electronic descriptors, together with model evaluation and SHAP-based interpretability functionality. By combining interactive molecular visualization, data analysis, and predictive modeling, QUPEX provides an accessible and extensible environment for investigating molecular datasets and identifying patterns in their structural and electronic properties. These capabilities can support the exploration of chemical space and inform the rational design of drug-like molecules with targeted QM properties.

Extended diffuse radio emission in the central regions of galaxy clusters is commonly associated with non-thermal processes in the intracluster medium (ICM), but its origin and the mechanisms responsible for sustaining it remain uncertain. We present the discovery and multi-wavelength analysis of two diffuse radio sources, MKTJ0355-4237 and MKTJ0355-4230, to assess their nature and investigate their radio spectral and magnetic field properties through radio polarimetric analysis. We use deep MeerKAT L-band (1.28 GHz) observations to perform spectral analysis of the diffuse emission and study its polarisation properties via rotation measure synthesis. These are complemented by eROSITA X-ray data and DESI photometric redshift catalogues to characterise the host cluster environments. MKTJ0355-4237 is confirmed as cluster-scale minihalo with extent of $\sim 400$ kpc, while the other diffuse source MKTJ0355-4230 remain uncertain and could be either associated with a radio minihalo or radio tailed galaxy. Both show steep spectra ($\alpha \approx -0.7$ to $-0.8$) that steepen toward the outskirts ($\alpha \lesssim -2.5$), consistent with spatial variations in electron ageing and re-acceleration. Polarised emission is detected in both systems, with fractional polarisation $\sim1\,\%$ in the centres and increasing in the outer regions of MKTJ0355-4237. MKTJ0355-4230 is associated with a previously uncatalogued cluster and shows an X-ray morphology offset from the brightest cluster galaxy, indicative of dynamical activity. MKTJ0355-4237 exhibits a sharply bounded internal radio deficit without a corresponding X-ray counterpart, within current sensitivity limits. The spectral steepening supports turbulent re-acceleration as the origin of the diffuse emission.

Deleting singular components offers a precise way to remove a capability from a language model, yet the first-order spectral saliency used to rank components predicts only a local loss change, whereas deletion is a finite intervention. In this paper, we study how prediction error affects selective editing, where selective editing requires degradation of a target task while preserving others. We decompose the error into derivative transfer across item splits and nonlinear response along the deletion path. We establish that outer interval screening retains every feasible candidate when every candidate's intervals contain its finite validation loss changes on every task. We evaluate these effects using one answer-only negative log-likelihood objective for search, validation, and test, with disjoint calibration and evaluation masks. The primary configuration targets arithmetic in Mistral-7B-Instruct-v0.3 while preserving code and question answering; extensions cover Llama-3.1-8B-Instruct and reversed target roles. In the primary study, which deletes 1024 coordinates from a support of 7168, calibrated intervals cover 968 of 1024 evaluation masks. Outer screening reaches the direct-selected edit after 25 verification checks, whereas direct verification abstains at a 32-check cap, but it rejects 4 of 74 feasible masks. All three selected edits pass validation, yet only one meets every test constraint. Interval coverage, feasible-candidate retention, and independent test preservation are therefore distinct properties and require separate assessment.

Post-training is crucial for improving text-to-image models, yet existing pipelines typically rely on manually curated training data and fixed training distributions. We introduce APT (Agentic Post-Training), a fully automated framework that adaptively post-trains a base model according to its evolving capability profile. APT coordinates three agents to construct evaluation sets from user requirements, diagnose model-specific strengths and failure modes, and generate reinforcement learning data with an adaptive prompt distribution that emphasizes underperforming capabilities. By repeatedly evaluating, diagnosing, and updating the generator, APT lets the current model's behavior shape its next training tasks, forming a feedback loop inspired by recursive self-improvement. For general-purpose settings without user-specified evaluation scenarios, we further develop an evaluation harness that enables broad and diverse evaluation set generation. Experiments across multiple base models, benchmarks, and generation architectures demonstrate that APT is model-agnostic, benchmark-agnostic, architecture-agnostic, and fully automated.

We give a proof of the convexity of the upper bild of a quaternionic matrix, a theorem of So and Thompson. After reduction to $2\times2$ matrices, we introduce real coordinates on a sphere and obtain two representations of the upper bild over the closed unit ball, involving a convex function and a concave function. Minimizing the first and maximizing the second over parameters with a fixed real part yield a convex lower boundary function and a concave upper boundary function, from which convexity follows.

AI companions provide users with emotional support and ongoing companionship, but their sustained relational interactions also introduce distinct safety risks. Prior work largely targets general harms or specific companion platforms and risk categories, while relying on manually collected conversations, limiting scalable and user-grounded evaluation and mitigation. To address this, we introduce CompanionSafe, a unified evaluation-to-mitigation framework for AI companion safety. Its evaluation component, CompanionEval, provides scalable multi-turn evaluation by constructing 1,300 relationally grounded settings from diverse personas, matched companion characters, and dialogue scenarios across four turn tiers. Its mitigation component, CompanionGuard, converts benchmark-exposed failures into turn-localized supervision for companion-specific risk detection. Our results show that even strong LLMs and existing guard models remain vulnerable to companion-specific relational harms, while both closed- and open-source models exhibit increasing safety risks as interactions become longer. Together, CompanionEval and CompanionGuard form a practical evaluation-to-mitigation loop for AI companion safety, turning relational safety failures exposed during multi-turn interaction into supervision for companion-specific guardrails.

Let $f$ be a dominant rational self-map of a normal projective variety over an algebraically closed field of arbitrary characteristic, or a dominant meromorphic self-map of a compact Kähler manifold. We prove that in every codimension, the degree sequence of $f$ differs from its dynamical-degree growth by at most a polynomial factor, with an explicit universal bound on the polynomial exponent. In particular, subexponential but superpolynomial degree growth cannot occur. At a strict dynamical-degree break, we prove the sharper asymptotic \[ \mathrm{deg}_{i,\omega}(f^n)=C_{f,\omega,i}\,\lambda_i(f)^n+O(\eta^n), \] for every $\sqrt{\lambda_{i-1}(f)\lambda_{i+1}(f)}<\eta<\lambda_i(f)$. This extends the degree-asymptotic theorem of Dang–Favre from codimension one in characteristic zero to arbitrary codimension and arbitrary characteristic, and recovers the surface theorem of Boucksom–Favre–Jonsson. Both results rely on a uniform estimate for the temporal discrete logarithmic Laplacian of the degree sequences, obtained by applying the Ptolemy inequality to ordered Hodge–Lorentz packages on varying finite-time orbit spaces.

Wheel-legged robots operating in outdoor spaces shared with humans require accurate perception, socially compliant navigation, future-scene reasoning, and scene reconstruction. However, existing datasets typically support these capabilities in isolation and rarely provide dense spatial and behavior-level supervision on real wheel-legged platforms. We introduce LynxScenes, a large-scale real-world dataset and benchmark collected with a LYNX M20 wheel-legged robot. It contains approximately 100K 30-s navigation clips spanning 833.6 h and 3,294.7 km, with 3.0M annotated frames. The synchronized recordings include four fisheye cameras, dual LiDARs, IMU, odometry, and robot states. Annotations comprise 20.82M oriented 3D boxes across 27 categories, 13.89M road-structure annotations, and 20 navigation instructions organized into three layers and aligned with continuous future trajectories. LynxScenes supports four complementary tasks: instruction-conditioned trajectory prediction, BEV-based perception of 3D objects and road structures, future scene prediction, and multi-view scene reconstruction. For trajectory prediction, we further introduce a log-replay-based pseudo-closed-loop evaluator that measures safety, progress, and instruction compliance beyond trajectory imitation. Extensive evaluations across representative navigation, perception, world-model, and reconstruction methods reveal substantial remaining challenges in close-range outdoor robot navigation. The dataset and evaluation toolkit are planned for public release.

Deep research (DR) agents address open-ended information needs through multi-step reasoning, long-horizon web search, and evidence synthesis. However, existing benchmarks primarily focus on academic research or synthetic tasks, leaving DR agents' capabilities in real-world life and professional productivity settings insufficiently evaluated. To bridge this gap, we introduce LifeSearch, a challenging benchmark comprising 203 Chinese and English tasks derived from real-user query seeds across 7 concrete life and productivity domains. With more than 4,500 hours of human annotation, we construct over 4,000 expert-written, fine-grained rubrics, covering both report-content criteria for coverage and accuracy and concrete criteria specifying values, units, dates, and URLs. We conduct extensive experiments on 12 advanced DR agents under a unified evaluation harness, systematically analyzing their performance patterns and failure modes. We find that even the best-performing frontier agent, GPT-5.6 Sol, achieves a score of only 63.4%, leaving substantial room for improvement on realistic life and professional DR tasks. We select the grading configuration by comparing candidate LLM judges against human rubric labels, and a human ranking study shows strong alignment between aggregate benchmark scores and human judgments (Spearman's $\rho = 0.89$, Kendall's $\tau = 0.81$). LifeSearch provides a rigorous evaluation framework and foundation for advancing DR agents toward real-world life and productivity.

The SKA Regional Centre Network (SRCNet) is a federated global network designed to archive, distribute, and process SKAO data products. This paper examines the evolving SRCNet architecture-focusing on the transition to version 0.2 (v0.2) requirements, including computation, orchestration, and multi-tiered storage-and details the strategy for establishing its proto-SRC infrastructure. We outline the prototype developments for the major and minor nodes in the context of v0.2. We describe the minor node compute and storage demands, establishing a pathway toward a fully operational Indian SKA Regional Centre (INSRC).

Ambiguous or incomplete task specifications complicate both execution and clarification for language-model agents. Yet agents' responses to these information gaps remain poorly characterized across models and execution harnesses. We present AM-Bench, a benchmark built from 48 tasks adapted from Terminal-Bench 2.0 and Harness-Bench. Each task includes a fully specified reference and six variants spanning ambiguous or missing goals, context, and constraints. We evaluate every pairing of five models and four harnesses over 20,160 runs. Our results reveal distinct execution deficits: goal gaps hinder completion, context gaps increase token use, and constraint gaps weaken compliance without necessarily preventing completion. Missingness lowers success more than ambiguity in all three domains. These effects also reshape system comparisons: advantages under complete information need not persist, and rankings depend on model $\times$ harness pairings and the evaluation criterion – completion, success, or repeat consistency. Estimates based on observed clarification requests and matched fully specified runs further suggest that clarification could recover unfinished work while leaving most constraint violations unresolved. Together, these findings motivate joint model-harness evaluation across information conditions and targeted clarification of unresolved requirements before dependent actions. To support future research on agents under task underspecification, we provide the AM-Bench project repository at https://github.com/s4-lab-cuhksz/AM-Bench.git.

AI has become increasingly helpful in scientific discovery, yet human expert review remains essential for those problems without reliable automated evaluation, posing a fundamental challenge as candidate generation scales beyond available review capacity. This paper studies verification under limited human effort, where rare valid solutions need to be prioritized while invalid candidates should be filtered out to reduce human workload. We adopt the one-sided verification objective that maximizes the rejection rate of invalid solutions (TNR) under a constraint on the false-rejection rate of valid ones (FNR), making human review cost an explicit term to minimize. Drawing on the intuition that verifying a specific error can be easier than discovering one, we introduce OSVerify, an algorithmic framework that decouples error proposal from error validation. The error proposer searches for errors in solutions across different granularities by hierarchical decomposition, while the validator distinguishes substantial errors from minor or hallucinated ones. Experiments on competition- and research-level benchmarks show that OSVerify reduces the number of human reviews of invalid solutions by 46% on average compared to voting baselines under the same empirical low FNR constraint. Our post-training of the validator further improves the reduction to 57%. As high-impact real-world use cases, we apply OSVerify to identify errors in published research papers that are subsequently confirmed by the original authors and help resolve three Langlands open conjectures that are confirmed by experts, demonstrating its utility to facilitate human-AI research collaboration.

Autoresearch systems increasingly undertake entire research projects. In practice, scientific research requires systems to pursue multiple interdependent claims through a continuous, multi-stage workflow and revise experiments as evidence accumulates. Existing evaluations of autoresearch systems, however, typically score isolated tasks or final artifacts, leaving these process-level capabilities largely unmeasured. We therefore introduce ResearchFlow-Eval, a fine-grained framework for assessing continuous scientific execution and iteration at both the stage and claim levels. Each evaluation is grounded in a published anchor paper, from which we derive stage-specific rubrics that decompose each research stage into dimensions and separately scored rubric items. Using these rubrics, we score each research stage and examine experimental execution in detail, focusing on multi-claim completion and revisions across attempts. We apply the evaluation framework to general-purpose agent harnesses, skill-augmented harnesses, and systems with research-specific orchestration. Across all evaluated systems, experimental execution consistently lags behind design and planning. Within execution, systems struggle to produce high-quality results and meet claim requirements, and repeated attempts rarely yield measurable improvements. Moreover, neither skill augmentation nor research-specific orchestration reliably yields higher scores. ResearchFlow-Eval thus extends autoresearch evaluation beyond isolated, single-objective runs to continuous workflows in which systems pursue multiple claims and refine their work across iterations.

Dynamics of biochemical systems are dictated by the stoichiometry and kinetics of reaction networks. These systems may admit positive steady states that could undergo qualitative change in response to varying rate parameters. These changes are called steady-state bifurcations, and they correspond to biologically meaningful processes. Classical bifurcation analysis relies on exact kinetics and rate parameters, which are often unknown or difficult to measure for complex systems. To address this, structural bifurcation analysis (SBA) was introduced to predict bifurcations using only the system's associated reaction network. In this work, the computational package NetBiF (Network Bifurcation Finder) is introduced to implement SBA. NetBiF is applied across diverse biochemical systems, including fundamental metabolic pathways, signaling and gene regulatory networks, and a large-scale carbon cycle model, to predict steady-state bifurcations. Crucially, for biochemical systems governed by power law kinetics, the implementation of NetBiF also classifies the steady-state bifurcations as saddle-node, transcritical, or pitchfork via a structural analog of Sotomayor's theorem. To this end, explicit formulations for the bifurcation criteria were derived for these biochemical systems. Determining and classifying bifurcation behaviors provide insight into biochemical systems' abilities to adapt to changing and fluctuating conditions. Collectively, the study presents NetBiF as a scalable, structure-based, and consistent computational tool to implement SBA. Our findings enable researchers to systematically study dynamical behaviors of biochemical systems through their reaction network structures without requiring explicit kinetic information.

We study the contributions of half-BPS surface defects to supersymmetric Casimir energy and the universal logarithmic term of supersymmetric Rényi entropy in four- and six-dimensional SCFTs. Using equivariant integration of defect anomaly polynomials and its extension to supersymmetric Rényi backgrounds, we obtain closed expressions for these observables in terms of defect 't Hooft anomalies. For Gukov–Witten defects preserving transverse rotations in four-dimensional $\mathcal{N} = 4$ super Yang–Mills theories, both observables depend on a single R-symmetry anomaly. For $\mathcal{N} = (0, 4)$ defects in six-dimensional $\mathcal{N} = (1, 0)$ theories, additional terms arise from the gravitational anomaly. We provide complementary checks using chiral algebras, five-dimensional localization, and holographic probe branes at large $N$, while localized chiral fermions reproduce the gravitational-anomaly contributions. The framework also recovers Wilson-surface results in six-dimensional $\mathcal{N} = (2, 0)$ theories.

We show that two Transformers representing the same function can follow different training trajectories. For example, doubling a query matrix and halving its key matrix preserves the model's function but changes the gradient scales seen by the optimizer. Our theoretical analysis establishes that standard block-local first-order optimizers fail to scale updates with parameters under a shared learning rate. For AdamW, transforming the first- and second-moment estimates alone does not correct the mismatch between parameter and update scales. To make runs restarted from equivalent checkpoints follow the same trajectory, we balance matrix pairs and transform their moment estimates together, bringing distinct but equivalent training states to the same starting point. To correct scale imbalance between paired Transformer matrices without changing predictions, we propose Symmetry-Aware Gradient Geometry Stabilization (SAGGS), which periodically equalizes the Frobenius norms of exact symmetry pairs, and its damped variant, Soft SAGGS. SAGGS reduces perplexity (PPL) by $0.374\pm0.026$ at 101M parameters on WikiText-103, and Soft SAGGS reduces PPL by $0.780\pm0.040$ in a 31M modern-architecture replication, both under scale imbalance. In a 123.8M checkpoint-resume experiment, reciprocally rescaling matrix pairs barely changes validation loss at restart but increases final PPL by $3.78\pm0.42$; hard and soft rebalancing recover to within $0.02$ PPL of the control.

It is observed that the dimension of the space of invariant spinors on the manifold $\mathrm{SU}(n)/T^{n-1}$ of full flags in $\mathbb{C}^n$ equals the number $\mathrm{RT}(n)$ of labelled regular tournaments of order $n$, for $n$ odd. This space is decomposed under a double cover of the Weyl group, and realized as a pair of eigenspaces, first for the Dirac operator, then for a twisted version of it which acts equivariantly; this is used to show that multiplicities of irreducible representations are even for $n\equiv 1\pmod 4$.

Scaling recursive self-improvement requires additional computation to produce useful research progress in reaching persistent objectives. Intuitively, more researcher agents can explore more hypotheses, but early evaluation scores might misrepresent their promise, shared findings could lose their applicability conditions, and useful procedures could remain confined to completed investigations. In this paper, we present AReaL-RSI, a framework for organizing a persistent research team of agents without updating backbone LLM weights. We formulate the scaling problem in terms of evaluated outcomes and whole-system resource expenditure. Concretely, a leader agent selects task-appropriate research orientations and guides ongoing investigations; conditional memory sharing distinguishes unresolved problems from supported findings and enables recipient adaptation. During recursive evolution, after each campaign, evidence-based review revises researcher orientation, knowledge, and skills for later campaigns. Experiments compare AReaL-RSI with Codex-Goal on downstream harness optimization, GPU kernel optimization, and AI research tasks using two backbones. Under the reported resource allocations, AReaL-RSI improves Terminal Bench performance by 2.2 percentage points for each backbone and increases mean KernelBench speedup by 32.2-36.8%; further scalability comparisons favor the design of AReaL-RSI over native scaling: combining experience sharing with specialized researcher roles yields 1.9-27.5% lower kernel latency than independent exploration and 1.3-33.9% lower latency than sharing alone across all seven comparable task-backbone pairs.

Long-horizon agents often struggle to recover from failures whose causes lie several steps earlier, beyond what local reflection or backtracking can resolve. We introduce BELIEFWEAVER, a framework that combines persistent evidence across attempts with prospective reasoning over repair directions. It maintains a relational belief state over frontiers, attempts, observations, and checkpoints. Execution evidence updates related frontier priorities across attempts and rollback, while diagnostic evidence gates execution. An implicit world model (IWM) evaluates repair hypotheses, predicts progress, and identifies relations among frontiers to guide exploration. We further distill these recurring IWM reasoning components into a 9B student through supervised fine-tuning and on-policy distillation (OPD). Across three terminal-based benchmarks, BELIEFWEAVER improves aggregate final score by 5.1 percentage points over native Terminus-2 continuation, with positive trends in exploration efficiency. The distilled 9B student improves final score by 9.8 percentage points over the reported native baseline while reducing estimated teacher API cost by 54.8% relative to the matched teacher. These results show that persistent evidence and prospective reasoning can improve recovery in long-horizon agent tasks while substantially reducing reliance on teacher-model inference.

We study the optimization inverse spectral problem (OISP) for the first $m$ eigenvalues of the Schrödinger operator on a compact metric graph. We prove the existence of a solution for every strictly increasing finite set of prescribed eigenvalues. On a graph without cycles, we obtain a representation of the optimal correction as a linear combination of squared eigenfunctions, provided that the selected eigenvalues are simple and separated from the next eigenvalue. On a graph with cycles, under the same simplicity and separation assumptions, we obtain a strong limiting representation of the optimal potential in terms of eigenfunctions of approximating operators. For a graph with a cycle, we give a counterexample with simple eigenvalues and linearly dependent squared eigenfunctions. We also prove that linear dependence of the squares of nonzero restrictions to an edge of eigenfunctions corresponding to distinct eigenvalues forces the potential on that edge to have an analytic representative

The Square Kilometre Array Observatory (SKAO) will provide unprecedented angular resolution for low-frequency solar radio imaging, enabling access to fine-scale coronal structures. However, the improved spatial resolution of SKA-Low also increases the sensitivity of solar images to ionospheric propagation effects. We investigate the impact of ionospheric fluctuations on simulated SKA-Low solar observations at 50, 100, 150, and 200 MHz using the Karabo simulator and turbulent, moving ionospheric phase screens. We quantify the resulting image distortions using spatial power spectral density (PSD) analysis and compare the SKA response with corresponding MWA simulations. The results show that ionospheric distortions are strongly scale- and frequency-dependent, with the maximum fractional PSD distortion decreasing with observing frequencies. SKA resolves ionospheric fluctuations over spatial scales that are largely smoothed by the MWA instrumental response, with significant distortions occurring on scales comparable to solar active-region structures. These results demonstrate that ionospheric propagation effects should be considered when interpreting high-resolution SKA-low solar radio images, particularly at the lower end of the frequency band.

Organisms have evolved diverse strategies to communicate. Beyond acoustic and visual signals, many species rely on chemical communication, including pheromones: volatile compounds involved in reproduction, defense, and coordination. Ant trail systems, a paradigm of pheromone use, have inspired decades of research in collective behavior, self-organization and optimization algorithms. Yet, despite their central role, individual pheromone deposits have never been directly visualized or quantified, limiting our understanding of how deposition events scale into collective trail formation. Here, we use interferometric imaging to reveal and quantify single pheromone deposits in the ant Lasius niger. This label-free, non-invasive approach enables precise measurement of single deposit volume (~1 pL, with x20-fold variability), morphology, and temporal dynamics. We uncover a two-phase volume loss process: most of secreted volume evaporates within seconds, forming a dried droplet, which then partially sublimates (~10%) over one hour. These findings challenge the assumption of homogeneous deposition and bring previously inaccessible properties of ant pheromone trails within experimental reach. Our method establishes a quantitative framework for studying the spatiotemporal dynamics of insect chemical communication, linking individual signaling to collective patterns.

Let $M$ be a finite-dimensional complete Riemannian manifold of bounded geometry. We consider a time-dependent vector field $X : \mathbb{R} \times M \to TM$ with $X_t:=X(t,\cdot) \in \mathfrak{X}^r(M)$ for all $t \in \mathbb{R}$ that satisfies some further uniform continuity assumptions. We suppose that $X$ admits a globally defined integral curve $\gamma : \mathbb{R} \to M$. To any isolated subset $\Omega$ of the Sacker-Sell spectrum of $t \mapsto \nabla X_t(\gamma(t))$, Sacker-Sell theory associates a subbundle $\mathscr{N}^\Omega$ of $T_\gamma M$ invariant under $\nabla X_t$. Under additional nonresonance conditions on $\Omega$, we prove, by an application of the parameterization method (Cabré et al., 2003), the existence of an invariant topological submanifold $\mathscr{W}^\Omega \subset \mathbb{R} \times M$ with $C^r$ fibers $W_t^\Omega:= \mathscr{W}^\Omega \cap \{t\} \times M$ that is unique in a sufficiently smooth subclass of invariant manifolds uniformly tangent to $\mathscr{N}^\Omega$ (made precise later). We moreover show regularity of $\mathscr{W}^\Omega$ with respect to parameters, and characterize the attraction towards $\mathscr{W}^\Omega$ via a foliation in the case $\Omega$ is the slowest part of the spectrum.

This article proposes rational quadratic kriging, a kriging estimator that addresses the limitations of existing approaches: the mean reversion issue of ordinary kriging and the diverging variance issue of rational kriging. Through the rational quadratic kernel, we establish a connection between rational quadratic kriging and kernel regression. The connection allows us to prove desirable theoretical properties of the new estimator and further propose a novel estimation procedure that utilizes factor weights from kernel regression. We also derive expressions to enable efficient leave-one-out estimation and conformal prediction. Extensive simulations across both deterministic functions and noisy datasets show significant improvements in both prediction and uncertainty quantification. A fast implementation is available in the open-source R package RQK.

The exploration of next-generation wide-gap semiconductors with extreme work functions is highly desirable for the continued advancement of electronic and optoelectronic devices. By using first principles calculations, we show that e̱ta}-TeO3, with a wide band gap exceeding 3 eV, emerges as a promising n-type semiconductor exhibiting ultrahigh work functions of up to ~8 eV. Intentionally or unintentionally incorporated interstitial H, Li, Na, Cu, Mg, and Zn impurities and substitutional F impurities are identified as shallow donors, whereas O vacancies act as minor carrier-compensating defects that locally trap electrons at neighbouring Te sites. The work function is evaluated across a series of low-index nonpolar surfaces. The presence of ordered O vacancies is energetically favoured on these surfaces and tends to reduce the corresponding work functions. These findings underscore the significance of precise control over the O chemical potential to suppress surface O-vacancy formation, thereby preserving the exceptional electronic performance of e̱ta}-TeO3 associated with ultrahigh work functions. Collectively, the results highlight the potential of e̱ta}-TeO3 for hole injection/extraction/transport layers as well as transparent electrodes for applications such as light-emitting devices and photovoltaic cells, while providing useful guidance on carrier doping and surface tuning for these practical applications through elucidating the effects of the point-defect and surface configurations on the electronic properties.

Selection bias is a difficult yet widespread problem in causal discovery, occurring whenever non-random selection processes lead to data that is not representative of the underlying populations. Due to its practical importance, related works have been proposed to address the problem under local [Versteeg et al., 2022] or interventional settings [Dai et al., 2025a], but general algorithms for observational data remain elusive. In this paper, we focus on truncated data (hard selection), and provide a general result for Additive Noise Models (ANM). We show that score-based methods are a surprisingly suitable candidate due to a special property of the score function ($\nabla \log p(x)$): deterministic truncation preserves both the score of the joint distribution as well as the Jacobian of the score. While established score-matching algorithms still fail in most settings, we actively leverage this observation to propose a new method for causal discovery that is robust under truncated data with ANMs. Overall, our approach offers a general, robust solution that is agnostic to external information about the selection process and still achieves comparable performance to the state-of-the-art approaches when selection is not present.

Liquid marbles interface is composed by a dense network of grains trapped by capillarity at their surface. The mix of capillarity and granular character make their interfaces remarkable, allowing non wetting, high mobility and strong robustness which are a basis for numerous applications. A canonical experiment showing out of equilibrium nature of granular material is the so called tapping experiment, where a dry granular medium under vertical vibration reorganize an evolve toward a denser final state function of the vibration amplitude In this paper we explore the out of equilibrium nature of densely covered liquid marbles by measuring their shape, compaction and stresses evolution under vertical vibration. We show that liquid marble do indeed reorganize when submitted to taps, leading to higher internal pressure and lower effective surface tension.