arXiv subjects

Peng Liu

Publications and source records attributed to Peng Liu.

At least 19 recordsLinked to original sources

arXiv2026

Multiplicity Bounds for Contractible Closed Reeb Orbits on Prequantization Bundles

We study the multiplicity of contractible closed Reeb orbits on prequantization circle bundles $(M^{2n+1},ξ)$ over closed symplectic manifolds $(B^{2n},ω)$. For even $n$, under suitable geometric hypotheses, we prove that every non-degenerate contact form supporting $ξ$ whose contractible closed orbits have nonzero mean index and whose good contractible closed orbits have nonzero Conley--Zehnder index carries at least $\frac{1}{2}χ(B)+\frac{1}{2}\dim H_n(B;\mathbb{Q})+1$ geometrically distinct contractible closed Reeb orbits. In dimension five, under the corresponding geometric hypotheses and assuming $H_1(B;\mathbb{Q})=0$, we prove the conjectural lower bound $\dim H_*(B;\mathbb{Q})$ for every non-degenerate supporting contact form whose simple contractible closed orbits have nonzero Conley--Zehnder index.

math.SG↗

arXiv2026

Robust distortion riskmetrics over Bregman--Wasserstein balls and their intersections

We study the worst-case values of distortion riskmetrics over Bregman--Wasserstein balls around a reference distribution. Unlike the squared $2$-Wasserstein distance, Bregman--Wasserstein divergences can penalize upward and downward deviations differently. Our main result applies to generalized distortion functions $g:[0,1]\to\R$ of bounded variation, with $g(0)=0$ and suitable endpoint regularity, which need not be monotone, normalized, or upper semicontinuous. For strictly convex generators satisfying a two-sided $p$-growth condition, we obtain a one-dimensional dual representation of the worst-case value. When a positive Lagrange multiplier makes the divergence constraint binding, we identify a unique quantile function through a least concave majorant and characterize when it attains the supremum. For absolutely continuous generalized distortion functions, we characterize the solution through an isotonic projection; we also study more general generators and shape constraints, including unimodality. Finally, we extend the analysis to intersections of Bregman--Wasserstein balls, describing models acceptable to several parties involved in decision making, and illustrate the results numerically.

q-fin.RM↗

arXiv2026

Multiplicity of brake Reeb orbits on real prequantization bundles

We prove multiplicity results for geometrically distinct brake Reeb orbits on real prequantization $S^1$-bundles under geometric and dynamical assumptions. The lower bounds are expressed in terms of the sum of the mod-two Betti numbers of the real locus of the base. Our proofs combine Lagrangian Rabinowitz Floer homology with the index iteration theory for brake orbits. As an application, we obtain a sharp lower bound for the number of brake geodesics on Finsler spheres with pinched flag curvature.

math.SG↗

arXiv2026

Rotation overcharges vectorized black holes

A charged black hole has a ceiling: extremality bounds the charge that a given mass and spin can support. Vector hair has so far only lowered it. In the Einstein--Maxwell--Vector (EMV) model, where a massless vector field couples nonminimally to the electromagnetic invariant, the spherically symmetric vectorized Reissner--Nordström black holes are strictly undercharged: vector hair is paid for in charge. Whether this ceiling is a property of the vector field or merely of spherical symmetry has remained open, because spherical symmetry hides the hair's mass as well: its Komar mass vanishes identically and the exact identity $M_V=2Ω_HJ_V$ degenerates to $0=0$. Rotation lifts both degeneracies at once. We construct the rotating solutions of the model, the first in this setting, and find that the hair's mass is not a free parameter but a second-order invariant of the rotational response, fixed by $M_V=2Ω_HJ_V$. Above a coupling threshold the ceiling gives way: the domain of existence crosses the extremal Kerr--Newman bound, reaching $q=Q/M>1$ with $q^2+χ^2$ up to $1.84$, while at $α=5$ the maximum charge stays below it. The shadow is where the hair becomes visible. At $(q,χ)=(0.9947,0.10)$, near the extremal bound, the hair contributes an ellipticity of $8.30\%$, against $0.44\%$ from the charge and $0.06\%$ from rotation --- a factor of $19$ that charging a Kerr black hole cannot mimic; at the overcharged solution $(q,χ)=(1.2527,0.10)$ the total ellipticity reaches $25.6\%$. Whether the branch is ghost-free remains open, but the existing no-go criteria do not settle it: they assume a background and a dispersion relation that do not hold here.

gr-qc↗

arXiv2026

Yb/Sr optical clock comparison at 2.2E-18 uncertainty over a 1350-km fiber link

Redefining the International system of Units (SI) second requires independent frequency-ratio measurements between clocks based on different laboratories, with an overall uncertainty below 5E-18, to validate individual clock evaluations through consistency checks. Reaching this uncertainty over long distances has remained challenging. So far, comparisons at this level have been achieved only a few times, between co-located clocks, and their results disagree markedly. Previous high-precision comparisons have therefore been limited to local or kilometre-scale links. Here we compare a ytterbium optical lattice clock in Wuhan with a strontium optical lattice clock in Shanghai over a phase-stabilized fiber link spanning 1350 km, and determine the Yb/Sr frequency ratio to be 1.207 507 039 343 337 716 0(26), with a Bayesian statistical uncertainty of 1.14E-18 and a total uncertainty of 2.18E-18. To our knowledge, this is the first intercity long distance frequency-ratio measurement, whose total uncertainty reaches the level required by the redefinition roadmap. The measured ratio exhibits a significant correlation with Earth tides and its response agree with the model within the statistical uncertainty. At intercity scale, this comparison demonstrates the capability of an optical-clock network for frequency comparison and Earths gravitational-potential sensing, a key step toward a wide-area optical-clock network.

physics.optics↗

arXiv2026

Current validation practice undermines surgical AI development

Surgical data science (SDS) is rapidly advancing, yet clinical adoption of artificial intelligence (AI) in surgery remains limited, with inadequate validation as an important contributing factor. Existing validation practices often neglect the temporal and hierarchical structure of intraoperative videos, yielding misleading or clinically irrelevant results. We introduce a comprehensive catalogue of validation pitfalls in AI-based surgical video analysis, derived from a multi-stage Delphi process with 92 international experts. Pitfalls span three categories: (1) data, (2) metric selection/configuration, and (3) aggregation and reporting. A systematic review of surgical AI papers reveals that these pitfalls are widespread. Experiments on surgical video datasets show that ignoring temporal and hierarchical data structures can understate uncertainty, obscure critical failure modes, and alter algorithm rankings. To address these shortcomings, we provide consensus-based best practices compiled. Together, this work provides an evidence-based framework for rigorous validation of surgical video analysis algorithms, guiding benchmarking, reporting, regulatory review, and clinical translation.

q-bio.OT↗

arXiv2026

Conditional Flow Matching for Generation of 3D Multi-variable Instantaneous Urban Microclimate Fields

Rapid and accurate prediction of urban wind and temperature fields is important for urban microclimate design and climate adaptation. Large-eddy simulation (LES) effectively resolves these instantaneous fields, but its application is limited in iterative design of urban microclimate applications due to high computational cost. Existing regressive data-driven models offers quick outputs, but they produce only deterministic point predictions that inherently fail to represent turbulent stochasticity. This paper adopts a novel generative framework of Conditional Flow Matching (CFM) that uses building geometry and mean flow as guidance to generate plausible three-dimensional instantaneous velocity and temperature fields for urban microclimate in seconds. To overcome the GPU memory bottleneck of pixel space 3D generation, the model operates in parallel on overlapping pixel space through a shared-noise initialization that preserves high spatial continuity of flow structure across the entire domain. Against reference LES data, the CFM surrogate can rapidly and accurately restore the first-order statistics with Normalized Root Mean Square Error (NRMSE) of 2.99% for wind and 1.77% for temperature, second-order turbulence metrics with NRMSE of 7.17% for wind and 8.84% for temperature, turbulent kinetic energy with NRMSE of 7%, probability density function and vertical profiles in representative locations. Wind engineering application of local gust prediction demonstrate that the speed and accuracy of CFM, supporting the use of generative AI for making turbulence-aware resilient urban design and climate adaptation more computationally feasible.

physics.flu-dyn↗

arXiv2026

Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data

Classification problem in the context of highly imbalanced data is a major challenge in many real-world applications (e.g., FinTech, healthcare, etc.). In these cases, the vast majority of instances belong to a single class and a small fraction represent the minority class (often the most critical class). Recently, diffusion models have emerged as powerful approaches to reduce the degree of ``imbalanced-ness'' in the dataset; they work by generating synthetic data by capturing complex data distributions using iterative transformations. However, standard diffusion models are not inherently suited to highly skewed or heavy-tailed data, due to inbuilt quadratic error loss, which lacks the structural sensitivity to capture rare, extreme values, and minority-class nuances. We propose a novel approach, namely, Quantile-TabDDPM, based on a quantile-regularized denoising objective that combines the standard quadratic error loss with a quantile loss term to explicitly capture rare events while preserving the theoretical grounding of the original denoising objective. We extensively evaluated our approach on a real-world credit card transaction dataset characterized by extreme class imbalance. The results demonstrate that the integration of diffusion-based synthetic data generation with a quantile-regularized denoising objective provides a robust and effective framework for fraud detection in highly imbalanced datasets.

cs.LG↗

arXiv2026

DR-IPC: Disturbance-Resilient Integrated Planning and Control for LiDAR-Based Quadrotor Navigation

LiDAR-based quadrotor navigation in cluttered environments remains challenging under external disturbances, particularly when obstacle-aware motion generation and disturbance-rejection control are handled in separate layers. This article presents disturbance-resilient integrated planning and control (DR-IPC), which combines lightweight path guidance with nonlinear model predictive control (NMPC) to directly generate angular velocity and thrust. An interconnected extended Kalman filter and nonlinear disturbance observer jointly provide filtered state estimates and reconstructed disturbances for NMPC prediction. The resulting formulation unifies nonlinear quadrotor dynamics, actuator constraints, local motion generation, and penalised safe-flight-corridor residuals without requiring a separate trajectory-optimization stage. Gazebo and MARSIM simulations, together with indoor and outdoor experiments, validate DR-IPC under wind, suspended payloads, narrow passages, ball impacts and reactive avoidance of a dynamic obstacle. In multi-goal navigation with disturbances, DR-IPC increases the number of completed missions from 1/10 to 9/10 in Gazebo and reduces the altitude RMSE from 0.34 to 0.01 m in experiments. The complete system operates onboard at 100 Hz. Supplementary videos are available on the project page https://drpp316.github.io/DR-IPC-Page/, and the source code will be released.

cs.RO↗

arXiv2026

Are Agents Ready to Teach? A Multi-Stage Benchmark for Real-World Teaching Workflows

Language agents are increasingly deployed in professional workflows, yet tutoring remains a high-stakes capability that existing evaluations only partially capture. Effective tutor agents require more than producing correct answers or executing accurate tool calls: they must infer a warranted teaching decision from evidence, adapt support as learner state changes, and carry an instructor's request through a learning-management system (LMS) to a completed, verified intervention. We introduce TeachArena, a source-grounded benchmark that jointly evaluates three complementary surfaces of teaching work: professional pedagogical judgment, situated multi-turn tutoring, and end-to-end LMS teaching workflows. Its 354 audited tasks are each built around a pedagogical insight, grounded in evidence, and evaluated with matched verifiers over observable turn-level responses, tutoring trajectories, and persistent artifacts or environment states. Across a comprehensive evaluation of frontier models, our findings reveal that current models are generally capable of bounded pedagogical judgment, but still fall short of professional teaching standards in situated tutoring and end-to-end teaching-workflow execution. By unifying teacher judgment, adaptive tutoring, and institutional action in one auditable benchmark, TEACHARENA provides a measurement foundation for developing tutor agents that can support realistic teaching work.

cs.AI↗

arXiv2026

GoCo: structure-guided conformal calibration for error-controlled Gene Ontology annotation release

Computational gene-function prediction generates annotations at a scale that experimental characterization cannot match, yet substantial errors remain even among leading methods. Explicit error-controlled calibration for Gene Ontology (GO) prediction remains largely undeveloped. We introduce GoCo, a structure-guided framework that calibrates how scores from an existing predictor are converted into released annotations. GoCo certifies a global threshold for a GO-hierarchy-aware gene-level false discovery proportion (FDP), then constructs a nested release path under the same asymptotic risk-control guarantee. At the primary operating point (alpha=0.10, delta=0.50), GoCo-M, developed on Wainberg co-essentiality modules and applied without retuning to three independent studies with the same shared-evidence structure, kept mean held-out gene-level FDP at or below target while releasing 6.3-17.6% more reference-supported GO terms than Multilabel. For gene-specific neighbourhoods, GoCo-N orders individual calls. Developed on FunMap and validated without retuning on the STRING v12.0 experiments-only network, GoCo-N released 33.8% and 36.4% more reference-supported GO terms than Multilabel on the same refined score grid in FunMap and STRING, respectively, while keeping mean held-out FDP below target. The same pattern held under the stricter delta=0.10 setting. Thus, predictor-native biological structure can be reused at calibration, not only prediction, to release more supported annotations at a chosen gene-level error target without retraining the predictor.

q-bio.QM↗

arXiv2026

Risk diversification for infinitely divisible distributions

In this paper, we study the diversification properties of convex combinations of iid infinitely divisible random variables. For Lévy processes with bounded variation sample paths, we characterize, in terms of subadditivity and concavity of the transformed Lévy tails, Lévy processes that exhibit the non-diversification phenomenon or the reverse diversification order with respect to the majorization order uniformly over all time horizons. For general symmetric Lévy processes without a Gaussian component, we show that the symmetric 1-stable Lévy process is the only nontrivial process exhibiting either phenomenon. We further investigate convex combinations of components of multivariate infinitely divisible distributions, allowing for dependent and heterogeneous components, and characterize the Lévy measures of multidimensional Lévy processes exhibiting the two adverse diversification phenomena uniformly over all time horizons. Explicit characterizations are obtained for the multidimensional symmetric Lévy processes, multidimensional $α$-stable processes and multidimensional compound Poisson processes. Finally, we show that the non-diversification phenomenon extends beyond Lévy processes to running maxima and integrals of increasing convex functionals of Lévy processes, while both adverse diversification phenomena are preserved for Lévy-driven stochastic integrals with nonnegative deterministic kernels. Applications to ruin theory, storage processes and stochastic volatility are also discussed.

math.PR↗

arXiv2026

Joint DNN Partitioning and Resource Allocation for Satellite-Terrestrial Collaborative Inference Systems

This letter investigates a satellite-terrestrial collaborative inference system for remote sensing information processing, where a ground station (GS) serves multiple low Earth orbit (LEO) satellites running heterogeneous deep neural network (DNN) inference tasks. By partitioning the DNN between the satellite and the GS, each satellite executes the front-end layers locally, transmits the resulting intermediate features to the GS, thereby offloading the remaining layers to the GS for inference completion. We jointly optimize DNN partitioning, satellite and GS computing resources, satellite-ground bandwidth allocation, and satellite transmit power to minimize the average task completion latency under per-satellite energy constraints. To address the coupling between discrete partitioning decisions and continuous communication-computing variables, we propose a two-layer optimization algorithm. The inner layer performs closed-form updates and efficient nested bisection searching to update the continuous resource variables, while the outer layer employs random-restart coordinate descent to refine the partitioning decisions. Simulation results show that the proposed algorithm effectively reduces task completion latency compared with conventional binary offloading.

eess.SP↗

arXiv2026

Robust distortion risk metrics with Wasserstein and Unimodal Constraints

We establish sharp upper and lower bounds for distortion risk metrics under distributional uncertainty. The uncertainty sets are characterized by four key features of the underlying distribution: mean, variance, unimodality, and Wasserstein distance to a reference distribution. We first examine a broad class of distortion functions, assuming only finite variation and imposing neither continuity nor monotonicity. This class includes important examples such as the Gini deviation, the mean-median deviation, and inter-quantile differences. When the uncertainty set is defined by a fixed mean, variance, and Wasserstein distance, we derive the worst- and best-case values of the distortion risk metric and identify the corresponding extremal distributions. We then impose an additional unimodality constraint. In this case, for absolutely continuous distortion functions, we again characterize the worst- and best-case values and explicitly determine the optimal distributions attaining these bounds. Moreover, an algorithm is developed to compute sharp upper bounds and the worst-case quantiles. We apply our results to a robust portfolio optimization problem of interest.

q-fin.RM↗

arXiv2026

Radiation-induced electron spin polarization in ultrarelativistic kinetic turbulence

Electron spin polarization in radiative plasmas with ultrarelativistic kinetic turbulence under highly magnetized conditions is investigated using particle-in-cell simulations. We observe that a significant spin polarization can be sustained when the leptons undergo energetic photon emission accompanied by spin flips during the nonequilibrium turbulent evolution. By analyzing the time evolution of spatially dependent spin polarization, we identify an electromagnetic (EM) regime of kinetic turbulence, distinct from the well-known density-dominated regime characterized by vortex currents and magnetic islands. While in the latter regime the spin polarization exists only transiently, in the EM regime significant anisotropic net polarization emerges and persists in non-dissipative scenarios. The correlation between spin signals and turbulence features is leveraged to introduce the characteristic parameter delimiting the EM regime via the ratio of electric and magnetic energy densities and to gain insight into complex plasma turbulence. This study demonstrates the versatility of a spin-resolved study of the plasma turbulence in extreme environments, such as black holes and magnetar magnetospheres.

physics.plasm-ph↗

arXiv2026

TRACE: Temporal Audit and Condition-aware Evaluation of Streaming Video Understanding

Streaming video understanding requires models to interpret evidence as it arrives, yet current evaluations often report task scores without specifying when evidence becomes valid, how visual history is maintained, or how responses are triggered. As a result, similar scores may correspond to different workloads, failure modes, and operational behavior. We introduce TRACE (Temporal Audit and Condition-aware Evaluation), a condition-aware benchmark and evaluation framework that makes these factors explicit. TRACE combines temporally audited visual tasks with evidence timing and instruction-dependent trigger annotations, a unified causal Core--Adapter protocol that controls information availability while recording actual history processing and response events, and multidimensional reporting of answer quality, timeliness, response-selection behavior, workload, completion, and reliability. On 1,240 records from 517 videos, we evaluate eight publicly available models or systems in eight configurations. We find that nearly identical QA accuracy can mask substantial differences in completion, answer validity, and generation workload, while proactive performance separates into response quality, response delay, false alarms (responses emitted while no target window is currently valid and a later one remains), and missed target windows. These results show that streaming-video performance should be interpreted as execution-conditioned system behavior rather than a single score. Our benchmark and code can be accessed at \href{https://github.com/om-ai-lab/trace-bench}{https://github.com/om-ai-lab/trace-bench}.

cs.CL↗

arXiv2026

Anisotropy and energy distribution of leptons and photons in radiative relativistic Alfvénic turbulence

The anisotropic evolution of relativistic particles in magnetically dominated Alfvénic turbulence is a fundamental process governing nonthermal emissions in high-energy astrophysical environments. In this work, we develop a theoretical framework by deriving scaling equations that characterize the pitch-angle dynamics of leptons and photons across both weak- and strong-radiative cooling regimes. Our model reveals a universal coupling between particle energy and angular distribution, arising from the interplay of field-aligned accelerations, perpendicular drift motions, and radiation reactions. The model can uniquely identify ``turning-point energies" that exhibit a nonlinear dependence on the local magnetic field and the energy-injection scale. The validity of this scaling model is confirmed through radiative particle-in-cell simulations. We show that the electron pitch-angle distribution fundamentally dictates photon emission characteristics, further revealing a pronounced statistical correlation between high-energy photon emission and turbulent vortices in the reconnection regions. By bridging the gap between small-scale kinetic interactions and broad-band spectral characteristics, this work provides a quantitative basis for interpreting the hardening of radiation spectra and complex polarization signatures in sources such as pulsar wind nebulae and gamma-ray bursts.

physics.plasm-ph↗

arXiv2026

Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong capabilities of neural networks, recent research is exploring the value of machine learning alongside conventional MILP solving. Although learning-based MILP methods have shown great promise, existing works typically learn policies for individual modules in MILP solvers in isolation, without considering their interdependence, which limits both solving efficiency and solution quality. To address this limitation, we propose Collab-Solver, a novel multi-agent-based policy learning framework for MILP that enables collaborative policy optimization for multiple modules. Specifically, we formulate the collaboration between cut selection and branching in MILP solving as a Stackelberg game. Under this formulation, we develop a two-phase learning paradigm to stabilize collaborative policy learning: the first phase performs data-communicated policy pretraining, and the second phase further orchestrates the policy learning for various modules. Extensive experiments on both synthetic and large-scale real-world MILP datasets demonstrate that the jointly learned policies significantly improve solving performance. Moreover, the policies learned by Collab-Solver have also demonstrated excellent generalization abilities across different instance sets.

cs.AI↗