Papers

We construct gauge-covariant unintegrated vertex operators in an antighost-independent subcomplex of the bosonic ambitwistor string. For a linearized gauge field, a world-sheet ghost-derivative term completes the standard vertex so that BRST closure imposes $\p^nF_{nmI}=0$ without the Lorenz condition. In the rank-two sector we use an antighost-free ansatz that is sufficient to isolate a diffeomorphism-invariant spin-two subsector. After eliminating auxiliary fields and consistently setting the antisymmetric and scalar combinations to zero, BRST closure gives $R_{mn}=0$ without imposing transversality. We distinguish this construction from the full relative BRST cohomology of the bosonic ambitwistor string, whose additional antighost-dependent states lead to the known higher-derivative spectrum.

We present evidence that the streaming instability (SI) can form planetesimals from millimeter grains inside axisymmetric pressure bumps, provided the bump is not too strongly reinforced. We conducted three-dimensional local shearing-box simulations of millimeter grains in a Gaussian pressure bump of amplitude $A = 0.6$, at a resolution of $160/H$. We varied only the Newtonian reinforcement timescale $t_{\rm reinf}$, the timescale on which the imposed bump is restored against particle back-reaction. Our reference run T1 uses $t_{\rm reinf} = 1\,\Omega^{-1}$. Particles pile up in a narrow axisymmetric band at the minimum-headwind point, cross the Roche density, and collapse through direct gravitational instability (GI). In our weakly reinforced run T100 with $t_{\rm reinf} = 100\,\Omega^{-1}$, the outcome is different. Particles drift through the bump roughly three times more slowly, and dense SI-like filaments develop across a wide radial region well before the Roche density is reached. These results are consistent with a residence-time criterion, which states that for the SI to grow, $t_{\rm cross} > t_{\rm grow}$, where $t_{\rm cross}$ is the time a particle spends inside the region where the ratio $Z/\Pi$ of the solid abundance $Z = \Sigma_p/\Sigma_g$ to the headwind parameter $\Pi = \Delta v/c_{\rm s}$ is high enough for strong clumping, and $t_{\rm grow}$ is the SI growth time. T1 violates this criterion, and T100 satisfies it. Our results suggest that the reinforcement timescale matters for millimeter grains because it helps set the crossing time, and therefore whether the SI has time to grow. We caution, however, that our reinforcement scheme is an idealised numerical construction rather than a physical bump-forming mechanism such as a planet, and a more definitive test of this picture will require simulations with a more physically motivated bump.

Volatility forecasts play a central role in financial risk management because their overall level and day-to-day movements affect downstream decisions. Most studies compare forecasting models while keeping the training loss fixed. Yet losses emphasise different errors and can target different properties of future volatility, so raw comparisons may combine persistent forecast-level differences with differences in daily forecast movements. This leaves unresolved whether the importance of loss choice comes mainly from the forecast level it targets or from differences that remain after level adjustment. We address this gap through a comparison of seven losses and five models across major cryptocurrencies. Validation-based alignment adjusts the forecast level before the raw and aligned forecasts are evaluated using statistical scores and one-day Value-at-Risk. Before alignment, marginal score variation is greater across losses. After alignment, model choice becomes the larger source of variation in the full five-model comparison, while cross-loss differences in VaR breach rates narrow substantially. Our contribution is a comprehensive evaluation of loss and model choice that shows why losses can appear so influential in raw comparisons and how this interpretation changes when forecast level and downstream risk are considered explicitly.

Let $k$ be a field of characteristic $p\ge0$. We prove that $m$ points and $n$ lines in $k^2$ determine at most $3(mn)^{2/3}+m+n+2mn/p$ incidences, the last term being omitted in characteristic zero. Over the prime field $\mathbb{F}_p$ the coefficient of $mn/p$ can be replaced by $1$. The proof uses the polynomial method, and for $m=n$ the bound is sharp up to an absolute constant over prime fields. As applications, over prime fields in which $-1$ is not a square we obtain the $L^2\to L^r$ extension estimate for the paraboloid in $\mathbb{F}_p^3$ for $r>10/3$. Over every odd prime field, we show that a two-source extractor construction of Bourgain has exponentially small error at every min-entropy rate greater than $1/3$. We also improve sum-product estimates for small sets in positive characteristic and obtain projection and Furstenberg estimates over prime fields. The incidence inequalities with exact constants have been formalized in Lean.

In this paper, we investigate the impact of adversarial attacks on identity encoders within a realistic de-identification framework. Our experiments show that the transferability of attacks transfers from an external surrogate model to the system model (e.g., CosFace to ArcFace) allows the adversary to cause identity information to leak in a sufficiently sensitive face recognition system. We present experimental evidence and propose strategies to mitigate this vulnerability. Specifically, we show how fine-tuning on adversarial examples helps to mitigate this effect for distortion-based attacks (i.e., snow, fog, etc.), while a simple low-pass filter can attenuate the effect of adversarial noise without affecting the de-identified images. Our mitigation results in a de-identification system that preserves its functionality while being significantly more robust to adversarial noise.

Linear arrays of omnidirectional microphones produce beampatterns that are symmetric about the array axis. For these arrays, a beamformer is considered steerable if its beampattern maintains the same shape in the semicircular plane across all look directions from 0{\deg} to 180{\deg}. For dual-microphone arrays, conventional differential beamformers are generally non-steerable and restricted to first-order, which significantly limits spatial selectivity. To address these limitations, this study presents a neural differential beamformer (NDBF) with a dual-microphone array. The contributions are as follows: (i) NDBF is steerable; (ii) NDBF achieves high-order frequency-invariant beampatterns; and (iii) NDBF enables stereo recording using only two closely spaced omnidirectional microphones. Experimental results demonstrate that NDBF outperforms existing methods while overcoming the limitations of classical differential beamforming.

Let $k$ be an algebraically closed field of characteristic zero and $G$ a finite group. We realize the based Grothendieck ring $R_G$ of ${\mathcal{R}\mathit{ep}}(D(G))$-module categories as the degree-two cocycle-decorated double Burnside ring and derive an explicit Clifford formula for multiplication and for the action of $R_G$ on the Grothendieck group of ${\operatorname{\operatorname{\mathsf{Vec}}}}_G$-module categories. We determine the extremal based ideals, study factorization through smaller groups, and prove a Mackey theorem for standard two-sided subgroup inductions. We prove that $\mathbb C\otimes_{\mathbb Z}R_G$ is semisimple exactly when $G$ is cyclic. We study the Brauer–Picard action on indecomposable ${\operatorname{\operatorname{\mathsf{Vec}}}}_G$-module categories and show that it is transitive exactly when $G$ is abelian of square-free exponent. For abelian $G$, we determine the possible abstract group types of Lagrangian subgroups of $G\oplus\widehat G$, apply the known orthogonal classification in the homocyclic case, and exhibit same-type nonconjugate Lagrangians for mixed exponents.

Scanning-probe x-ray tomography is useful for imaging nanoscale structures of a sample. The image resolution, which can reach down to 10 nm by the increased brightness and coherence of the x-ray optics, however, is highly susceptible to experimental error. Failure to address these errors can lead to a smeared image and, in the worst case, to misinterpretation of the imaged object's structure. In this work, we present a novel optimization-based approach to calibrate a common yet challenging source of experimental error, the drifts of the scanning positions, while simultaneously reconstructing the object. This approach uses the coupled and complementary information from different measurements to enforce consistency between the measurements and the reconstruction. We illustrate the proposed approach on both synthetic and real tomography images and show its superior performance compared with reconstruction without explicit error calibration.

Residual vector quantization (RVQ) turns physiological waveforms into compact token sequences, but conventional masked modeling treats every incorrect token as equally costly. We propose GeoRVQ, a coarse-to-fine masked token model whose objective reflects the local response of a frozen waveform decoder. Decoder-induced costs define geometry-aware soft targets and expected distortion, while quantizer-causal prediction follows residual dependencies from coarse to fine levels. In a descriptive aggregate over MIMIC-IV Waveform, VitalDB, and CODE-15%, GeoRVQ increases exact token accuracy from $.133\pm.004$ to $.143\pm.003$, reduces decoded distance from $.606\pm.006$ to $.393\pm.007$, and increases R-peak F1 from $.784\pm.004$ to $.837\pm.008$ under matched model and training conditions. Across 45 held-out code substitutions, decoder-induced cost has a Spearman correlation of $.85$ with realized decoded cost, compared with $.54$ for Euclidean codeword distance. These results indicate that decoder-aware objectives can improve waveform and event preservation without requiring a large increase in exact token accuracy.

Accurate channel state information (CSI) is critical for advanced multi-antenna wireless networks. While high-fidelity and site-specific ray-tracing (RT) equipped wireless digital twins can overcome overhead for CSI acquisition. However, computing deterministic, calibrated RT based CSI from a wireless digital twin for every orthogonal frequency-division multiplexing (OFDM) symbol violates the strict microsecond latency budgets of the 5G NR numerology. To overcome this computational bottleneck, this paper investigates three approaches within a calibrated 3D digital twin framework, namely (i) the generalization of the channel twin, (ii) the performance enhancement using a neural receiver, and (iii) a data-driven interpolation framework for scalability. We compute high-precision CSI for a sparse subset of temporal anchors and employ an attention-based Transformer to predict the remaining symbols. Unlike polynomial splines or sequential long short-term memory (LSTM) networks, the Transformer exploits a global receptive field to capture the non-linear multipath dynamics while enabling parallelizable, real-time inference. To achieve spatial scalability, we introduce channel twin generalization. By fine-tuning the 3D RT models alongside the Transformer, the framework leverages the CSI dataset of one location to infer the channel behavior of an unseen environment. Transfer learning further adapts the model to a new environment using only a small fraction of locally collected data. Simulation results demonstrate that the proposed architecture substantially outperforms the baseline interpolators, achieves robust spatial transferability, and lowers the bit error rate through the unified neural receiver. These results establish a scalable, environment-agnostic foundation of distributed channel twins for high-quality, low-overhead CSI acquisition in next-generation cellular networks.

Outpatient appointment scheduling must balance provider idle time, overtime, and patient waiting under uncertain service times, punctuality, and attendance. These factors may follow patient-and-time-dependent probability distributions, which existing models rarely incorporate simultaneously because of modeling and computational complexity. We propose a stochastic programming model that captures exponentially many scenarios with polynomially many variables and constraints, without sampling. It accommodates patient-dependent service times and patient-and-time-dependent no-shows and arrival times. We also discuss estimating these distributions from electronic health records. We examine how personalized reminders and changes in attendance due to incentives or negative clinic experiences affect scheduling. Our model optimally solves instances of up to 14 patients in reasonable computational time. Its schedules outperform classical Bailey-type rules. Even the best-performing variant has 97% higher expected cost on average. Incorporating patient-dependent service times reduces total costs by 34% on average. Accounting for patient-and-time-dependent unpunctuality and no-shows reduces costs by 12% and 67%, respectively. Personalized reminders can reduce costs by 23%, and sensitivity analyses show that these gains withstand moderate errors in estimated distributions. These findings show how modeling individual patient behavior and tailoring communication can reduce waiting, idle time, and overtime.

We developed an anatomy-aware deep learning framework to synthesize post-contrast breast MRI from pre-contrast images, emphasizing tumor and background parenchymal enhancement (BPE) regions. This retrospective study included 649 patients with 6,251 paired pre-contrast and post-contrast images. The framework integrates breast mask consistency, lesion-region supervision, and BPE-region supervision into an image-to-image translation model. Evaluation included quantitative image quality metrics, a reader study with two breast radiologists, and downstream Ki-67 classification. The proposed method outperformed Pix2Pix, Pix2PixHD, diffusion-based synthesis, and mask-supervised baselines in whole-image and regional evaluations. Ki-67 classification showed no statistically significant performance differences across real- and synthetic-image training and testing settings, although this does not establish equivalence. These findings suggest that anatomy-aware supervision improves synthesis fidelity and support further investigation of synthetic post-contrast MRI for contrast-free imaging workflows.

Legal contracts are structurally complex documents in which contradictions may emerge across distant and interconnected provisions. Although large language models (LLMs) improve legal language understanding, contradiction analysis remains a human-centered and evidence-grounded review task. We present ContraVis, a visual analytics system for human-in-the-loop contradiction analysis in legal contracts. The system models contracts as typed paragraph graphs that combine explicit contractual references with semantic relationships between paragraphs. This graph plays a dual role: it conditions LLM reasoning and serves as the interactive representation the analyst explores, keeping model context and human inspection aligned across coordinated views. In a controlled comparison, graph-conditioned reasoning recovered more injected contradictions than standalone LLM analysis as contract length grew, while surfacing additional candidates for analyst validation. A formative study with contract-domain lawyers indicated that in-context evidence comparison supported contradiction validation, and we distill design implications for evidence-grounded, LLM-assisted document review.

It is unclear if host star metallicities differ between systems with one detected transiting planet ("singles") or multiple detected transiting planets ("multis") around FGK dwarfs. Here, we find strong evidence that they do for M dwarfs. We use a homogeneous sample of FGK and M dwarf chemical abundances to demonstrate that M dwarf multis are significantly more metal-poor than singles ($p$ = 0.00079), even when we only consider small (<4 $R_{\oplus}$) planets ($p$ = 0.0013). This result emerges at the late-K to M dwarf transition. We observe that M dwarf multis become more metal-poor as a function of increasing planet multiplicity. Additionally, planets in singles have significantly higher eccentricities and shorter orbital periods compared to planets in multis. We interpret these findings as evidence that M dwarf singles lead relatively active dynamical lives, and the different planetary architectures of singles and multis arise from distinct dynamics influenced by metallicity. This may not occur in FGK systems because their more massive protoplanetary disks may supply enough planet-forming material to instigate dynamics that lead to only one transiting planet, even when the host star metallicity is low. Another possibility is that multis are less compact around FGK dwarfs because they form from larger disks, which may often cause them to be observed as singles in transit data.

Public health measures at mass gatherings work only if people follow them, and adherence depends both on how instructions are communicated and what others do. We link these behavioural factors to pathogen transmission in a local-scale, agent-based exposure model combining pedestrian dynamics with airborne transmission. Rather than fitting a parametric behavioural model, agents draw their adherence at run time from survey respondents (2,170 attendees of UK sports and music events) who reported the same context: we vary stewards' communication effectiveness and adherence of role models, as well as agents' shared social identity with each, assuming that strong shared social identity increases their influence. In a ticket-checkpoint queue of 101 agents, effective communication combined with strong shared social identity with stewards reduces the number of highly exposed agents by 82% for mask wearing. In contrast, strong shared social identity with non-adhering role models gives almost nine times as many highly exposed agents as with adhering role models. Physical distancing was not monotonically beneficial, because adherence changes how agents move: an infectious agent that kept distance moved along the edge of the queue, leading to similar results across conditions. Our pipeline transfers to any survey that includes behavioural measures and contextual variables.

Target-oriented face de-identification models aim to anonymize the identity of a target individual across different images or video frames, such that the target can no longer be reliably recognized, while maintaining key characteristics of the visual data. Such models commonly leverage generative encoder-decoder architectures to manipulate facial appearances, enabling them to produce realistic high-fidelity de-identification results, while ensuring considerable attribute-retention capabilities. However, target-oriented models also carry the risk of inadvertently preserving subtle identity cues, making them (potentially) reversible and susceptible to reconstruction attacks. To address this problem, we introduce in this paper a novel (robust) face de-identification approach, called HYDRO, that combines target-oriented models with a dedicated diffusion process specifically designed to destroy any imperceptible information that may allow learning to reverse the de-identification procedure. HYDRO first de-identifies the given face image, injects noise into the de-identification result to impede reconstruction, and then applies a diffusion-based recovery step to improve fidelity and minimize the impact of the noising process on the data characteristics. To further improve image fidelity and better retain gaze directions, a novel Eye Similarity Discriminator (ESD) is also introduced and incorporated it into the training of HYDRO. Extensive quantitative and qualitative experiments on three diverse datasets demonstrate that HYDRO exhibits state-of-the-art (SOTA) fidelity and attribute-retention capabilities, while being the only target-oriented method resilient against reconstruction attacks. In comparison to multiple SOTA competitors, HYDRO reduces the success of reconstruction attacks by 85.7% on average.

Three adaptive global tracking controllers for fully actuated Euler-Lagrange systems, with verifiable performance improvement over existing designs, are reported in this letter. Two of these controllers ensure global exponential convergence under a weak interval excitation condition. Besides, one of the proposed controllers features a simple adaptive PID-like structure that-unlike classical solutions-avoids the need for additional filtering. We adopt a composite adaptation architecture, invoke a novel parameterization of the system dynamics and use a high performance estimation scheme recently introduced in the literature. Real-time experiments and a comparative study with a learning-based adaptive controller on a two-degrees-of-freedom manipulator arm illustrate the effectiveness of the proposed controllers.

Large language models are increasingly applied to high-risk domains such as law, yet complex legal reasoning remains limited by two structural challenges. First, existing RAG and GraphRAG methods emphasize lexical or semantic similarity while overlooking normative relations among legal provisions. Second, vanilla Chain-of-Thought prompting may generate plausible rationales without enforcing the normative structure of legal reasoning. To deal with the bottleneck of pipelines in the legal reasoning domain, we propose LEGO, a dual-module framework that synergizes Legal Expert GraphRAG and expert Chain-of-thought for complex legal reasoning. ExpertGraphRAG uses an expert-annotated civil code graph encoding these normative relations with a greedy normative-coverage retrieval algorithm to dynamically extract instance-specific provision subgraphs, while ExpertCoT organizes the retrieved provisions and case facts into structured Provision-Fact-Conclusion reasoning. With a Qwen3-8B backbone, LEGO achieves 40.53% exact-match accuracy on LawExamQA_Civil, outperforming the evaluated RAG and CoT baselines and performing comparably to the evaluated larger models, while remaining robust on multi-hop questions. It also achieves the best results among the evaluated baselines on the open-ended benchmarks. Ablation studies confirm the individual and complementary contributions of both modules, demonstrating LEGO's effectiveness in improving LLMs' complex legal reasoning ability. Code and dataset can be found in the link: https://github.com/BLK-WHT/LEGO

We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[\mu] = \frac12\iint_{M\times M}K(x,y)\,\mathrm d\mu(x)\,\mathrm d\mu(y) \] on a closed manifold $M$. For kernels diagonal in a Laplace eigenbasis with nonnegative spectral coefficients, we prove a differential inequality relating the relative entropy to the energy gap. Consequently, for any nonnegative initial density $u_0\in L^p(M)$, $p>1$, the energy gap is integrable in time and satisfies \[ \mathsf E[\mu_t]-\mathsf E_{\min}=o(t^{-1}). \] If all spectral coefficients are positive, the flow converges weakly to the constant measure. These interaction energies need not be geodesically convex in Wasserstein space, and the associated flows contain no diffusion; their global convergence therefore does not follow from standard Wasserstein gradient flow theory. The kernels covered by our results include zonal kernels on spheres, kernels arising in transformer models, regularized Riesz kernels, and inverse fractional Laplacian kernels. We also investigate the sharpness of the $o(t^{-1})$ rate. For any smooth kernel in this class with infinitely many positive spectral coefficients and any $\delta>0$, we construct a solution of the linearized flow whose energy is comparable to $t^{-1-\delta}$ along a sequence of times tending to infinity. Moreover, for any $\delta>0$, by choosing a suitable inverse fractional Laplacian kernel on the flat torus, we construct an exact solution of the nonlinear Wasserstein gradient flow whose energy is comparable to $t^{-1-\delta}$. The nonlinear construction is based on uniform-in-time estimates for the evolution of the dyadic Fourier coefficient blocks and a blockwise energy-persistence argument. These estimates also yield a uniform-in-time quantitative comparison between the nonlinear Wasserstein gradient flow and its linearization.

Optical-resolution photoacoustic microscopy (ORPAM) provides label-free optical-absorption contrast at millimeter-scale tissue depths with micrometer-scale lateral resolution. However, its volumetric coverage is limited by the short depth of focus of conventional optical lenses, whereas system miniaturization is constrained by bulky optics and ultrasound transducers. Here, we present an extended-depth ORPAM system that combines an ultra-thin metalens for optical excitation with a planar transparent ultrasound transducer (TUT) for photoacoustic detection. Fabricated from piezoelectric lithium niobate, the chip-scale TUT provides ~80% optical transparency and enables coaxial optical excitation with simultaneous acoustic detection at 14.4 MHz center frequency. This architecture eliminates the need for bulky acousto-optic combiners and large-volume acoustic coupling arrangements between the transducer and imaging target. We evaluate three ultra-thin metalens designs as hyperbolic, quadratic, and extended depth-of-focus (EDOF), which provide effective axial ranges of 0.3, 0.8, and 1.3 mm, respectively, with lateral resolutions of 1.1 micron for hyperbolic, 1.2 micron quadratic lenses, and 1.5 micron for EDOF across the full axial range. Phantom experiments demonstrate improved visualization of multilayered, inclined, volumetrically distributed targets with the EDOF design compared with the two other metalenses. Label-free imaging in awake, head-fixed mice further demonstrates that EDOF provides extended-depth visualization of subcortical microvasculature without being subjected to anesthesia-induced confounds. This chip-scale metalens-TUT architecture provides a foundation for developing compact photoacoustic microscopy systems.

We present a laser-tracker-assisted hand-eye calibration method for camera-equipped mobile robots. The method combines laser-tracker-based 3D metrology with camera-based 2D observations. Building on our previous laser-tracker-assisted camera-to-robot calibration method for ground-observing mobile robots, we present a generalized formulation for calibrating the camera pose in the coordinate system of tracker-localized mobile robots. The new approach relaxes assumptions of our previous method on robot and camera configuration by chaining multiple calibration targets resulting in a more general approach supporting various camera-equipped mobile robot systems.

We focus on the problem of rearranging multiple objects within a constrained workspace via pushing using a team of car-like robots. While the use of multiple robots offers the potential for more efficient execution, the need for conflict resolution and the kinematic constraints arising from physics, robot design, and the workspace boundary make this problem especially challenging. Our key insight is that by exploiting the structure introduced by the car-like kinematics of the domain, we could relax the problem into an ordered assignment of Dubins curves to robots. To this end, we introduce MultiPush, a reinforcement-learning based framework that jointly determines an efficient schedule of pushing tasks and their allocation to available robots by leveraging a constraint-aware traversability graph. Across extensive simulated trials with up to 14 objects and teams of two to four robots, MultiPush reduces the makespan by up to 16% compared to the baselines while requiring up to 2.9 times faster planning time. We demonstrate MultiPush on a real-world scenario involving the rearrangement of 12 objects by two and three robots (1/10-scale racecars) in a constrained space.

Quantisation is considered as an action of classical point operators on field states at the Planck scale of the phase space. Emphasis is placed on the sequence of physical variables. A "state language/Dirac notation" for classical mechanics is introduced; in many cases, it replaces the principle of stationary action for conservative systems. Observed classical and quantum dynamics are considered as different vectorisations of the free semigroup contribution of time. There is a dream of describing classical dynamics as complex transformations of state vectors over such a free semigroup, rather than solving differential equations. The transition from the alphabet to states, from states to state functions, and from state functions to measurable quantities is managed by projectors. An attempt is made to provide a derivation of the Legendre transformation. The trivial multiplication of the potential energy by the wave function in the coordinate representation and its non-trivial operator action in the momentum representation are obtained without a Fourier transform nor the Planck scale. The quantisation procedure is divided into two stages: first, the action of point-like classical operators on field functions; and second, accounting for the physically finite scale of the Planck length against the backdrop of the possible infinitesimality in the classical phase space. The concept of an angle between states is introduced, defining the measure of "quantumness". The free semigroup time contribution is studied in the context of the Born rule.

Runway walking requires coordinated control of posture, stride, foot placement, and whole-body motion to effectively present clothing and convey a distinctive style. However, humanoid robots used in fashion shows typically rely on locomotion policies optimized primarily for stability and walking speed, limiting their ability to reproduce expressive, human-like runway motions. In this work, we present an end-to-end framework that transforms monocular runway videos into deployable humanoid locomotion policies through motion recovery, robot retargeting, motion correction, policy training, simulation-based evaluation, and physical deployment. We evaluate the proposed framework on the Booster K1 humanoid robot using runway-style catwalk motions. The learned policy completed every physical trial without falling, while reproducing the characteristic narrow foot placement and coordinated movement of the legs, torso, and arms. The results demonstrate that our proposed training framework enables the Booster K1 to perform stable and expressive catwalk motions, highlighting its potential for humanoid robotic applications in fashion shows and other performance-oriented scenarios.

Nonlocal models have found great success in recent years. In particular, models that replace spatial derivatives with strongly singular integral operators involving finite interaction radii are used in a wide range of applications, including image processing, continuum mechanics, and many other areas. However, from the perspective of mathematical analysis, difficulties arise when considering the appropriate notion of “boundary” conditions. (The nonlocal analogue of the boundary is often called a “collar” and is typically not a lower-dimensional set.) For instance, merely enforcing homogeneous Dirichlet-type constraints on the collar fails to guarantee a number of essential properties used in the analysis and numerical simulation of these models, as we show in the present work. In the local setting, working in a Sobolev space of functions that are zero on the boundary allows one to integrate by parts with no boundary term, approximate by test functions, extend by zero to the full space, and apply the Hardy and Poincaré inequalities. We prove that the nonlocal analog of each of these fails if one only requires the functions to be zero on the collar, and that one must move to a smaller, more restrictive space to enjoy these properties. In addition, we introduce a new lifting operator, correct an error in a previously published result on a nonlocal Green's theorem, and establish how the properties listed above relate to existing notions of fractional Sobolev spaces.

We investigate humanoid locomotion with a fly-inspired recurrent controller and identify the pathways supporting its deployed behavior. The controller couples 3,609 continuous neural states to a simulated Unitree G1 through body-observation projections, a motor-neuron-labelled readout, and joint servos. We formulate this neural-body feedback system and evaluate a fixed checkpoint across seven terrain instances, three speeds, and three initial yaw offsets. It completes 61/63 conditions under a survival-and-forward-progress criterion; a privileged reference completes 62/63. At nominal yaw, resetting the recurrent motor state before every policy call changes success from 19/21 to 0/21. Conversely, depth and upstream-state substitutions at 252 recorded states leave actions unchanged, with zero measured descending output throughout the intact rollouts. Recorded trajectories and state-matched images connect these findings to sustained movement, lateral drift, and termination events. The study characterizes an embodied recurrent control system whose tested locomotion is supported by direct body-and-command input and carried motor state, providing a concrete basis for subsequent comparisons of circuit structure and control resources.

We develop a first-principles theory for nonadiabatic surface dynamics, providing a fit-free connection between density functional theory (DFT) calculations and the effective multi-orbital Anderson-Newns (AN) theory. Our theory contains two main advances. First, we outline the multi-orbital AN theory with orbital overlap and derive closed-form expressions for the hybridization energy, electronic dynamics, and electronic friction. Second, we describe a procedure to map the DFT Hamiltonian into the effective AN Hamiltonian with nuclear-position dependence. We obtain the electronic part of the AN Hamiltonian solely from the adsorbate-projected density-of-states matrix. We then define the bare nuclear potential as the difference between the total energy and the hybridization energy. The theory is applied to H and CO on the Cu surface, where widely used assumptions about the hybridization function, including the wide-band limit, semi-elliptical forms, and separability in energy and nuclear coordinate, are found to fail, and the single-orbital description breaks down qualitatively for CO. We expect this work to be broadly useful for first-principles modeling of coupled nuclear-electronic dynamics and chemical reactions at metallic surfaces.

We identify and analyze the little red dots (LRDs) in the AMBRA cosmological hydrodynamic simulation, by producing mock observations of the galaxies and active galactic nuclei (AGN) between redshifts 5 and 8. We produce these mock observations with both a standard AGN emission model, and a “gas-enshrouded” model, and find that the presence of a gas-enshrouded AGN is instrumental to the reproduction of dim LRDs (F444W magnitude $>$ 26.0). We find a steeper decrease in LRD density between $z=5$ and $z=8$ within AMBRA than seen in observations, resulting in a relative underproduction of LRDs beyond $z\sim6$ in AMBRA. With the addition of unresolved AGN variability, the decline with redshift flattens, and the LRD redshift evolution in AMBRA becomes broadly consistent with other theoretical datasets, and closer to that seen in observations. We find that the LRDs in AMBRA are pre-existing black hole–galaxy systems that are undergoing an LRD phase, selected primarily by the brightness of the AGN relative to its host. While the exact duration of these LRD phases is not possible to determine due to the unresolved nature of the AGN environment, we use the available time-series data to place limits on the lifetimes of the LRDs in AMBRA. We find that the vast majority of LRDs in AMBRA have lifetimes between $\sim3$ and $\sim 300$ Myr with LRD lifetime increasing with both black hole and host galaxy mass. The lower mass LRDs are more dependent on housing a gas-enshrouded AGN, and have shorter lifetimes ($\rm \sim30~Myr$). The higher mass LRDs are less sensitive to their AGN environment, but require more compact host galaxies, and have longer lifetimes ($\rm \sim100~Myr$).

Recent JWST observations have revealed a sample of high-$z$ galaxies with highly enhanced N/O abundance ratios, $\log\rm (N/O)\gtrsim -1.1$. Strong optically-thick winds of rotating massive stars going through the Wolf-Rayet (WR) phase provide a viable explanation for such N/O enhancements, supported by the direct spectroscopic WR signatures discovered in a few galaxies. Such strong winds are also needed to reproduce the single WR stars in the Small Magellanic Cloud (SMC). Here, we compute the metal yields of massive ($\sim 20-100\ \rm M_\odot$), metal-poor stars using two sets of MESA single stellar evolution models with and without optically-thick winds in a dense grid of metallicities ($Z_\star\sim 0.001-0.0045$) and initial spins ($\omega\equiv\Omega/\Omega_{\rm crit}\sim 0-0.7$). Considering an initial spin distribution based on observations of O-type stars in the SMC, we find that both sets produce strong N/O enhancements up to $\rm \log(N/O)\sim 0.1$ within a few Myr after a starburst. The models with optically-thick winds undergo a rapid transition from high N/O to the `normal' state of $\rm \log(N/O)\sim -1.5$ at $t\sim 3-4$ Myr driven by C/O-rich winds, while the transition is slower and weaker without optically-thick winds. The optically-thick-wind scenario can reproduce the nebular C, N, O, and He abundance patterns of three representative high-$z$ galaxies showing direct WR signatures: RXCJ2248-ID, Sunburst Arc, and MARTA 4327, with stellar metallicities and ages similar to those inferred from SED-fitting. This can be interpreted as a coherent evolution sequence captured before ($t\lesssim 3$ Myr), during ($t\sim 3-4$ Myr), and after ($t\gtrsim 5$ Myr) the transition. In contrast, the optically-thin-wind-only scenario ejects much less C and O via winds and cannot reproduce Sunburst Arc and MARTA 4327. The yields are available at https://zenodo.org/records/22897057.

We establish an exact parametrized reduction of the classical Willmore flow of Hopf tori in the round three-sphere to the spherical elastic flow. In Willmore-flow time the reduction is $(\partial_t\gamma)^{\perp}=-4\nabla_{L^2}\mathcal E(\gamma)$; its global reconstruction uses a pullback-circle-bundle normalization and does not require preservation of simplicity along flow lines. Combining the known global subconvergence of the spherical elastic flow with Pozzetta's full convergence theorem then yields full smooth convergence of flow lines, modulo domain diffeomorphisms, for every simply parametrized Hopf torus at arbitrary initial energy. We then obtain quantitative conclusions for the unreparametrized trajectory: finite normal $L^2$-metric length, total-variation convergence of the pullback area measures, bounded-Lipschitz convergence of the image measures, and explicit tail estimates. The density of the full varifold endpoint equals the covering multiplicity of the limiting elastic profile, and Pinkall's marked flat lattices converge. In particular, a simple initial Hopf immersion with energy arbitrarily close to $4\pi^2$ from above can smoothly converge to some parametrization of the Clifford torus with multiplicity two, although its limiting conformal class in moduli space is exactly the square class.