Papers

Membrane composition plays a central role in determining how antimicrobial peptides (AMPs) interact with and alter the physical properties of lipid membranes. Here, we investigate the composition-dependent mechanical and structural response of lipid membranes to the AMP aurein using neutron spin-echo (NSE) spectroscopy, neutron membrane diffraction (NMD), and pressure (P)-area (A) isotherms, complemented by previously reported quasielastic neutron scattering (QENS) measurements. In a zwitterionic DMPC membrane, aurein induces progressive softening, manifested by a concentration-dependent decrease in both the bending rigidity and area compressibility modulus. NMD reveals a slight bilayer thinning but no prominent peptide-associated contribution within the deuterated hydrocarbon region, indicating that the progressive mechanical softening is not accompanied by increasingly deep peptide penetration into the hydrophobic core. In contrast, anionic phosphatidylglycerol (PG)-containing DMPC/DMPG membranes exhibit a non-monotonic response, with initial softening followed by pronounced stiffening at higher peptide concentrations. Complementary P-A isotherm measurements independently reproduce these contrasting mechanical responses, showing progressive softening of DMPC but stiffening of DMPC/DMPG. Most importantly, the combined NSE and QENS results reveal a striking multiscale decoupling: aurein suppresses molecular-scale lipid lateral diffusion while simultaneously reducing collective membrane stiffness at the mesoscopic scale, demonstrating that molecular lipid dynamics and collective membrane mechanics can evolve in opposite directions under the same peptide perturbation.Together, these results show that membrane composition governs the collective mechanical response to aurein, while molecular lipid dynamics can respond independently at shorter length and time scales.

This paper is concerned with the existence and local gradient regularity of solutions to a quasilinear elliptic Dirichlet problem with finite Radon measure and a degenerate matrix-valued weight. Under a small log-BMO condition on $\mathbb M$, we first prove the existence of a SOLA (solution obtained by a limit of approximations) and then establish a local Calderón-Zygmund estimate for $|\mathbb{M}|^{\frac{1}{p-1}}\mathbb{M} Du$ in terms of the fractional maximal function $\mathcal{M}_1(\mu)^{\frac{1}{p-1}}$.

Generative AI speeds, and mostly improves, professional work, but there is concern that users who delegate both the production and the evaluation of an answer may accept weak output and engage less with the underlying reasoning (cognitive surrender). Interventions proposed so far, such as unassisted practice or slowing adoption, sit outside the working task. We tested a different approach: an interactive metacognitive scaffolding layer (Cognistance, a prototype developed at the Oxford Centre for Impact Research (OCIR) that asks users to clarify context, choose a strategic direction and explain their reasoning before the AI generates a deliverable). Mean composite quality was 32% higher with the scaffold, with the same direction for every rater. Gains were largest for trade-off articulation and strategic coherence and absent for technical specificity. A large part of the aggregate effect reflected rescue of weak prompts: floor-scored (off-task) deliverables fell from 34% to 5%. Among participants whose own prompt already stated the data-localisation problem, the advantage was 21%. Treatment participants reported greater involvement and took about 2.4 minutes longer on average (10.46 minutes). Immediate recall scores were higher, which tentatively suggests better retention, but in this limited experiment, was not robust to sensitivity analyses. Self-ratings of quality did not track rated quality in either condition. Structured elicitation before generation improved the rated quality and task relevance of AI-assisted strategy documents at modest cost in time. Delayed retention, error detection and effects in live organisations are the priorities for the next stage of research.

We propose a simple scenario of boson-fermion atomic dark matter, in which the dark matter abundance originates from a primordial particle-antiparticle asymmetry. The dark sector consists of a complex scalar and a Dirac fermion carrying opposite charges under an unbroken U(1)$_D$ gauge symmetry. Their asymmetries are generated non-thermally through the CP-violating decays of heavy Majorana fermions produced by inflaton decay, in close analogy with non-thermal leptogenesis in the visible sector. The symmetric components efficiently annihilate into massless dark photons, while the surviving scalar and fermion populations cannot annihilate with each other and instead recombine into neutral boson-fermion dark atoms. Remarkably, the same interactions responsible for generating the primordial asymmetry induce atom-antiatom oscillations after recombination, so that the present-day dark matter can be approximately symmetric despite its asymmetric origin. Residual ionized components or sufficiently extended dark atoms can also give rise to appreciable dark-matter self-interactions, potentially leaving observable imprints on the formation and structure of dark matter halos and offering complementary cosmological and astrophysical probes of the dark sector. The massless dark photon survives as dark radiation, yielding a characteristic contribution $\Delta N_{\rm eff}\simeq0.05-0.07$ for the thermal history considered here. This prediction lies within the reach of future precision CMB observations, providing a direct cosmological test of the scenario.

Conditional density estimation targets the full distribution of a response given covariates, as required, for example, for per-galaxy photometric redshifts. We develop a scalable Bayesian estimator based on the logistic Gaussian process. The log conditional density has a separable covariance: a Matérn kernel along the response, represented in a truncated Fourier basis on a circle, and a covariate kernel represented by Nyström features, which accommodate non-stationary kernels with input-dependent amplitudes and length scales. Instead of a Laplace or variational approximation, we sample the latent field of this finite-feature model. Given the hyperparameters, its posterior is strongly log-concave with a uniformly bounded Hessian, and we draw from it by simulating kinetic Langevin dynamics with symmetric minibatch splitting in Kronecker-whitened coordinates. Marginal-likelihood gradients follow from Fisher's identity as posterior expectations. Under the conditions of our analysis their bias is controlled by the sampler's step size and run length, and the predictive averages over the non-Gaussian latent posterior instead of a Gaussian around its mode. On photometric-redshift benchmarks with up to 3.9 million training observations, trained on a single GPU, the estimator is competitive with state-of-the-art tabular foundation models on density and calibration metrics.

Long-running autonomous agents must reuse accumulated reasoning experience without allowing explicit historical memory and LLM context to grow indefinitely. However, existing memory mechanisms mainly retrieve, summarize, or compress past content and do not directly learn when particular kinds of thinking should be activated or discover new thinking knowledge from temporally dispersed experiences. This paper proposes a situation-conditioned thinking memory framework that transforms historical reasoning experience into a lightweight policy for predicting what should be thought about in the current situation, while leaving detailed reasoning to a large language model. Situations may represent temporal or spatiotemporal evolution rather than only current states. Temporary experiences are also periodically analyzed across multiple independent episodes to identify repeated long-range regularities, which are consolidated into new thinking knowledge and further internalized by the lightweight policy. Experiments show that the learned policy achieves 1.000 F1 on temporal-rule generalization, improves DeepSeek reasoning F1 from 0.789 to 0.868, reduces online processing time from 0.3636 ms to 0.0382 ms per query at 30,000 historical situations, and reaches 1.000 relation-discovery F1 and future-thinking accuracy after sufficient repeated cross-experience evidence.

Purpose: To compare dual- and single-suggestion AI support for radiographic interpretation by residents, particularly when the shared AI suggestion was incorrect. Materials and Methods: This prospective, multicenter, randomized three-arm reader study was conducted at three hospitals in China from July to September 2026 (ChiCTR2600129243). After specialty stratification, 132 residents with fewer than 3 years of clinical experience were randomized 1:1:1 to GPT-5.4 alone (group A), GPT-5.4 plus Kimi-K2.6 (group B), or GPT-5.4 plus Gemini-3.6 Flash (group C); 123 were analyzed. Participants interpreted 60 radiographs before and after AI support. The primary outcome was accuracy change. Welch ANOVA and Holm-adjusted t tests compared support conditions; HC3 linear models assessed specialty interaction. Results: Among 123 residents (mean age, 24.1 years +/- 1.4; 65 women), radiology residents showed greater accuracy improvement with dual- than single-suggestion support (B-A, 6.69 percentage points [95% CI, 0.97-12.40]; C-A, 7.87 percentage points [95% CI, 1.64-14.11]; Holm-adjusted P = .030 for both), whereas accuracy change did not differ in non-radiology residents (P = .20). When GPT-5.4 was incorrect, AI-assisted accuracy was higher with dual- than single-suggestion support in radiology residents (40.1% and 40.4% vs 20.0%) and non-radiology residents (31.3% and 31.0% vs 12.1%) (all Holm-adjusted P < .001). The dual-suggestion effect differed by specialty (interaction difference, 10.44 percentage points; 95% CI, 4.36-16.52; P < .001). Conclusion: Dual-suggestion support may mitigate the influence of erroneous AI suggestions, with greater accuracy improvement observed in radiology but not non-radiology residents.

Deploying robots as Complex Adaptive Systems (CAS) in unknown and dynamic environments necessitates a transition from rigid command libraries toward intention-based autonomy, as natural language represents the only medium capable of articulating complex goals beyond the capacity of finite instruction sets. While Large Language Models (LLMs) offer a path toward natural language goal description, their integration introduces significant challenges: the formalization gap between imprecise intentions and executable actions, the taxonomy gap induced by unpredictable environments, and the challenge of maintaining temporal state and progress awareness. This work introduces an architectural framework that enables robotic control by leveraging generative AI. The system follows a dual-AI design: an LLM translates high-level intentions into executable program code restricted to a formal robotic library and constrained by verifiable syntax, while a Vision-Language Model (VLM) provides semantic grounding via a distillation process. To ensure robustness, the framework incorporates environment-driven replanning triggers based on geometric and semantic thresholds, complemented by continuous runtime monitoring and an adaptive planning loop. Benchmarked across frontier models, our framework architecture demonstrates that grounding generative AI in a reactive, constrained loop enables robust fulfillment of complex intentions in dynamic and unknown environments.

Reasoning capabilities are critical for advancing Large Language Models, yet current approaches either require massive computational budgets or struggle to effectively distill reasoning to smaller models. Standard distillation methods rely on outcome-based rewards, failing to distinguish between sound reasoning and lucky guesses. We propose Collaborative Reasoning Distillation (CRD), a framework that enhances reasoning in compact models through three innovations: (1) interactive cross-feedback where teachers iteratively critique each other's reasoning, (2) fine-grained step-wise quality assessment capturing logical validity independent of final answers, and (3) coherence-aware step stitching that synthesizes complementary strengths. Students are trained via Reasoning Quality Optimization (RQO) with budget constraints. Our model, CRD-4B, achieves 97.3% on MATH-500 and 70.3% on AIME'25, surpassing baselines while using only 50K training examples, up to 12 times smaller than the datasets of comparable models.

Investigations involving the event-by-event fluctuations of conserved quantities, like net charge, net baryon number, and strangeness in heavy-ion collisions, provide insights into the properties of quark-gluon plasma (QGP) and the phase diagram of strongly interacting matter. Event-by-event fluctuations of net electric charge in pp collisions at $\sqrt{s} = 13$ and $13.6$ TeV and for OO, Ne-Ne, and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.36$ TeV are studied by analysing the data collected by the ALICE detector at CERN Large Hadron Collider. The analysis is carried out in terms of the variable $\nu_{\mathrm{dyn}}[+,-]$, chosen for its robustness against detector efficiency losses. The observed dependence of $\nu_{\mathrm{dyn}}[+,-]$ on the charged-particle density shows a smooth, energy-independent decrease in the magnitude of $\nu_{\mathrm{dyn}}[+,-]$ from smaller to larger collision systems. The negative values of $\nu_{\mathrm{dyn}}[+,-]$ indicate a dominance of correlations between oppositely charged particle pairs compared with those arising from like-sign charge pairs. Since $\nu_{\mathrm{dyn}}[+,-]$ is known to have an intrinsic dependence on multiplicity, an appropriate scaling is applied. The variable is therefore scaled with the mean multiplicities, $\frac{1}{\frac{1}{\langle N_+ \rangle} + \frac{1}{\langle N_- \rangle}}$. The dependence of the scaled values of $\nu_{\mathrm{dyn}}[+,-]$ on charged particle density is also looked into. The results are compared with model calculations from PYTHIA, EPOS4, AMPT and HIJING.

Ship internal arrangement is a complex spatial design problem in which competing functions within a fixed volume affect spatial relationships, mass distribution, trim, and stability. Exploring these trade-offs requires many layouts in a common format, yet public general-arrangement drawings are scarce, inconsistent, and two-dimensional. This study develops a common framework for generating conceptual 3D internal arrangements across six vessel families: bulk carriers, tankers, container vessels, offshore support vessels, patrol vessels, and yachts. Each arrangement uses paired voxel grids and topological graphs for spatial and connectivity analysis. The framework is evaluated through three experiments: (i) comparison of 50,000 generated arrangements with 23 reconstructed real references, (ii) envelope-constrained reconstruction of one reference per family, and (iii) response of generated layouts to requested function volumes. Generated design spaces broadly align with references within each family's sampling range. Searching alternative spatial subdivisions improves reconstruction across all families, with voxel accuracy reaching 75.5%. Fuel and ballast allocations respond near-proportionally to requested volume, while other functions depend on subdivision capacity, compartment eligibility, and discrete assignment. A fixed-hull offshore support vessel application shows that the same hull and requested programme can produce different adjacency and trim outcomes, with five nondominated concepts among 119 of 500 alternatives meeting stability and programme criteria. The results support layout design-space exploration across vessel families and changing requirements, with spatial organisation remaining important beyond volume compliance. The generator and conceptual general arrangement dataset are released publicly for reproducible analysis, benchmarking, and learning-based design studies.

Classical approximation complexity asks what solution quality can be guaranteed with polynomial-time computation. The classes APX, PTAS, and FPTAS distinguish a fixed approximation ratio, approximation to any fixed accuracy, and approximation schemes whose running time is also polynomial in inverse accuracy. Their randomized counterparts are R-APX, R-PTAS, and R-FPTAS. We define bounded-error quantum counterparts BQ-APX, BQ-PTAS, and BQ-FPTAS. Membership requires a uniform quantum algorithm that, on every input, returns a feasible classical solution achieving at least the claimed approximation ratio with probability at least 2/3. Scores (objective values) must be efficiently classically computable. Running time includes parameter selection, preparation, measurement, decoding, and repetition. Many quantum optimization methods are used heuristically, and high benchmark scores alone do not establish these guarantees. We further establish a conditional hierarchy for logarithmic, polynomial, and exponential approximation factors. Assuming NP $\nsubseteq$ BQP, the quantum classes form a strict hierarchy. Problems based on prime factorization and discrete logarithms give conditional quantum-classical separations. Certified Maximum Order has an exact quantum algorithm, while any randomized polynomial-time algorithm guaranteeing at least an inverse-polynomial approximation ratio on every input would yield efficient factoring. Discrete-Logarithm Fitting has an exact quantum algorithm and a deterministic one-half approximation, but any fixed improvement over one half would give a randomized polynomial-time algorithm for the safe-prime discrete logarithm problem. Our results show, under explicit complexity assumptions, that quantum computation can improve worst-case approximation guarantees. A quantum-classical gap for common problems such as MaxCut or MaxSAT remains open.

Familial amyloid-$\beta$ (A$\beta$) variants alter aggregation kinetics, but their interaction with structural brain connectivity remains incompletely understood. We developed a mutation-aware mechanistic model coupling a coarse-grained monomer–oligomer–fibril aggregation–fragmentation system to graph diffusion on the 540-node Budapest Reference Connectome component. Experimental A$\beta_{42}$ nucleation scores scaled primary nucleation rates for seven variants relative to wild type. Robustness was examined using mutation-score uncertainty, alternative kinetic mappings, global sensitivity analysis, seed and edge-weight perturbations, degree-preserving randomized connectomes, spatial propagation analysis, synthetic ABC-SMC parameter recovery, posterior prediction, and Chemical Langevin simulations. E22G showed the earliest threshold crossing and greatest cumulative oligomer burden, whereas A2V was delayed under the selected mapping. Mutation rankings persisted across tested network perturbations, although regional burden patterns depended on topology. Connectome distance from seed regions was associated with later oligomer arrival (Spearman $\rho\approx0.92$). Under inferred parameter uncertainty, the mean timing-rank correlation was 0.990 and cumulative-burden ordering was preserved in every posterior draw, while exact peak-amplitude ordering was less stable. Stochastic ensemble medians retained the deterministic ordering despite overlap among trajectories. Within this proof-of-concept framework, mutation-dependent kinetics primarily influence aggregation timing and cumulative burden, while connectivity shapes spatial propagation. Nominal background rates, model-time units, and synthetic parameter recovery limit interpretation to mechanistic comparisons rather than clinically calibrated prediction.

In this paper, we establish the absence of absolutely continuous spectrum for scalar one-dimensional Laurent operators with multiplicative disorder and critical long-range hoppings. In particular, the requirement of at least quartic off-diagonal decay rate in the existing theory is bypassed by exploiting the finite-difference bound of the convolution kernel, which is available even when the interaction decays only as $|n|^{-1}\log^{-\beta}|n|$ with $\beta>1$. We then apply the abstract main result to a concrete physical model, the capacitance operator in subwavelength physics. For a chain of three-dimensional resonators with one resonator per period, we verify the required decay and finite-difference estimates and conclude the absence of absolutely continuous spectrum. These results leave open the distinction between pure point and singular continuous spectrum, but constitute a key step in proving Anderson localization in wave systems with critical long-range interactions.

Forensic reconstruction of LLM-agent actions requires not only recovering the correct value, but establishing which preserved record supports that finding. Tool logs, generated explanations, and local citation identifiers capture different parts of this evidence, yet a citation identifier does not establish a source unless its binding to a record is preserved. We audit this distinction using 64 mechanically checkable cases from saved AgentDojo Banking executions. Two LLM readers reconstruct source relationships under controlled variations in visible evidence and identifier-to-record bindings. We separately evaluate complete-record agreement, evidence-grounded findings, justified abstention, and unsupported assertions. With original identifiers and no binding table, Sonnet recovered every literal source location but made unsupported citation-source assertions in 26 of 28 cases requiring the missing relation; 22 nevertheless matched the complete reference. Adding explicit bindings improved grounded reconstruction for both readers, whereas identifier renaming alone provided no consistent remedy. A deterministic same-packet comparator correctly resolved the bounded task or abstained throughout. These results show that factual agreement alone is insufficient for evaluating forensic reconstruction of agent logs and motivate preserving explicit record bindings to distinguish supported findings from correct guesses.

Research software sustainability is often assessed through the FAIR principles: findability, accessibility, interoperability and reusability. While important, FAIR does not cover all relevant sustainability concerns. Research software should also be environmentally responsible and secure over time. Excessive resource consumption increases environmental cost, while insecure software creates maintenance overhead, technical debt and barriers to reuse. To this end, in this paper, we extend a previously proposed fitness function framework for sustainable research software beyond FAIR. We introduce two additional sets of fitness functions: environmental functions targeting resource efficiency and execution footprint, and security functions targeting dependency health, vulnerability exposure and secure configuration. Together, these functions broaden continuous software assessment from FAIR compliance to a more complete view of sustainability. The resulting framework treats research software sustainability as a multidimensional property that includes FAIR, environmental responsibility and long-term security.

Trajectory optimisation for cone-beam computed tomography (CT) determines which information sparse-view scans acquire. Fixed candidate pools prevent off-grid refinement and require new object-specific precomputation for each acquisition manifold. We make every source pose an individual continuous variable and move all poses jointly by gradient ascent on the scanner's kinematic manifold. The objective combines soft-Tuy plane coverage, continuous View Covariance Loss, and an analytic attenuation-aware ray-bundle penalty. The same optimiser handles circular, limited C-arm, two-axis, and freesphere parametrisations. On a Defrise flange, continuous selection recovers laminar defects invisible to a circular orbit, matches discrete swap search on the free sphere at the sparser budget, and leads at the denser one, with the same objective evaluated in every arm. A moderate elevation band already recovers most of the free-sphere gain at the defects, so the same optimiser transfers to bounded scanner envelopes. Photon noise preserves the ordering on the flange and compresses it on a dense fuel nozzle. Sparseprescan planning benefits from matching prescan and planned acquisition manifolds. Selection takes seconds rather than minutes without an object-specific reconstruction basis. Prescan-planned poses were executed on a robot CT bench and reconstructed in a common frame, demonstrating feasibility but no consistent metric gain over uniform band sampling. Continuous pose optimisation incorporates attenuation and scanner constraints directly into sparse-view acquisition design.

The purpose of this paper is to study Faber–Krahn inequality of Dirichlet eigenvalues $\{ \lambda^{\ln,\mu}_{k}(\Omega)\}_{k\in \N}$ for the logarithmic Hardy operator \[ \mathcal{L}_{\mu}=(-\Delta)^{\ln}+2\mu\log\frac{1}{|x|} \] on a bounded Lipschitz domain $\Omega\subset\mathbb{R}^{N}$ containing the origin, with $\mu>-1$. We establish a Faber–Krahn inequality for $\mu\in(-1,0)$, the ball centered at the origin minimizes the first eigenvalue at fixed volume, with equality only for that ball. Finally, we show this inequality fails for $\mu>0$ via an explicit two-ball-and-tube construction.

We study finite-horizon online resource allocation with i.i.d. requests and an endogenous Markov state on a finite state space: each action affects the transition of the state that governs future rewards and resource consumption. In this problem, a transient fluid LP benchmark upper bounds the expected reward of every nonanticipating policy, while a stationary LP supplies randomized state-dependent controls. We assume that the stationary LP has a unique optimum and identify primal nondegeneracy and irreducibility of the optimal induced kernel as important regularity conditions in this framework. With a known request prior, we show that, under nondegeneracy and irreducibility, both frequent and infrequent re-solving attain $O(1)$ regret. However, under a degenerate optimum, irreducibility yields the sharp worst-case $\Theta(\sqrt{T})$ rate for infrequent re-solving, while frequent re-solving can incur $\Omega(T)$ regret. Thus, more frequent optimization can perform asymptotically worse. With an unknown request prior, we develop a three-phase U-shaped infrequent re-solving policy that coordinates learning and inventory correction with $O(\log\log T)$ LP solves. When the optimal induced kernel is irreducible and the algorithm is given the optimal target state class and a constant-cost entrance policy, it attains $O(1)$ regret under nondegeneracy and $O(\sqrt{T})$ regret under degeneracy. Without the target-class information, linear minimax regret is unavoidable. Numerical experiments further illustrate the instability of round-by-round re-solving relative to epoch-wise infrequent re-solving, show that thresholding greatly mitigates its loss, and find that infrequent schemes remain dominant under both known and estimated priors.

Nonadiabatic molecular dynamics provides mechanistic insight into light-driven processes and informs the design of molecules and materials for solar energy conversion, photocatalysis and photo switching. Accurately describing these processes requires a representation that respects electronic symmetry and consistently relates energies to interstate couplings. Here we introduce PEACE, which combines a parity-equivariant latent Hamiltonian with a learned electronic connection. Controlled ablations reveal the complementary roles of symmetry-allowed state mixing and electronic-frame variation in reproducing crossing structures and relaxation dynamics. PEACE closely reproduces excited-state population dynamics from first-principles simulations, while its extension to spin-orbit coupling enables simulations of intersystem crossing. These results demonstrate that a more complete incorporation of the underlying physics into learned electronic representations leads to more accurate predictions of nonadiabatic dynamics.

Identifying the process relevant to planet formation is still a major task. Mechanisms have been identified that can trap dust, preventing it from migrating inwards. A particular hydrodynamic instability, known as the streaming instability, is of high interest because it may be responsible for the formation of dust clumps from which the first planetesimals form. We aim to compare the outcome of non-linear streaming instability simulations using both fundamental approaches in a more realistic global disk model. The results will not be used to identify or disentangle the effect of, e.g., numerical diffusion in fluid simulations or the possibility of having crossing particle streams. Instead, they will enable us to determine whether the Lagrangian particle approach is the most suitable for numerical studies of the streaming instability. Methods: We perform 2D, axisymmetric, global, and isothermal hydrodynamic simulations using the two codes FARGO3D (dust fluid) and PLUTO (fluid, particles) to investigate the temporal evolution of dust scale height, midplane dust-to-gas ratio, and maximum dust density as well as to study velocity distributions and vorticities. For PLUTO particle simulations, we also investigate the influence of the gas Riemann solver and spatial reconstruction orders. Our results from a resolution study up to 5120 cells per gas scale height indicate convergence between PLUTO fluid and FARGO3D. Both yield a Gaussian profile dominated by small-scale, dust-depleted voids. Particle simulations with PLUTO have not yet converged, as a transient midplane dust component persists, indicating the need for even higher resolution or more particles. Using a more accurate Riemann solver or a higher-order spatial reconstruction scheme helps to bring the dust density profile closer to the converged structure.

From cells to cities, ecosystems to economies, complex networks exhibit peak intensities that define their empirical limit. Estimating these limits traditionally requires domain-specific knowledge. We demonstrate that a wide range of complex networks share a capacity frontier that constrains these maxima. We formalize this regularity by proposing Structural Capacity Theory for Network Substrate Structured Systems. These systems couple a fixed network substrate with an observable dynamical process. The frontier is learned from a vector representation of the network substrate and modulated log-additively by a vector representation of the dynamical process. Frontiers trained on one set of domains reliably bound empirical maxima of entirely different ones without observing their peak intensities or simulating their dynamics. Independent learning paradigms converge on consistent upper bounds. Frontier performance is stable under perturbation, yet degrades under deliberate falsification, with no performance gain under ablation. These findings support the capacity frontier as a generalizable constraint that describes how network structure bounds dynamical processes across otherwise unrelated systems.

Goal-conditioned dynamic manipulation of deformable linear objects has mainly specified goals as positions for a rope tip to reach. Many tasks, however, depend on how the tip arrives. We therefore study single-swing rope striking with goals that specify the tip's 3D position and arrival direction, across the workspace and on different ropes. This is challenging because rope dynamics are hard to model, no demonstrations exist, distinct swings reach the same goal with different reliability, and the sim-to-real gap extends beyond the rope. To address these challenges, we extend the state-of-the-art DLO simulator DeformX with GPU acceleration, a stable Cosserat rod solver, and a cross-flow aerodynamic model, yielding DeformX2.0, which is more than $20{,}000\times$ faster. We then propose TRACE (Trace-rooted Adaptive Cross-Entropy), which generates striking data by warm-starting each new target from the stored swing whose tip path passes closest to it. Its cost penalizes rope bending and abrupt tip motion to favor repeatable swings. A conditional flow-matching policy trained on this data reaches 92.1% accuracy in simulation. Finally, we propose RECAP (Residual Calibration Policy), which fits the simulator's rope and rig parameters to a few calibration swings and adapts actions with a correction policy trained in simulation. On a real robot, across three ropes, RECAP raises success within 5cm from 72% to 87% for position goals, and within 10cm and 10{\deg} from 50% to 79% for goals that also specify the arrival direction.

This paper proposes a new method for proving the confluence of an abstract reduction system (ARS) by clarifying the sufficient conditions, called compatibility and edge commutativity, for expanding a given finite sub-ARS into a confluent one by adding rewrite edges. This method can be regarded as an extension of our earlier work, which showed that a weakly non-overlapping, shallow, and non-collapsing term rewriting system (TRS) is confluent. Furthermore, we apply our method to demonstrate that a non-$E$-overlapping and weakly shallow TRS is confluent. Here, a term is weakly shallow if each defined function symbol occurs either at the root or in the ground subterms, and a TRS is weakly shallow if both sides of all its rewrite rules are weakly shallow. This drops the non-collapsing condition assumed in our previous work on weakly shallow TRSs. Moreover, since a weakly shallow TRS is non-$E$-overlapping whenever it is non-$\omega$-overlapping, and the latter property is decidable, we also obtain a decidable sufficient condition for confluence: non-$\omega$-overlapping and weakly shallow TRSs are confluent.

Negation is an essential feature of human language, yet large language models (LLMs) remain unreliable in processing it. We evaluate recent open-source and closed-source LLMs on our negation benchmark and find that, in 37-71% of cases, they repeat the same answer under negation (e.g., "Madrid" for "What is not the capital of Spain?"). To understand and address this brittleness, we mechanistically examine how models operate under negation. Our main finding is that specialized attention heads and MLP neurons jointly implement negation by (1) suppressing retrieval of the original answer (e.g., "Madrid") while (2) promoting a favored candidate within the answer category (e.g., "Paris"). This contrasts with accounts of human negation processing, in which information about the original answer helps to determine what should be excluded. Furthermore, we find that this difference from human processing is a key source of negation failures: the model's mechanism relies on suppressing the original answer rather than using it to determine what to exclude, so the model can repeat the original answer when suppression is too weak or when a bias toward particular answers prevents it from selecting an alternative. To address this weakness in the model's negation mechanism, we propose a training objective that requires larger shifts in answer preference for more confident original predictions, and show that it reduces negation failures with less degradation of general capabilities than standard fine-tuning baselines. Together, our results demonstrate how mechanistic analysis can reveal why a linguistic capability fails and guide training that targets the underlying limitation.

Let an Itô semimartingale be observed at times satisfying $\tau_{i+1}^n-\tau_i^n=(n\theta_{\tau_i^n})^{-1}$, where $\theta$ is adapted and càdlàg, and $\theta$ and its reciprocal are bounded on compact intervals. Under the usual hypothesis (H) on the semimartingale, we prove fixed-time stable convergence for test functions whose Hessian is $o(\norm{x})$ at zero. The limit is a sum of jump contributions with sampling scale $\theta_{T-}^{-1}$ and separate pre-jump and post-jump volatilities. The proof establishes joint stable convergence of the local Poisson positions and Brownian increments on the endogenous grid, and controls infinitely many small jumps by a uniform Itô estimate. Three examples identify the left-limit sampling scale and show why positivity and càdlàg regularity alone cannot replace local control of the reciprocal sampling intensity.

Large language models (LLMs) are increasingly used for emotional support, raising concern that sustained use may draw users away from their real-world relationships. Yet existing evaluations primarily focus on the safety, empathy, or helpfulness of responses, leaving under-examined a relational question: where does the model orient the user for continued support? To address this question, we introduce relational orientation, a property operationalized through two non-exclusive dimensions: inward-facing (IF) language, which positions the AI as the user's ongoing source of support, and outward-scaffolding (OS) language, which encourages real-world human connection. Grounded in psychological and sociological literature, we formalize a taxonomy of relational orientation and present RELATE, a persona-conditioned framework for measuring inward-facing and outward-scaffolding language at the sentence level in multi-turn dialogues. RELATE pairs 76 help-seeking situations adapted from naturally occurring questions with three simulated user styles, providing 228 evaluation stimuli. In our experiments, we evaluate seven LLMs using dialogues with six assistant turns each, yielding 1,596 dialogues and 69,194 assistant sentences. We assess these sentences using a primary rubric-based LLM judge and apply a secondary judge to a subset. Under automated evaluation, we find that the proportion of sentences labeled as IF is higher at the sixth assistant turn than at the first, while the proportion labeled as OS is substantially lower for hesitant, indirect simulated users than for explicit, reassurance-seeking users. RELATE provides a reproducible framework and a sentence-level signal for auditing and steering the relational orientation of supportive LLMs.

A complete characterization of earthquake induced ground motions require three translational and three rotational components, together with the six components of the strain tensor. Despite the importance of rotational ground motions, their characteristics are not yet completely recognized. Limited observational database and challenges of simulating them in realistic geological media has primarily constrained the research in this domain. In the present study, we develop an extension of the spectral-element package SPECFEM3D that directly evaluates rotational ground motion from spatial gradients of displacements at the Gauss-Lobatto-Legendre integration points during the numerical solution. The implementation is validated against analytical solutions for a homogeneous elastic medium, showing good agreement in arrival times, amplitudes, waveform characteristics, and spatial propagation. For analyzing the propagation patterns of rotational ground motions, we introduce Peak Ground Rotation Rate (PGRR) maps, analogous to Peak Ground Velocity (PGV) maps. Comparison of PGRR and PGV maps revealed that the critical locations of translations and rotations do not coincide. Rotational ground motions are subsequently simulated in a layered medium for two earthquake source mechanisms, demonstrating the variation in PGRR maps for different source characteristics. Finally, a three-dimensional (3D) model of the Indo-Gangetic Basin is developed to show that low-velocity sedimentary deposits substantially amplify and redistribute rotational ground motions. The spatial distribution of PGRRs in the basin changes significantly relative to the corresponding generic layered medium. The developed framework provides a basis for investigating rotational ground motions in complex geological environments and assessing its potential relevance to sensor deployment strategies, seismic hazard and earthquake engineering.

We prove the Gowers uniformity of the von Mangoldt function minus its Cramér model in all short intervals $[X,X+X^{3/5+\varepsilon}]$, improving on the work of the first and fourth authors with Shao and Tao, where the exponent was $5/8$. This also implies a local-to-global theorem for linear equations in primes in such short intervals. We also show that the Möbius function has cancellation in all intervals $[X,X+X^{19/35+\varepsilon}]$, improving on the work of the first and fourth authors, where the exponent was $11/20$. Both improvements are based on improved treatment of trilinear sums over short intervals which naturally reduces to estimating mean values of products of three Dirichlet polynomials. In a general setting, we reduce the task of estimating mean values of products of Dirichlet polynomials with given large value bounds to the task of showing that a certain piecewise linear function is positive. This reduction allows recent large value estimates to be incorporated. Combining this general framework with the most recent large value estimates stemming from the work of Guth and Maynard, we prove a Heath-Brown–Iwaniec type estimate for type I/II sums in intervals of length $X^{19/35+\varepsilon}$ and a Baker–Harman–Pintz parallelogram type estimate for general trilinear sums in intervals of length $X^{3/5+\varepsilon}$.

Imitation learning policies that integrate multiple sensory modalities are prone to overreliance on a dominant modality, such as vision, during training, which can disrupt policy execution when that modality is lost at inference time. In this paper, we introduce Targeted Modality Dropout (TMD), in which the dependence on each modality is estimated using attention and the most dominant modality is selectively dropped. This is combined with entropy regularization over the dependence distribution. Through real-robot evaluation using a bimanual manipulator, we show that under vision loss the success rate of the baseline policy drops substantially, whereas TMD sustains task execution. In contrast, a conventional dropout that selects the dropped modality at random, without the entropy regularization, fails on many tasks even without vision loss.