Papers

We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing/decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number Rm$_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations/wavenumbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating B$_{\phi}$ from B$_r$. We calculate the expression for the growth rate in the limit of large Rm$(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times Rm$^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.

Let $z_{n,j}(\lambda)$ denote the positive zeros, in decreasing order, of the ultraspherical polynomial $C_n^\lambda$, $\lambda>-1/2$, with the reduced limiting interpretation at $\lambda=0$ specified below. Our principal result settles three higher-monotonicity questions of Gautschi: two as printed and the natural open-interval form of the third, whose printed endpoint $\lambda=0$ is singular. For every $n\geq3$, $$ \sqrt{\lambda+1}\,z_{n,j}(\lambda) $$ becomes a complete Bernstein function after translation of its parameter interval to $(0,\infty)$. For every $n\geq2$, $$ \sqrt{\lambda}\,z_{n,j}(\lambda) $$ is a complete Bernstein function on $(0,\infty)$. For every $n\geq4$, the largest-zero trajectory $$ \sqrt{\lambda+\frac{2n^2+1}{4n+2}}\,z_{n,1}(\lambda) $$ has the same property, whilst for every other positive zero the derivative of this scaling fails to be completely monotone. Separately, an exact calculation in degree $4$ provides a counterexample to a fourth conjecture of Gautschi, concerning the linear scaling $\lambda z_{n,j}(\lambda)$.

Let $1 < \rho < n$ and let Omega be in $L^\rho(S^{(n-1)})$ with vanishing mean. We prove that the maximal truncation $T^*_\Omega$ of the rough singular integral $T_\Omega$ is pointwise dominated by finitely many sparse potentials of the form: $\sum_{Q \in S} l(Q) * ( (1/|Q|) * \int_Q |\nabla f|^p )^{1/p}$, where $1/\rho~ = 1/\rho' + 1/n$ and $\rho~ \leq p < n$. This estimate is uniform in the truncation parameter and extends the subcritical bound of Hoang, Moen, and Perez for $T_\Omega$ to $T^*_\Omega$. Since the argument does not require the boundedness of $T^*_\Omega$ on the target space, it yields two-weight Sobolev inequalities: $\parallel T^*_\Omega f \parallel L^q(u) \leq C * \parallel \nabla f \parallel L^p(v)$, under joint two-weight conditions, while the target weight u itself is only required to belong to $A_\infty$. Additionally, we prove a Hedberg-type estimate involving a Morrey norm of the gradient and apply it to weighted grand Lebesgue spaces. Further consequences are obtained in weighted Lebesgue, Orlicz, and variable Lebesgue spaces.

(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.

Whether human or large language model (LLM), an agent in a discussion reads only a few of the others' contributions, bounded by cognition, context, or cost. LLM collectives can settle on a wrong consensus even when a majority starts out correct; we ask how far that reading bound alone decides the outcome. We model the bound with one number, the message capacity, which sets how many of the others' messages an agent reads, and generate the communication network from it. Over 31,824 randomized queries, we found that an 8-billion-parameter model's judgment of a claim effectively reduces to a logistic function of a weighted sum of its inbox, the update rule of a stochastic binary neuron with divisively normalized weights. From these weights and the network's degree statistics alone, the wrong consensus should become unreachable from any start once agents read, on average, fewer than 6.4 of their 31 sources. In 1,414 episodes with assigned starts the prediction failed: the correct side won in fewer than 50% of episodes from every start, and in only 28-45% when 75% of agents started correct. The failure traces to the field, the threshold that a claim's wording sets for the agent's answer before any message is read: the experimental claims' fields lay below the calibration mean, and with each claim's own field the same weights reproduce the outcomes. Reversing the wording showed that the threshold follows what a claim asserts, not whether it is true. On a second 8B model the pipeline predicts claim-dependent bistability; transition points appeared where computed, and an eight-claim calibration matched in 15 of 16 conditions. At 70B the assertion bias is not detected. Thus a collective's fate is largely set by two single-agent measurements: the threshold a claim's wording sets, and the message capacity that sets the transition point.

Benchmarks are central to how progress in large language models (LLMs) is assessed and communicated. Yet model rankings alone reveal little about how evaluation requirements themselves are changing. The expanding variety of benchmarks offers another perspective: what researchers expect LLMs to do, and what they count as successful performance. We systematically map 14,767 papers introducing or updating evaluation resources from arXiv submissions between January 2022 and August 2026. Using staged screening and automated full-text coding, we examine changes in target systems and domains, evaluation materials and conditions, and scoring mechanisms. The collection shows growing emphasis on action, interaction, and professional applications, while established and newer design elements frequently coexist. Model participation also develops unevenly: LLM-based scoring grows within both agent and non-agent groups, whereas model-generated materials show no comparable sustained increase in recent cohorts. These findings illuminate how public research translates capability expectations into concrete tests and criteria for success. As AI participates in constructing tests, performing tasks, and judging responses, they also raise a question: does expanding evaluation provide more independent evidence, or risk reproducing the preferences and blind spots of its participating models?

We consider interaction functionals of the form \begin{equation*} \nu\mapsto {\mathscr E}(\nu)=\int\_{{\mathbb R}^N}\int\_{{\mathbb R}^N} W(x-y)\intd\nu(y)\intd\nu(x)+\int\_{{\mathbb R}^N} V(x)\intd\nu(x)\text{,} \end{equation*} involving an anisotropic kernel $W$ and a general confinement potential $V$. Under standard assumptions on $W$ and its Fourier transform, we show that the minimizer of ${\mathscr E}$ has $L^2$ density. Our argument relies on a careful analysis of nonlocal variational inequalities, which may be of independent interest.

Language models face unique challenges in analyzing interdisciplinary scientific research literature. In biophysics research, faithful answers require grounding observed data in source evidence, interpreting it through a quantitative physics model, and linking it to a biological mechanism. To address this challenge, we introduce BioPhys-Bridge, a novel benchmark dataset for evidence-grounded scientific reasoning over biophysical literature. Each case contains evidence blocks, stable evidence IDs, quantitative values, units, equations, assumptions, mechanisms, and next decisions as grounding targets for question answering (QA) and retrieval-augmented generation (RAG). The initial release contains 500 cases, 1,517 agent-facing tasks, and covers six biological domains and nine physical model families, including three sparse families reserved for future expansion. We enforce strict quality gates for all cases in schema, evidence-integrity, quantitative-grounding, source-license, duplicate, unit-normalization, with domain expert review and annotation for 81 cases. Preliminary evaluations show that DeepSeek-V4-Flash obtain the highest evidence-ID $F_1$ score (0.360), followed by Qwen3.7-Max (0.316) and GPT-4o-mini (0.294). BioPhys-Bridge is an interdisciplinary benchmark for evaluating attribution, faithfulness, hallucination reduction, and biological experiment design with complex, multi-step scientific reasoning. Future works will increase the size and complexity of the dataset and perform comprehensive evaluations. Code and data are available in the GitHub repository and on Hugging Face.

In the current context of energy and climate transition, the preventive conservation of historic buildings is particularly important due to their impact on architecture and works of art. Establishing the correlation between environmental variables and the condition of artworks in situ requires comprehensive and individualized monitoring, allowing for an understanding of cause-and-effect mechanisms. To address this challenge, the EPICO method provides a systematic framework for assessing deterioration risks in palace-museums through multi-scale monitoring and correlation between environmental parameters and object condition. The aim of the proposed topic is to enhance this decision-making tool with the creation of digital twins. These digital twins being fed with three-dimensional hyperspectral and LiDAR mapping of spaces and objects.

Magnetic resonance imaging (MRI) is among the most energy-intensive medical imaging modalities. To facilitate the development of more energy-efficient MRI protocols and sequences, we developed an interpretable data-driven deep learning (DL) framework to characterize the factors driving energy and power consumption. The aim was to identify the most influential acquisition parameters and their interactions on MRI energy and power demand, and to prospectively predict energy and power consumption on a per-sequence level. Two separate DL models were trained to predict energy and power consumption from MRI acquisition parameters. Attention weights were analyzed to identify the most influential parameters and their interactions. The proposed DL models successfully captured the variability in the data (energy model: $R^2 = 0.963$, power model: $R^2 = 0.843$). Energy was primarily driven by temporal parameters, whereas power depended on more complex sequence, gradient, and RF-related interactions. These results demonstrate that energy and power consumption can be accurately predicted from MRI acquisition parameters alone. The proposed framework reveals that a small subset of parameters governs energy and power demand, providing interpretable insights to support the development of more energy-efficient scanning protocols and sequences.

For integers $n,r,t$ with $2\le t\le r-1$, let $f(n,r,t+1)$ denote the largest possible minimum degree of a balanced $r$-partite graph with parts of size $n$ and containing no copy of $K_{t+1}$. Lo, Treglown and Zhao identified $f(n,7,4)$ as the only remaining case in their treatment of the $K_4$-free family. I determine this function for every $n\ge1$. First, the corresponding three-colourable extremum $\delta(n,7,3)$ is reduced to a $7\times3$ integer matrix problem and determined exactly. Second, a structural argument shows that every balanced $7$-partite $K_4$-free graph $G$ with $\delta(G)>\frac{132}{31}n$ is three-colourable. Consequently, $f(n,7,4)=\lfloor30n/7\rfloor$ except when $n\equiv4\pmod7$ and $n\ge11$, where it is one less.

Multi-organ segmentation is often challenged by partially annotated datasets and domain shifts across different imaging sources. To address these limitations, we propose a two-stage learning framework that efficiently leverages partial supervision. In the first stage, the model learns from available annotations to produce accurate segmentations of annotated organs, establishing robust feature representations. In the second stage, we introduce learnable organ prototypes and a Sinkhorn-triplet loss to enforce organ-wise feature consistency across datasets. This encourages latent embeddings of the same organ to remain close, while increasing separation between different organs, even when annotations are missing. Our approach achieves performance comparable to state-of-the-art methods on the BTCV dataset, while remaining computationally efficient. By explicitly aligning feature distributions rather than relying solely on pseudo-labels, the framework effectively mitigates domain shift, making it particularly suitable for medical image segmentation tasks with limited annotation resources.

We study single-particle Penrose extraction from a rotating black hole whose mass decreases in time, described by the ingoing Kerr-Vaidya metric, imposing exact four-momentum conservation at the decay. We prove that the local efficiency is bounded by the instantaneous Kerr value, through a covariant bound that reduces to the Bardeen-Press-Teukolsky limit at the horizon, and we derive an exact transport law, dE/dtau = -dm/dt (r/Sigma) p_r^2 for fixed spin parameter, by which every timelike geodesic gains energy while the hole loses mass. The net energy gain therefore splits into a local Penrose term and two transport terms, which we compute numerically as functions of spin and mass-loss rate for two mass-loss laws. With fixed spin parameter, extraction is possible only below a critical rate alpha_crit(a) = (M-a)/Delta v, set by the approach of the hole to extremality; with fixed a/m no such boundary exists. The transport law extends to the Kerr-Newman-Vaidya family, and the regime where the dynamics matter is shown to lie far outside astrophysical mass-loss rates.

Sparse mixture-of-experts models route each token through a sequence of expert selections. We ask whether the immediately preceding selection adequately summarizes this trajectory for predicting the next router. Using frozen OLMoE and JetMoE models, we measure the held-out predictive gain from earlier expert selections while retaining the most recent selection as a common baseline. In OLMoE, extending the history from one to eleven layers raises router-logit $R^2$ from 0.59879 to 0.66544. A preregistered JetMoE replication yields four-layer gains of 0.14275 and 0.20528 at two target depths, with paired bootstrap intervals above zero. These gains survive nonlinear decoding: adding history to a small multilayer perceptron improves $R^2$ by 0.17137 and 0.21861, whereas nonlinear decoding of the recent state alone adds 0.00139 and 0.00936 over a linear probe. Parameter-matched controls preserve the advantage, and cross-fitted history residuals predict target residuals with $R^2$ of 0.20549 and 0.23556. These findings identify residual predictive structure in expert-selection trajectories beyond adjacent-layer persistence.

Exploiting the equality restrictions that nested Markov models encode requires their tangent-space geometry. For strictly positive finite-state models on arbitrary acyclic directed mixed graphs (ADMGs), we differentiate the recursive-head chart and prove that the range of its score map is the full tangent space. Intrinsic-set coordinate blocks form an algebraic direct sum, blocks of distinct districts are orthogonal, and the resulting Gram projection needs neither mb-shieldedness nor a district order. Exact counterexamples show that observational centering and kernel normalization alone do not certify tangency. For the node, complete-source edge, and compatible path-specific intervention targets considered here, boundary substitution yields a normalized configured active law and an order-free canonical-gradient formula, extended to finite mixtures by independent source redraws. A coherent one-step estimator with an exact remainder identity and a model-valid chart-flow targeted maximum likelihood estimator are efficient under stated local conditions. On a narrower source-isolated fixed-node subclass, a sequential estimator has an exact transition-factorized drift and up to $2^m$ nuisance-correctness regimes over $m$ active-district transitions; its all-correct influence function projects onto the canonical gradient, and an exact rational law exhibits a strict variance gap. These results separate order-free efficiency on arbitrary finite-state ADMGs from multiple robustness of a narrower construction.

The classic theory of Landau damping requires the velocity distribution function (VDF) to be analytically continued into the complex plane, implicitly requiring analyticity, which imposes constraints far more severe than infinite smoothness. Yet physical plasmas—encountered in discrete simulations, noisy spacecraft measurements, or truncated fusion distributions—are inherently non-analytic. This discrepancy poses a foundational “smoothness paradox”: why does Landau damping robustly persist in systems where the mathematical prerequisite of analyticity is profoundly violated? Here we resolve this paradox by demonstrating that wave-particle interaction is governed by a time-dependent resonance width $\Delta v_\mathrm{res}\sim 1/kt$. Using a dispersion-free Lagrangian time-domain solver, we show that this finite width kinematically coarse-grains microscopic VDF defects at early times, acting as a natural low-pass filter that validates smooth analytical proxies—explaining the observed robustness. However, as $t\to\infty$ the resonance width narrows, inevitably forcing the wave to resolve exact topological non-smoothness. This late-time resolution triggers three distinct breakdowns: VDF truncation arrests the resonant phase transition to yield undamped discrete Van Kampen modes; observational noise induces transient algebraic spikes via linear phase-space aliasing; and step-like gradients drive anomalously violent reactive instability growth. We establish the breakdown timescale $t_b\sim 1/k\delta v$, where $\delta v$ is the characteristic scale of the non-smooth defect, providing a quantitative criterion that redefines the validity boundaries of analytic continuation in kinetic theory.

The kinetic Motsch-Tadmor (in short, KMT) model is a kinetic flocking model with a normalized communication weight. In this paper, we study the emergent dynamics of the phase-spatially extended KMT model. We first establish a global well-posedness theory in the fully noncompact spatial-velocity setting. To this end, we introduce a direct Lagrangian formulation in which the unbounded part of the initial velocity distribution is separated from an interaction-generated bounded remainder. This decomposition allows us to construct global Lagrangian weak solutions without truncating the velocity distribution and to propagate finite phase-space moments. We then investigate the long-time collective behavior of the resulting solutions. When the initial velocity support is compact while the spatial support is allowed to be noncompact, a time-varying effective-region argument yields a uniform contraction mechanism for the normalized interaction and leads to exponential weak support flocking. When both the spatial and velocity supports are noncompact, support-level flocking is in general impossible. Nevertheless, the same effective-region mechanism, combined with the Lagrangian decomposition and a bootstrap argument for the interaction-generated remainder, yields exponential weak moment flocking. In particular, pairwise spatial moments remain uniformly controlled while velocity fluctuations converge exponentially to zero. These results provide a unified framework for the well-posedness and flocking dynamics of the KMT model beyond the compact-support regime.

In this work, benefiting from the increased sample of neutron stars with measured masses and radii as well as the incorporation of the chiral effective field theory and perturbative QCD constraints, the tidal parameter $\kappa_2^T$ is constrained to be $78^{+17}_{-11}$ (68.3% credible interval, mainly adopted in this work unless mentioned specifically) for the binary neutron stars involved in GW170817. Such a $\kappa_2^T$ is in favor of strong gravitational wave radiation in the post-merger phase and the corresponding energy is estimated to be $E_{\rm GW,p} \simeq 0.051^{+0.022}_{-0.017}\,M_\odot c^2$. Assuming the remnant from binary neutron star merger is a supramassive neutron star, as suggested by the modeling of the electromagnetic counterparts of GW170817, we examine the maximum mass of nonrotating neutron stars ($M_{\rm TOV}$) while accounting for the uncertainty in the remnant's lifetime ($t_{\rm c}$). Our results show that $M_{\rm TOV}$ varies from $2.09^{+0.11}_{-0.09}\,M_\odot$ for $t_{\rm c}=0.1$ s to $2.18^{+0.10}_{-0.09}\,M_\odot$ for $t_{\rm c}=1$ s. This result is consistent with that independently inferred from the re-construction of the equation of state of neutron star matter, i.e., $M_{\rm TOV,exc}=2.16^{+0.10}_{-0.07}M_\odot$, particularly if the very massive neutron stars with masses measured indirectly have been removed in constructing the prior distribution of $M_{\rm TOV}$. The consistency of the maximum mass of nonrotating neutron stars found in different approaches suggests a reasonable understanding of this key parameter for dense-matter physics.

The LUX-ZEPLIN experiment reported a candidate nuclear recoil at $248\,\mathrm{keV}$. This work proposes that endothermic self-scattering $\chi_1+\chi_1\to\chi_2+\chi_2$ in the Galaxy can produce an excited dark matter population, whose exothermic scattering $\chi_2+\mathrm{Xe}\to\chi_1+\mathrm{Xe}$ in xenon can account for the LZ candidate event. In a benchmark with a light scalar mediator, the conversion cross section is large enough for high-velocity Galactic dark matter particles to generate an excited fraction at the percent level. For dark matter masses near the TeV scale and mass splittings $\delta\gtrsim 500\,\mathrm{keV}$, the xenon recoil spectrum covers the candidate region and can yield an $\mathcal O(1)$ event count. The $\chi_2$ population produced in the Galaxy is colder than a relic population from the early Universe and yields a different nuclear recoil spectrum.

Non-ionizing radiation is the subject of several applications, such as the microwave oven, which is very popular. Its use is characterized by direct user operation and reduced distances between users and the NIR source. Therefore, the level of human exposure in this scenario deserves attention as it is a potential cause of biological effects. In this sense, this paper presents the measurement of a microwave oven with a high level of NIR (above the limit defined by the standard) before and after two types of suggested repairs: the use of epoxy putty (Repair 1) and the replacement of the external surface of the oven (Repair 2). The definitions of measurement methodology, based on FDA and INMETRO standards, are presented and discussed. Finally, we describe an analysis of the efficiency of these repair methods aiming at the safety operation.

In conflict and disputes, especially, emotion acts as a salient force in influencing outcomes. Prior work shows negative affect can obstruct collaborative behaviors, which typically lead to “win-win” outcomes. Thus, some suggest mediators may help regulate emotion and achieve joint gains. With the proliferation of AI, we posit LLMs may perform well at this task, with the added benefit of better accessibility compared with a human mediator. To examine the effectiveness of AI versus novice human mediators, we conduct a between-subjects experiment, where participants engage in a dispute mediated by a human, AI, or no mediator. We first analyze how well the mediators regulate emotions within a dispute – finding AI mediators perform significantly better than humans at reducing negative emotion. We next examine whether AI mediators facilitate disputants better realizing joint gains in disputes with high integrative potential (IP) – we find a marginally significant interaction between IP and condition (AI versus human), indicating LLMs may outperform humans at aiding disputants realize joint gains. Lastly, we perform an analysis of the messages the mediators sent, finding the AI sent significantly more messages suggesting trade-offs compared to the humans.

The demand matching problem generalizes both the knapsack problem and the $b$-matching problem. In this problem, each edge of a graph has a demand and a weight, and each vertex has a capacity. The goal is to find a maximum weight subset of edges such that, at each vertex, the total demand of the incident selected edges does not exceed the vertex capacity. Parekh [IPCO 2011] proved that, if each edge is individually feasible, the natural LP relaxation for demand matching has integrality gap at most $3$, yielding a $3$-approximation algorithm. This bound is tight for the natural LP relaxation, matching the lower bound of Shepherd and Vetta [Math. Oper. Res. 2007]. We present a randomized $(3/2 + \sqrt{2} + \varepsilon) \approx (2.914 + \varepsilon)$-approximation algorithm for the demand matching problem for every $\varepsilon > 0$, giving the first approximation ratio strictly better than $3$. For bipartite graphs, we obtain a randomized $(2 + \varepsilon)$-approximation algorithm for every $\varepsilon > 0$. Both algorithms run in time polynomial in $1/\varepsilon$ and the input length. Our algorithms use a strengthened LP relaxation based on intersecting the integral knapsack polytopes associated with the vertices, together with a multiple-choice generalization. As a key ingredient, we prove the existence of a $(q, 1/(1+q))$-balanced contention resolution scheme for the integral knapsack polytope for every $q \in [0, 1]$, which may be of independent interest. The balance guarantee $1/(1+q)$ is tight in the worst case over all knapsack instances.

We study the radical and screen distributions of a lightlike hypersurface of an indefinite statistical manifold with respect to the induced connections arising from the ambient dual affine connections. Necessary and sufficient conditions are obtained for each distribution to be parallel with respect to both induced connections. These conditions are expressed through the screen shape operators, the local screen fundamental forms, the mean induced connection, and the tangential difference tensor. When both distributions are parallel, we characterize the screen projection and obtain a block decomposition of the tangential difference tensor, whose mixed radical-screen part vanishes. We also obtain equivalent conditions for the induced connections to be metric connections. In the metric case, the induced screen connections coincide with the Levi–Civita connection on each integral manifold of the screen distribution, and the curvature tensors of the three induced connections agree on screen directions. We further determine the action of these curvature tensors on the radical direction. An explicit example shows that both distributions may be parallel although neither induced connection is a metric connection and their curvature tensors need not vanish.

As AI agents take on long, autonomous tasks, we increasingly oversee rather than perform the work, yet we still judge them almost entirely by whether they finally succeed. An outcome cannot reveal where a run went wrong, whether the agent recovered, or the irreversible harm it caused along the way, and where long-horizon agents fail remains unmapped. We study $2518$ agent trajectories across software engineering, computer use, and science, close to real deployment, and classify $6967$ mistakes into $78$ failure types. Failure follows a recurring signature: after its first mistake an agent often fails to recover and rarely catches the error itself, so the run continues unchecked while still looking correct; whether an agent recovers depends on the task and the environment's feedback, not on the agent framework running it. Long-horizon agents can do real harm on the way to a passing result: even runs scored as solved delete data, corrupt systems, or fabricate success rather than earning it. We release these human-verified annotations as Traverse, a benchmark on which six frontier judges struggle to locate failure regardless of scale: even the strongest correctly identifies the first mistake in fewer than a third of runs. Yet Scout, a $4$B verifier we trained, locates failure far better than these judges and transfers to domains it never saw. Used at test time to select among an agent's candidate runs, it raises task success above the agent's own single-attempt performance, without retraining the agent. By making failure cheap to locate and correct, this work is a foundation for more trustworthy long-horizon agents that learn from their own mistakes, and a practical path to overseeing increasingly autonomous AI.

Accurate seafloor mapping is essential for marine science, archaeology, and environmental monitoring. However, integrating data from different sensors, such as side-scan sonar and optical cameras, collected across separate survey sessions, remains challenging due to positioning drift and sensor offsets. This paper presents a multi-session, multimodal underwater mapping framework based on factor graph optimization. The method jointly optimizes vehicle trajectories, 3D landmark positions, sensor extrinsics, and per-session global alignment transformations. By combining rigid inter-session corrections with local trajectory deformations, it compensates for both inter-session offsets and intra-session distortions from accumulated navigation errors. The proposed methodology was validated on real-world datasets collected along the Catalan coast. Results show measurable improvements in map consistency over both unoptimized and rigid-alignment baselines across all metrics, including Pixel Accuracy and mean Intersection over Union. The method achieves a 3.4% improvement in pixel accuracy over the unoptimized baseline, corresponding to improved semantic labelling across approximately 14700 $\text{m}^2$ of mapped area. Qualitative results further show consistent co-registration between sonar and optical maps, even in the presence of significant trajectory distortions and inter-session misalignments. These findings demonstrate the potential of the proposed framework to generate coherent multimodal seafloor maps from heterogeneous underwater surveys.

Primordial black hole dark matter is formed from the collapse of enhanced primordial density fluctuations. The formation of primordial black holes is accompanied by scalar induced gravitational waves whose infrared scaling only depends on the equation of state, $w$, of the background at leading order. Establishing whether this characteristic scaling remains robust under corrections of arbitrary perturbative order, including in the presence of non-Gaussianities, requires a physical understanding of the infrared scaling. In this work, we provide such a physical interpretation. We find that the stress of sound waves with nearly equal frequencies produces a slow beat. Although the incoming waves oscillate rapidly, this slow beat continues to source the long wavelength tensor perturbation before its horizon entry, thus generating an infrared scaling that only depends on the expanding background. We show that higher order interactions generate freely propagating waves that finally lead to the same slow beat deep inside the horizon. Since non-Gaussianities would not change the speed of the freely propagating waves, they do not modify the infrared scaling. As the source with a slow beat has enough time to accumulate before the horizon entry of the infrared tensor mode, it records the background expansion and thus the infrared scaling could provide a robust probe of the cosmological equation of state.

This paper proposes a deterministic bilevel optimization framework for the coordinated operation of Virtual Power Plants (VPPs) embedded in an active distribution network. The Distribution System Operator (DSO) acts as the upper-level leader, minimizing a weighted combination of expenditure, active losses and voltage deviation subject to nonlinear AC power flow constraints, while each VPP operates as a lower-level follower that maximizes its profit under the uniform price signal issued by the DSO. Unlike most existing formulations, which linearize the lower-level subproblem to obtain a Mixed-Integer Linear Program (MILP), the proposed model retains the full AC Optimal Power Flow (AC-OPF) equations, producing a bilevel Mixed-Integer Nonlinear Program (MINLP). The lower-level problem is replaced by its Karush-Kuhn-Tucker (KKT) optimality conditions and the Strong Duality Theorem, yielding a single-level Mathematical Program with Equilibrium Constraints (MPEC). Complementarity conditions are then linearized via the Fortuny-Amat big-M transformation. The framework is validated on the IEEE 33-bus feeder over a 24-hour horizon, with four distributed resources aggregated into a single VPP. Compared with individual dispatch against a regulated time-of-use tariff, aggregation reduces active losses by 10.5 %, the accumulated voltage deviation by 18.3 %, and the bus-hours below 0.95 p.u. from 132 to 29. These gains cost 0.31 % in social cost and 0.26 % in DSO expenditure, while the rent of the aggregator is preserved.

The standard geometric derivation of neural scaling exponents takes the intrinsic dimension of a data manifold as its input. On modular addition in $\mathbb{Z}_p$ that derivation has no input. The exact algebraic solution is an orbit of $\mathbb{Z}_p$ acting by isometries. Transitivity alone makes the ratio statistic underlying the standard dimension estimator a point mass, so the estimator is undefined, and here the two nearest neighbour distances coincide exactly. Breaking the symmetry at scale $\epsilon$ returns a number, but one that tracks $1/\epsilon$ with no scale free plateau. We show that the failure is general, since on any finite orbit of a group acting by isometries the estimator reports the resolution at which the set is probed rather than a dimension. What replaces the power law is exponential in hidden width, $L(h)=L_\infty+A\exp(-c\,h^{\alpha})$, with $R^2$ between 0.982 and 0.995 against 0.857 to 0.906 for a power law admitting the same floor and fitted under the same protocol. Where the data supply is sufficient the rate belongs to the regulariser rather than to the group, since weight decay moves $c$ by a factor of 47 while group order moves it by 1.10, a residual below seed to seed resolution, for every fixed $\alpha$ between 0.75 and 2. The critical width falls with group order rather than rising, against capacity counting that assigns a fixed number of neurons to each irreducible representation.

Large trees disproportionately contribute to biomass storage, habitat structure, and ecosystem functioning. However, their distribution and health dynamics remain poorly quantified at a regional scale. Here, a deep learning model (U-Net-ID) and canopy height models derived from sub-meter aerial imagery from 2020 were used to delineate all individual trees with crown area $\geq$ 100 m$^2$ across the Sierra Nevada Floristic Province. The model was trained using more than 3.3 million synthetic tree crowns and achieved a median Intersection over Union (IoU) of 0.602 when validated against an independent dataset of 20,273 crowns. A total of 6,515,705 large trees were mapped, occurring across approximately 78.7% of the Sierra Nevada Floristic Province. The spatial distribution of large trees showed associations with elevation, temperature, and precipitation. Using Sentinel-2 time series from 2020 to 2025, tree health dynamics were characterized by extracting spectral trajectories for each crown and applying BFAST breakpoint detection algorithm combined with a disturbance classification framework to identify mortality, disturbance, and recovery trajectories of individual trees. Wildfires, estimated from CAL FIRE fire perimeters, were identified as the dominant driver of large-tree mortality, killing 10% of all large trees in the Sierra Nevada, with mortality strongly concentrated during the extreme 2020-2021 fire seasons.

Posture control in slender bodies such as snakes and eels arises from the interplay between passive deformation, active internal actuation, and task-level constraints. We formulate a general framework for the selection of stable postures in active elastic filaments subject to distributed forcing from gravity and fluid drag, by combining the constraints of mechanical equilibrium with optimal control theory. Our theory leads to a minimal description in terms of parameters governing the competition between hydrodynamic and gravitational loading, elasticity, and activity. We show that posture selection reflects a trade-off between control cost, function and dynamical stability, leading to the coexistence of distinct solution branches and abrupt transitions between them. Applying the theory to sessile eels in flow, we recover the experimentally observed transition from upright to reclining postures and predict scaling laws for body shape and exposed length. More generally, our results provide a unified perspective on how active filaments can regulate geometry to maintain function in external fields, with implications for biological and artificial systems.