Papers

Recent cosmological constraints on the sum of neutrino masses have reached, and in some analyses fallen below, the minimum value implied by the normal mass ordering, suggesting a possible tension with neutrino-oscillation measurements. We investigate whether this discrepancy can be alleviated in a mass-varying-neutrino (MaVaN) cosmology in which a canonical pseudo-Nambu-Goldstone boson (pNGB) drives late-time cosmic acceleration and controls the masses of massive neutrinos through an exponential coupling. Using current cosmic microwave background, baryon acoustic oscillation, and type Ia supernova data, we reconstruct the neutrino-mass evolution and show that the cosmologically inferred effective neutrino mass can fall below the present-day normal-ordering floor while remaining consistent with oscillation constraints. The same interaction produces a distinctive late-time signature, with 96% of the posterior expansion histories exhibiting a crossing of the apparent phantom divide, $w_{\rm app}=-1$, at $z_{\rm cross}=0.90^{+0.28}_{-0.13}$ at 68% C.L. The underlying scalar field nevertheless remains canonical, with $w_\phi \geq -1$. Our results therefore show that neutrino mass variation can simultaneously alleviate the apparent neutrino-mass tension and generate the phantom-crossing behavior favored by current cosmological data, without introducing a phantom field or violating the null energy condition.

Switching stochastic differential equations (SSDEs) describe continuous-time dynamics whose parameters switch according to a latent regime process that follows a continuous-time Markov chain (CTMC). By allowing dynamics to change between regimes, SSDEs represent heterogeneous system behavior and have been applied across diverse fields. However, Bayesian inference for SSDEs remains difficult, and existing SSDE inference methods have limited applicability, with restrictions such as noise-free observations, univariate states, linear drift, or state-independent diffusion. In this study, we propose an approximate Markov chain Monte Carlo sampler for SSDEs using uniformization and factorized neural likelihood estimation (FNLE), a simulation-based inference method. Uniformization provides an exact representation of the CTMC but requires SDE transition densities over arbitrary time intervals. We approximate these densities by training a time-conditioned FNLE model. The resulting sampler is broadly applicable to SSDEs without requiring analytically tractable transition densities. In synthetic-data experiments, our method recovered regime paths and parameters for three SSDE models for which previous methods have limited applicability. We also applied our method to a real dataset and detected a regime transition.

A comprehensive (start-to-end) simulation was performed regarding the formation of a front-tilted laser pulse and the subsequent acceleration of non-relativistic electrons moving along a reflective grating structure. The laser pulse tilt was formed using another diffraction grating – either reflective or transmissive. The pulse had a spectral range (FWHM) of 803–863 nm and an initial duration of approximately 17 fs. Acceleration under normal laser pulse incidence was also calculated for comparison. Research results indicate that the use of a femtosecond laser pulse with a front, tilted by means of a reflective diffraction grating, significantly enhances the efficiency of laser acceleration of non-relativistic electrons compared to the case of a pulse at normal incidence. Furthermore, it was found that using a transmissive diffraction grating to shape the tilted pulse front also increases acceleration efficiency relative to normal incidence on the accelerating grating, although the acceleration rate is lower than when a reflective diffraction grating is used.

We study rational approximation to logarithms of positive rational numbers and give a separated-weight determinant argument for $\mu(\log r)=2$ whenever $r\in\mathbb Q_{>0}\setminus\{1\}$. The geometric input is an interpolation theorem for logarithmic jets at points with distinct multiplicative coordinates. Its successive weight thresholds are independent of the interpolation centres; the eventual degree threshold may depend on them. A local intersection-length bound and a curve inequality lead to surjectivity through a blow-up and Serre vanishing. For a fixed rational argument, this produces a nonzero rational determinant. Clearing denominators gives an arithmetic lower bound, while an exact row translation and repeated Taylor indices yield a contradictory analytic upper bound. The consequences include nonzero rational linear combinations of such logarithms, rational affine changes, and logarithms of positive numbers with a rational positive integer power. We also give a bounded-fibre interpolation extension, an explicit bound for the final analytic degree, and a counterexample to interpolation under the volume condition alone.

The radiation-ionic effect was recently reported in 3 mol% Gd-doped CeO$_2$ (3GDC): under $^{60}$Co gamma irradiation at 35 Gy/min, the grain-boundary (GB) ionic resistance of a bulk pellet decreased 680-fold at room temperature, because electrons trapped at the GB core lower the space-charge potential. The effect has been demonstrated only with photons. Gd has the largest thermal-neutron capture cross section of any stable element and is also the dopant that creates the GB barrier in GDC, so the same mechanism could link GB impedance to thermal-neutron sensing; whether it does, and under what conditions, has not been examined. Here the thermal-neutron response of 3GDC is modelled with the gamma-calibrated Mott-Schottky/Seager framework, with unmeasured parameters carried as intervals and propagated jointly. Each capture deposits about 50 keV by conversion and Auger electrons within 1 $\mu$m, the remaining 8 MeV leaving as prompt photons; Gd segregation to the GBs adds a factor of only 1-2 because the electron range exceeds the grain size. A thermal flux of $8\times10^{9}$ cm$^{-2}$s$^{-1}$ (6-12$\times10^{9}$) matches the GB-effective generation rate of the 35 Gy/min calibration, and the predicted room-temperature GB resistance ratio is 110 (70-170) at $10^{9}$ and 970 (600-1500) at $10^{10}$ cm$^{-2}$s$^{-1}$, falling to 2 at 61 (55-68) and 81 (73-92) $^\circ$C. The neutron case differs from gamma irradiation in three respects: capture events are discrete, so the continuous-source approximation depends on the unmeasured trapped-charge lifetime; self-shielding (mean free path 0.27 mm) makes the response thickness dependent; and capture photons absorbed in the pellet add a gamma term comparable to the local term for pellets of 0.3 mm or more. The intervals are conditional on the model and exclude its structural error. The conditions under which the prediction can be tested are given.

We analyze the first-order deterministic diffusion sampler of Karras et al. (2022), termed EDM, in 2-Wasserstein distance by separating two sources of error: local discretization error and its amplification by subsequent learned steps. We prove that local error admits a universal bound: for any data distribution with finite second moment, the one-step discretization error is quadratic in the step size, with an explicit constant that does not depend on the data distribution. Error propagation, in contrast, depends on the learned network. At high noise levels, we exploit the network parametrization of EDM to derive an explicit contraction criterion. At low noise levels, we measure propagation through the amplification realized on the distributions transported by the sampler; this realized amplification can be arbitrarily smaller than the worst-case Lipschitz constant. This analysis yields an $O(e^{\Lambda_K}/K)$ global discretization error for $K$ sampling steps, where $\Lambda_K$ is the low-noise log-amplification. Experiments on a one-dimensional Gaussian mixture show how measured amplification accounts for slower error decay on finite sampling grids. Diagnostics on a pretrained CIFAR-10 model illustrate related stability mechanisms without certifying the global assumptions.

Paying particular attention to the different types of gluons, collinear, soft and Glauber, we argue that, in its standard formulation, the CGC does not contain the collinear sector required for a meaningful comparison with TMD factorization. The CGC Wilson lines usually identified as part of the proton matrix element should instead be interpreted as the equivalent of a soft factor. Restoring the missing collinear exchanges, we obtain a new definition of small-$x$ PDFs from an explicit calculation of the DIS cross section using CGC Feynman rules. The resulting expression can be cast in a form resembling TMD factorization without being equivalent to it. Finally, we discuss the evolution of these small-$x$ PDFs with respect to the rapidity cutoff $\Lambda$ and the Bjorken variable $x_b$.

Let $n\ge2$, $0<s<1$, and $p,q>0$. We prove a Liouville theorem for the fractional Lane–Emden system \[ (-\Delta)^s u=v^p,\qquad (-\Delta)^s v=u^q, \qquad u, v>0 \qquad\text{in }\R^n. \] More precisely, we show that the system does not have a strictly positive entire solution whenever \[ \frac1{p+1}+\frac1{q+1}>\frac{n-2s}{n}. \] No radial symmetry, global boundedness, finite-energy assumption, or prescribed decay at infinity is required. Our proof adapts the localized potential-kernel virial and source-layer interval-pressure method recently introduced for the classical Hénon–Lane–Emden system. The basic reason the method also works in the fractional setting is simple: the Riesz kernel associated with $(-\Delta)^s$ has the same logarithmic derivative structure as the Newton kernel, with $n-2$ replaced by $n-2s$. However, two genuinely nonlocal points require special treatments. When $2s\le1$, the individual kernel-gradient terms are not locally absolutely integrable, so the two equations must be combined before the diagonal limit is taken. When $2s>n-1$, the kernel restricted to a line is not integrable at infinity, and the interval comparison must therefore be formulated using nonnegative extended integrals. After these issues are resolved, a localized virial identity, a one-dimensional interval-pair inequality, and an averaged source-layer estimate yield a universal local energy bound. The subcritical scaling then forces the same energy to diverge, giving the desired contradiction.

Split Gibbs sampling (SGS) is a popular framework for posterior sampling in Bayesian imaging inverse problems. It decouples a Gaussian data-fidelity term from a complex prior through an auxiliary variable, so the data variable is updated exactly and only the prior-side conditional is hard to sample. Existing samplers treat this conditional in one of two ways. Plug-and-play SGS runs a multi-step diffusion denoiser at every iteration, which is expensive and lacks non-asymptotic guarantees. Langevin-within-SGS takes cheap overdamped Langevin steps but needs many iterations. We propose RED-KLwSGS, which keeps the exact Gaussian update for the data variable and updates the auxiliary variable with underdamped (kinetic) Langevin diffusions driven by a one-shot denoising score, at the same per-iteration cost as Langevin-within-SGS. We prove non-asymptotic Wasserstein-2 convergence in continuous and discrete time for strongly log-concave priors. We also introduce Joint-RED-KLwSGS, which applies kinetic Langevin diffusions to both variables. Experiments with Denoising diffusion probabilistic models as diffusion priors on FFHQ and ImageNet datasets show faster convergence and high-quality image reconstruction.

Bayesian optimization (BO) is widely used as a standard approach for expensive black-box optimization. However, BO algorithms often involve parameters that must be specified in advance, and their performance can strongly depend on these choices. We propose a framework for optimizing such parameters using sample paths drawn from a Gaussian process (GP) inferred from the information available at the start of BO. We use cumulative regret as the performance metric for a BO algorithm. By running the BO algorithm on the generated sample paths, we obtain an empirical estimate of its expected cumulative regret for a given parameter configuration. Optimizing this estimate allows us to identify parameter configurations that, given the currently available information, are expected to achieve low cumulative regret. Since this parameter optimization is itself a black-box optimization problem, we employ another BO procedure to solve it, which we refer to as outer BO. Through experiments, we demonstrate that the proposed framework can effectively select parameter configurations that achieve strong performance among a range of candidate configurations.

Mediators coupled predominantly to the electron remain weakly constrained above the kinematic reach of the $B$~factories, a region that is difficult to access at hadron colliders and only partially covered by existing $e^+e^-$ data. We point out that the asymmetric $\mu^+e^-$ mode of the proposed $\mu$TRISTAN collider, operating at $\sqrt{s}=346$~GeV, is well suited to this window, and quantify its reach for two minimal realisations: an axion-like particle and a $Z'$ gauge boson, treated as effective interactions with the electron current. Both are radiated off the electron line and decay to an electron-positron pair, giving a common four-lepton signature whose Standard Model counterpart is under good control. A resonance search in the electron-positron invariant mass, performed for mediator masses between $5.5$ and $300$~GeV, yields projected $95\%$~CL sensitivities to couplings of order $10^{-5}$ at the light end of this range, improving on existing bounds by more than four orders of magnitude for the pseudoscalar and by up to two orders of magnitude for the vector, and providing the only constraint on the heaviest masses considered.

Developing optimization models for production scheduling requires substantial expert effort. Research on large language models (LLMs) has followed two directions: specialized approaches for automated modeling, mostly for mixed-integer linear programming, which often rely on dedicated training or problem-specific architectures that limit industrial deployment; and agentic artificial intelligence for operational decision support, which generally assumes that the optimization model already exists. This study bridges both directions by assessing whether general-purpose LLMs, orchestrated as agents without task-specific training, can formulate and implement constraint programming models from natural-language problem descriptions. Singleagent and multi-agent architectures are integrated with a Model Context Protocol server that provides context-aware retrieval of solver documentation to mitigate hallucinations during implementation. Both are compared with a direct LLM baseline on six industry-oriented problems covering flow-shop, job-shop, flexible job-shop and resource-constrained warehouse scheduling, using three LLMs and assessing modeling accuracy, execution success, latency and token consumption. Formulation proves largely within reach of current LLMs, whereas implementation is the main barrier. The multi-agent workflow raises the share of scripts that run correctly as generated from 14.8% with a direct LLM call to 59.3%, reaching 80.6% on the four less complex problems, while tightly coupled intralogistics models remain an open challenge.

Long video understanding increasingly relies on external memory to organize massive visual streams into compact representations. However, most memory-based methods dynamically adapt how information is retrieved for different questions, while largely fixing what is remembered. This mismatch makes missing details costly to recover, whereas stored information is valuable only when it can be reliably retrieved. To address this issue, we propose VideoEvolve, a novel self-evolving framework that jointly evolves memory and retrieval for long video understanding. Specifically, starting from a coarse low-frame-rate overview, VideoEvolve couples a Memory Evolver for selective memory augmentation with a Retrieval Evolver for adaptive retrieval over the evolving memory. We then co-evolve the two Evolvers through alternating agentic reinforcement learning (Agentic RL), updating one while freezing the other. To steer this alternating evolution, Bottleneck-Aware Evolution Feedback (BEF) identifies whether the current bottleneck lies in memory or retrieval and directs optimization toward the more limiting side. Furthermore, VideoEvolve introduces Capability-Aware Evolution Feedback (CEF) to alleviate downstream feedback from over-specializing memory to a fixed set of training questions, shifting training toward underdeveloped yet learnable video capabilities. By integrating Agentic RL with BEF and CEF, VideoEvolve transforms downstream reasoning experience into transferable capability updates, providing a concrete path from static long-video systems toward experience-driven, self-improving multimodal intelligence. Extensive experiments on multiple long video understanding benchmarks demonstrate the effectiveness of VideoEvolve.

AI-generated faces can be difficult to distinguish from real ones, leaving viewers to rely on source labels when judging an image. Yet prior work has made it difficult to separate the effects of what an image actually is from what viewers are told it is. We validated faces as AI-generated or human in an online study (N=169), then crossed actual source (AI, human) with label (none, Made with AI, Made by a human) in a lab study $N=30), recording event-related potentials (ERPs) and gaze. ERP responses were equivalent for AI-generated and real faces, but varied with the label: labels drew early attention (N2), while labels that conflicted with the face's actual source prompted re-evaluation of the face (P3). Affective processing and initial gaze orienting were unchanged, but labels altered visual exploration. We provide a validated stimulus set and evidence that attributed origin shapes face processing, with implications for disclosure design.

Robots operating in dynamic environments require reliable detection of how their surroundings change over time. Existing learning-based methods largely rely on pairwise 2D image features, which struggle under large viewpoint changes and occlusions, are sensitive to noise, and show limited generalization across domains, while explicit 3D approaches typically require costly offline optimization. We show that the implicit 3D knowledge of Geometric Foundation Models (GFMs) provides a strong basis for addressing these limitations. We introduce Argos, which adapts GFM features for joint scene change detection and 3D reconstruction. To address data scarcity and take a step toward a foundation model for scene change detection, we introduce a large-scale benchmark comprising two synthetic datasets and one real-world dataset, and train jointly across diverse datasets to improve cross-domain generalization. We further introduce Argos-SLAM, a real-time system designed for robotics, which performs online change detection and change-aware 4D mapping. Across benchmarks, our framework substantially outperforms existing baselines, with gains of up to 42.01% in change IoU and 27.91% in F1, while supporting scalable deployment in changing real-world environments.

This paper presents a fully actuated 4-DOF robotic finger using a joint-specific hybrid remote-actuation architecture. The metacarpophalangeal (MCP) joint is driven by two coordinated rigid-link transmission sets, whereas the proximal interphalangeal (PIP) and distal interphalangeal (DIP) joints are independently actuated by closed-loop wire transmissions incorporating circular rolling-contact joints (RCJs). A larger transmission radius is used at the PIP joint than at the DIP joint. The RCJ wire geometry maintains the total wire-loop length during joint rotation, and the DIP wire routing is designed so that PIP motion does not affect its differential actuation for a fixed MCP configuration. The distal wire transmission, MCP linkage, and fingertip kinematics are analytically modeled. In experiments, the transmission behavior was quantitatively evaluated from the ball-screw displacements measured using ArUco-marker tracking. MCP actuation produced measurable displacements of the PIP and DIP transmission units, whereas isolated PIP and DIP actuation with the MCP fixed supported the intended mechanical decoupling between the distal transmissions. The mean peak fingertip forces under isolated MCP, PIP, and DIP actuation were 21.28 N, 9.22 N, and 5.75 N, respectively. The resulting finger postures were also examined using objects of different geometries and sizes.

Search agents enable Large Language Models (LLMs) to iteratively retrieve and use information for complex multi-hop questions. Reinforcement Learning with Verifiable Rewards (RLVR) offers a promising approach for post-training such agents, but its reliance on sparse, outcome-based supervision can make credit assignment difficult and limit learning efficiency. In this paper, we systematically investigate how intermediate supervision can improve reinforcement learning for search agents. We study a range of reward-shaping and credit-assignment strategies that provide learning signals from intermediate retrieval steps. Building on these insights, we develop a training framework that combines intermediate signals with final outcome rewards to improve learning from multi-step search trajectories. Experiments across multiple benchmarks under matched training conditions demonstrate improvements in aggregate search-agent performance and show that both the choice of intermediate signal and where its credit is assigned affect training behaviour. These findings show that reward design and credit assignment are important design dimensions for training effective search agents.

Vision-Language-Action models are designed to generalise across environments and task descriptions, raising the question of whether their action generation actually depends on the language instruction, or whether they largely rely on visual cues and superficial correlations. Robustness to variance in the visual and linguistic observation space is critical for real-world deployment, yet VLAs lack explicit grounding modules and instead rely on the intrinsic language grounding capabilities of their Vision-Language model backbones. For this reason, we conduct a controlled mechanistic interpretability study on the language grounding capabilities of two state-of-the-art Vision-Language-Action models, $\pi_{0.5}$ and GR00T N1.7, by applying activation and attribution patching to the residual stream of the action generation modules. We systematically corrupt the task instruction of input samples of the LIBERO benchmark following five strategies: synonym replacement, semantic scaling, directional corruption, random object substitution, and empty string. Our experiments find that both models are comparatively insensitive to abstract rephrasing and to referencing non-existent objects, but react strongly to empty task descriptions and, especially, to directional language. During action generation, this sensitivity is concentrated in different loci for each model: mainly in the early, periodic cross-attention layers for GR00T N1.7, versus distributed across the earliest and selected later layers for $\pi_{0.5}$. For GR00T N1.7, directional perturbations drive some of the largest causal effects while leaving the internal representational geometry comparatively unchanged, a dissociation we do not observe clearly for $\pi_{0.5}$. Finally, the reliability of attribution patching is model-dependent: it closely tracks activation patching for GR00T N1.7 but not for $\pi_{0.5}$.

In this paper we study the least positive integer $G(n)$ such that the integers $a\leq G(n)$ with $(a,n)=1$ generate $(\mathbb Z/n\mathbb Z)^\times$. We prove that, for every $\varepsilon>0$, \[ \sum_{n\leq x}G(n)\ll_\varepsilon x(\log x)^{8/3+\varepsilon}, \] improving the previously known bound $\ll x(\log x)^{97}$. We also prove that $G(n)\leq(\log n)^2$ for almost all $n$, unconditionally. Thus, for almost all $n$, we obtain the same logarithmic exponent $2$ as in the classical pointwise bound under GRH.

The security of a secret sharing protocol is compromised if one or more dishonest participants can reconstruct the secret by deviating from the prescribed protocol, particularly when such malicious behavior remains undetected. Semi-Quantum Secret Sharing (SQSS) is a variant of secret sharing in which the participants possess only classical capabilities, such as preparing and measuring qubits in the computational ($Z$) basis, while a quantum-capable third party assists the dealer in generating and distributing quantum shares of a classical secret. The limited quantum capabilities of the participants in SQSS protocols may introduce vulnerabilities to collusion attacks, enabling an assisting quantum third party, in collaboration with a dishonest classical participant, to jointly recover the secret even without detection. In this work, we propose a novel SQSS protocol that eliminates this vulnerability and achieves information-theoretic security against collusion attacks. We further prove that the proposed protocol is secure against a broad class of external and internal attacks. Finally, a comparative analysis demonstrates that our construction advances existing SQSS protocols by simultaneously optimizing qubit efficiency, involves a classical dealer, and resilience against DCNA attacks using basic Bell states.

Optically exciting a typical low-dimensional semiconductor produces a nodeless \(s\)-type exciton as its lowest-energy bound state. Here, we explain how Coulomb phase matching stabilises a quantum-vortex exciton as the lowest bound state in flat Chern bands. Using a prototypical Yin–Yang kagome lattice, we demonstrate that increasing the spin–orbit coupling drives a transition of the lowest exciton from a quantum-vortex state to a zero-winding state, while leaving the band Chern numbers unchanged. We trace this behaviour to a gauge-invariant combination of exciton phase differences and Bloch-overlap phases that can reduce the Coulomb energy. By comparing states with identical wavefunction amplitudes, we isolate this phase contribution and show that it is sufficient to drive the reversal in exciton ordering. We classify exciton topology by the momentum-space wavefunction winding relative to the conduction–valence Chern-number difference,connecting the competing states to circular-polarisation selection rules. We then show that the resulting reordering can be tracked directly in the optical absorption spectrum, through the transition from a dark vortex exciton to a bright zero-winding exciton. These findings establish a microscopic link between exciton topology, Coulomb binding, and optical response that extends beyond the information contained in the underlying electronic band Chern numbers.

Bayesian optimization often involves multiple objectives, constraints, and fidelity levels. We address the challenge of jointly selecting where and at which fidelity to evaluate to identify the highest-fidelity feasible Pareto frontier in this combined setting. From a unified information-theoretic perspective, we measure query utility by the information gain about this frontier, provided by an observation. Since this mutual information is intractable, we derive a variational lower bound using a mixture of under- and over-truncated approximations to the Pareto-consistent region. Multi-fidelity surrogate models propagate the information to arbitrary fidelities, yielding a cost-aware acquisition function without separate heuristics for fidelity selection or constraint handling. Experiments on synthetic, benchmark, and real-world problems demonstrate effectiveness across diverse objective, constraint, and fidelity settings.

Personalized news platforms are often evaluated as if stated preferences, logged recommendation exposure, and click consumption form a single coherent pipeline. Collapsing these layers can distort audit conclusions: a platform may appear more aligned or diverse than observed click consumption supports, which can misdirect diversity governance or algorithmic intervention. We introduce a reusable Preference-Exposure-Consumption (PEC) audit framework that separates stated preference, observed weighted profile state, logged recommendation exposure, app-surface pathways, and click consumption under explicit observability boundaries. Using six months of logs from a deployed mobile news application, we audit 1,583 user profiles, 95,143 logged recommendation items, and 17,512 click events. Each trace type contributes distinct information; none directly substitutes for another. Preference-consumption alignment exceeds chance-based null baselines but captures only part of users' top-consumed category set. Logged recommendation lists contain clicked articles more often than a date-matched candidate-pool baseline predicts (11.29% vs 9.13%; top-5 lift 1.47x), but many clicks arrive through other app surfaces. Raw exposure-consumption diversity gaps shrink under count matching, yet concentration mismatch persists in the audit-eligible cohort (HHI gap 0.082). Together, the results show that audit conclusions change depending on whether platforms measure stated preference, logged exposure, or click consumption.

We take a revealed-preference approach to study the welfare effects of price discrimination. An analyst observes price and quantity data before and after a monopolist segments the market. The analyst knows neither the aggregate demand curve nor the information available to the monopolist. We characterize the set of observable price-quantity pairs that are rationalizable by some market segmentation. We then obtain sharp bounds on the change in consumer surplus arising from some segmentation. Finally, we provide conditions under which the data identifies an unambiguous increase (decrease) in consumer surplus.

The stability of the Berezinskii–Kosterlitz–Thouless phase against long-range interactions remains an open problem. We address this question in the two-dimensional XY model with couplings decaying as $r^{-2-\sigma}$, by developing a real-space renormalization-group treatment near the Gaussian manifold of quasi-long-range ordered (QLRO) states. We retain the full many-body vortex interaction and show that, at leading order in the fugacity, screening by small vortex–antivortex pairs preserves its Gaussian-average representation without an expansion in the long-range coupling. Including spin waves perturbatively then yields a local stability criterion: a stable QLRO interval exists only for $\sigma>7/4$. We also investigate a Wilson–Fisher-like fixed point at finite coupling for $\sigma<7/4$, for which the retained flow predicts $\nu^{-1}\sim\sqrt{7/4-\sigma}$ as it merges with the Gaussian line.

Retrieval-augmented generation systems increasingly rely on document-structure treatments: structure-aligned chunking, LLM-generated chunk contexts, heading-path metadata, and hierarchical two-stage retrieval. Separate studies support each on different corpora, embedders, and metrics, and none control for a shared confound: any text prepended to a chunk perturbs its embedding. We present a mechanism-isolating ablation testing all four treatments under one protocol, matching chunk sizes across conditions and adding a semantically null placebo—heading paths that are structurally valid but shuffled across documents. We score retrieval with a coverage-aware nDCG and test four pre-registered contrasts via document-clustered bootstrap with Holm correction, on two distant corpora: 200 Wikipedia Featured Articles (951 queries) and 1,585 QASPER papers (4,303 questions). Organization helps, and the cause is content, not tokens: structure-aligned chunks with real heading paths beat contextualized fixed windows (+0.022 / +0.012 cov-nDCG@10) and the placebo (+0.010 / +0.016). Naive two-stage hierarchical retrieval hurts (-0.033 / -0.015), traceable to first-stage section recall. Gold structure beats LLM-induced structure on Wikipedia but not on QASPER. Effects are small ($dz$ 0.06-0.11) but Holm-significant and consistent across corpora.

We construct unitary, local, 3+1-dimensional conformal field theories with finitely many fields whose thermal state breaks a continuous global symmetry at every temperature. They are finite-$N$ versions of the Chaudhuri–Choi–Rabinovici theories, whose planar circle of fixed points has an ordered arc. The circle is lifted at order $1/N^2$, and an infinite family of fixed points on this arc reaches arbitrarily weak coupling, where the superfluid is under parametric control. We also show that weakly gauging the symmetry gives a superconductor over an exponential range of temperatures.

Split conformal prediction uses prediction errors on held-out (calibration) data to determine how wide the prediction intervals should be. It guarantees distribution-free finite-sample coverage when these errors and the error at the target site are exchangeable. This assumption may fail under spatial dependence and nonrandom sampling geometry. Existing spatial methods use fitting residuals to remove the predictable part of spatial variation from calibration and target errors. However, the spatial variation that only the calibration residuals can predict remains in both the target and calibration errors, reducing the efficiency and stability of the interval. We address this by additionally conditioning on the calibration residuals sequentially, which scales to large networks through nearest-neighbour approximations. Under a correct working covariance and an elliptical residual law, the resulting interval has exact finite-sample coverage under any spatial design, and under further conditions it is asymptotically oracle efficient. We also bound coverage loss under covariance misspecification and develop a diagnostic that identifies regions at risk of undercoverage. In simulated data, our method produces narrower and more stable intervals than global and localized state-of-the-art alternatives. In a national PM2.5 application, it produces narrower intervals within the network and identifies regions at risk of coverage failure.

Policy learning in digital experimentation faces three challenges: weak signal-to-noise ratios, rich covariate spaces, and massive data volumes. We formalize this regime by modeling treatment-effect estimates from increasingly fine covariate partitions as Gaussian observations with bounded signal-to-noise ratios. We establish that, in general, the optimal treatment policy is not learnable in this setting. Even learning the optimal policy value suffers from impractically slow rates. However, when treatment effects vary smoothly, we derive minimax-adaptive policies based on linear smoothers that achieve vanishing welfare regret. We demonstrate the practical value of our framework by applying it to large-scale real-world experiments at Netflix, showing that personalized linear-smoothing policies can dominate unpersonalized policies even in this challenging empirical setting.

We consider the Dirichlet problem for the Lorentz–Minkowski mean curvature operator in a radial setting, $$ -\operatorname{div}\left(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\right) = \lambda u + \mu g(u) \quad \text{in } \mathcal B_R, \qquad u = 0 \quad \text{on } \partial\mathcal B_R, $$ on a ball of radius $R$ centered at the origin $\mathcal B_R \subset \mathbb{R}^N$, where $\lambda, \mu \geq 0$ are parameters, and the nonlinearity $g$ satisfies suitable growth assumptions at zero. We first prove an a priori dichotomy for the asymptotic behaviour, as $\mu \to +\infty$, of solutions with a prescribed number of zeros: either they converge uniformly to $0$, or they converge to a piecewise affine limit function $u_\infty$, with $|u_\infty'|=1$ a.e., having the same nodal properties. We then show that, when the number of zeros is appropriately prescribed, both alternatives are actually realized. More precisely, building on the multiplicity result in [A. Boscaggin, F. Colasuonno, and R. Ziegele, Positive and nodal solutions for the Minkowski mean curvature equation: multiplicity and asymptotics, arXiv:2607.15956 (2026)], we refine the shooting construction therein to obtain a family of small solutions converging to zero and, through a backward shooting argument, a family of large solutions converging to a saturated piecewise affine profile.