arXiv subjects

Na Liu

Publications and source records attributed to Na Liu.

At least 19 recordsLinked to original sources

arXiv2026

Operator Barron Regularity for Elliptic Equations and Application to Neural Operator Approximation

We develop a spectral Barron regularity framework for nonlinear operators between infinite-dimensional function spaces. Using Hilbert-valued Fourier representations of finite-dimensional input truncations, we establish bounds that are uniform in the input truncation dimension and prove arbitrary-order Barron regularity for a class of elliptic solution operators. Second, we use this operator Barron regularity to derive approximation error bounds for an FNO-type neural operator, with explicit dependence on the input truncation dimension, output reconstruction dimension, and network width. For a fixed input truncation dimension, optimizing the neural approximation bound over the Barron regularity order yields stretched-exponential decay of the approximation error in the network width. We also show some numerical experiments to support the predicted rate.

math.NA↗

arXiv2026

Template Ageing and Longitudinal Verification in Fixed-Text Keystroke Dynamics: A Subject-Disjoint Study Across Eight Weeks

Behavioural biometric templates are widely believed to degrade as the gap between enrolment and verification grows, but few studies measure this template ageing effect directly under controlled conditions. We collected a longitudinal dataset of 40 fixed passwords, each typed four times per weekly session over eight consecutive weeks. We compare a scaled-Manhattan matcher (M1), a gradient-boosted classifier (M2), a TypeNet-style recurrent embedding model (M3), and a TypeFormer-style Transformer (M4) under a 5-fold subject-disjoint protocol and a design that jointly varies mechanism and the enrolment-to-query gap, from 0 to 7 weeks. Template ageing proves large and systematic. Error increases monotonically with the gap for every mechanism, from an EER of 14.6-27.2% at a gap of zero to 25.5-37.1% at seven weeks, or 1.7% of decision error per week elapsed (p < 0.001). However, the choice of mechanism matters more than its rate of ageing. Baseline accuracy spans 12.6 percentage points across the four mechanisms, the degradation each accumulates over seven weeks spans only 2.3 points, and ageing never reorders them. A matcher can therefore be chosen on same-session accuracy, with ageing managed by re-enrolment scheduling rather than by matcher selection. The two properties are nonetheless distinct, as M3 is the least accurate mechanism yet ages significantly more slowly than M1 under every specification tested. Training randomness also matters differently by architecture, with 58% of the recurrent model's fold-to-fold variance attributable to seed noise against 19% for the Transformer. Because the smaller ageing-rate differences are sensitive to modelling choices, while the accuracy differences and the ageing effect are not, we recommend that comparative ageing-rate claims be supported by seed-level score fusion, independent replication, and an alternative outcome-model specification.

cs.CR↗

arXiv2026

Stabilized Higher-Order Influence Functions: Statistical Theory of a Class of Bilinear Forms

Higher-order influence functions, introduced in a series of articles (Robins et al., 2008, 2009a; van der Vaart, 2014; Robins et al., 2016, 2023; Liu et al., 2017), are a unified framework for constructing rate-optimal point estimates of a class of statistical functionals under various complexity-reducing assumptions on the posited statistical model that generates the observed data. Although higher-order (influence functions) estimators are theoretically appealing, they have very limited practical uptake compared to their first-order counterparts. The original higher-order estimators proposed in Robins et al. (2008) and Robins et al. (2017) involve nonparametric density estimation of multi-dimensional covariates, a highly nontrivial statistical and computational problem on its own. The density estimator is, in turn, used in the evaluation of the inverse population Gram matrix $Ω$ of a set of $k$-dimensional basis transformations of covariates. There, $k$ is allowed to be as large as $o (n^2)$. To partially address this potential shortcoming, Liu et al. (2017) restrict $k$ to $o (n)$ and instead estimate $Ω$ directly using the inverse sample Gram matrix estimator, but computed from an independent sample often obtained by sample-splitting. Liu et al. (2017) refer to this alternative estimator as the empirical higher-order estimator. Although the empirical higher-order estimator bypasses density estimation, it suffers from numerical instability due to inverting a large-dimensional sample Gram matrix. In this article, for a class of bilinear forms/functionals that often appear in substantive fields, we propose a new stabilized higher-order estimator without sample splitting, which exhibits more stable finite-sample performance compared to the empirical higher-order estimator. We also prove that this new class of higher-order estimators enjoys similar statistical guarantees.

math.ST↗

arXiv2026

Operationalizing open-ended biological discovery across single-cell representations

Single-cell studies are typically initiated from predefined research questions, leaving much of the biological information encoded within existing data unexplored. We formalize open-ended discovery as an analytical paradigm, in which data-derived signals are identified before biological context is interrogated and subsequently evaluated according to their potential to justify prospective experimental investment. Here we develop PROSPECTor, an end-to-end framework that searches for reproducible biological structures across conventional expression representations and diverse foundation-model embeddings, translating robust signals into quantitatively testable candidate hypotheses. Projection into unseen datasets then evaluates their generalizability and phenotype association, providing a scalable screen for candidates that warrant prospective validation. Supported signals emerged from different representation spaces and search strategies. PROSPECTor-nominated hypotheses were then examined in independent biological settings: fibroblast extracellular-matrix programmes demonstrated transferability to an independent mouse cohort with an intervention context, while a patient-resolved gastric-cancer T-cell programme recurred across single-cell, bulk and spatial cohorts. PROSPECTor establishes an auditable framework for systematically revisiting single-cell datasets across expanding representation spaces, turning retrospective collections into prospective resources for biological discovery that can motivate new research questions.

q-bio.QM↗

arXiv2026

Generation of energy-time entangled triphotons in a six-level cold atomic system

Multiphoton entangled states are pivotal resources for implementing optical quantum information protocols. Recently, energy-time-entangled triphotons have been observed in hot atomic ensembles. However, in these protocols, the complex fifth-order nonlinear susceptibility entailed by four- or five-level systems limits our understanding of triphoton generation. Here, to directly capture the generation mechanism of triphotons and their associated optical properties, we investigate the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble. The fifth-order nonlinear susceptibility indicates the existence of two sets of spontaneous six-wave mixing in the system. Notably, triphoton generation in this system is subject to stringent timing constraints. Collectively, these characteristics give rise to threefold coincidence counts, which -- dominated by the fifth-order nonlinear susceptibility -- exhibit asymmetrically damped Rabi oscillations in the two-dimensional time domain. Furthermore, we analytically derive that the temporal correlation properties of conditional two-photon states are preserved -- a unique feature of $W$-class tripartite entanglement. These results not only lay the groundwork for the experimental preparation of triphotons using six-level systems but also provide key support for understanding the generation mechanism of triphotons involving more complex fifth-order nonlinear susceptibilities.

quant-ph↗

arXiv2026

A simple, high-order and compact WENO limiter based on control volume for spectral volume method

The spectral volume(SV) method constructs a high-order polynomial for SV based on the average value of control volume(CV), but for discontinuous problems, a limiter is required to mitigate oscillations. This paper presents a novel CV-based high-resolution limiter to effectively suppress oscillations and maintain CV resolution. Drawing inspiration from the SWENO method [43], we utilize a nonlinear weighting approach to reconstruct a novel high-order polynomial for the target control volume by combining the high-order reconstructed polynomial and linear polynomials which are reconstructed by the cell average of the target CV and its neighboring CVs. The new high-order polynomial breaks the continuity in the SV, thus the utilization of numerical flux at the boundaries of troubled CVs and the SV boundaries. However, at other boundaries of CVs where physical quantities remain continuous, direct calculation of flux based on the values of physical variables is feasible. The limiter is simple, as it only requires several linear polynomials in the limitation process. Moreover, it still maintains the compactness of the SV method and preserves the resolution of CV. Numerical results for one- and two-dimensional scalar and system of conservation laws verified that the high-order property of the CV-SWENO limiter is effective in solving both smooth and strongly discontinuity problems.

math.NA↗

arXiv2025

Ultrahigh-Q chiral resonances empowered by multi-head attention deep learning

High quality (Q) factor optical chiral resonators are indispensable for many chiral photonic devices. Designing ultrahigh Q-factors in chiral metasurfaces traditionally relies on extensive parameter scanning, which is time-consuming and inefficient. While deep learning now provides a rapid design alternative, conventional models still face challenges in accurately predicting ultrahigh Q-factor spectral characteristics. In this study, we introduce a multi-head attention network (MuHAN) to accelerate the design of ultrahigh Q-factor optical chiral resonators in bilayer metasurfaces. MuHAN achieves forward spectral predictions in approximately 10ms, thousands of times faster than finite-difference time-domain simulations, boasting 99.85% and 99.9% accuracy for forward and inverse predictions, respectively. By transferring the learned physical principles, we perform inverse design of nanoscale structures with ultrahigh Q-factors (up to 2.9910E5) based on chiral quasi-bound states in the continuum (quasi-BICs) at minimal computational cost. Our rapid design tool, based on MuHAN, enables high-performance encryption imaging, bridging deep learning with high-Q chiral metasurfaces for advanced sensing, laser, and detection applications.

physics.optics↗

arXiv2025

Leveraging Contrast Information for Efficient Document Shadow Removal

Document shadows are a major obstacle in the digitization process. Due to the dense information in text and patterns covered by shadows, document shadow removal requires specialized methods. Existing document shadow removal methods, although showing some progress, still rely on additional information such as shadow masks or lack generalization and effectiveness across different shadow scenarios. This often results in incomplete shadow removal or loss of original document content and tones. Moreover, these methods tend to underutilize the information present in the original shadowed document image. In this paper, we refocus our approach on the document images themselves, which inherently contain rich information.We propose an end-to-end document shadow removal method guided by contrast representation, following a coarse-to-fine refinement approach. By extracting document contrast information, we can effectively and quickly locate shadow shapes and positions without the need for additional masks. This information is then integrated into the refined shadow removal process, providing better guidance for network-based removal and feature fusion. Extensive qualitative and quantitative experiments show that our method achieves state-of-the-art performance.

cs.CV↗

arXiv2025

Many-Body Entanglement in Solid-State Emitters

The preparation and control of quantum states lie at the heart of quantum information science (QIS). Recent advances in solid-state quantum emitters (QEs) and nanophotonics have transformed the landscape of quantum photonic technologies, enabling scalable generation of quantum states of light and matter. A new frontier in solid-state quantum photonics is the engineering of many-body interactions between QEs and photons to achieve robust coherence and controllable many-body entanglement. These entangled states, including photonic graph and cluster states, superradiant emission, and emergent quantum phases, are promising for quantum computation, sensing, and simulation. However, intrinsic inhomogeneities and decoherence in solid-state platforms pose significant challenges to realize such complex entangled states. This review provides an overview of the fundamental many-body interactions and dynamics at the light-matter interfaces of solid-state QEs, and discusses recent advances in mitigating decoherence and harnessing robust many-body coherence.

quant-ph↗

arXiv2025

A GPU-based Monte Carlo framework for IMRT QA using EPID transit dosimetry

Purpose: We presented a GPU-based MC framework, ARCHER-EPID, specifically designed for EPID transit dosimetry, with improving accuracy and efficiency. Methods: A comprehensive MC framework was developed to perform full radiation transport simulations through three distinct zones: a detailed linear accelerator head model, a CT-based patient/phantom geometry, and a realistic, multi-layered EPID model. To convert the simulated absorbed dose to a realistic detector signal, a dose-response correction model was implemented. The framework was validated by comparing simulations against experimental measurements for 25 IMRT fields delivered to both a solid water phantom and a anthropomorphic phantom. Agreement was quantified using Gamma analysis. Results: The GPU-accelerated ARCHER-EPID framework can complete the simulation for a complex IMRT field in about 90 seconds. A 2D correction factor lookup table is generated by parameterizing radiological thickness and effective field size to account for the EPID's energy-dependent response. The data revealed that for small fields, beam hardening is the dominant effect, while for large fields, the contribution from patient-generated scatter overwhelms this effect. The average 2D gamma passing rates (3%/3 mm criteria) between simulation and measurements are 98.43% for the solid water phantom and 97.86% for the anthropomorphic phantom, respectively. Visual comparison of the images and dose profiles between simulation and measurements show a high degree of agreement. Conclusions: We have successfully developed and validated a GPU-based MC framework that provides gold-standard accuracy for EPID transit dosimetry in radiotherapy. The results demonstrate that our proposed method has potential for routine application in PSQA.

physics.med-ph↗

arXiv2025

Awakening Facial Emotional Expressions in Human-Robot

The facial expression generation capability of humanoid social robots is critical for achieving natural and human-like interactions, playing a vital role in enhancing the fluidity of human-robot interactions and the accuracy of emotional expression. Currently, facial expression generation in humanoid social robots still relies on pre-programmed behavioral patterns, which are manually coded at high human and time costs. To enable humanoid robots to autonomously acquire generalized expressive capabilities, they need to develop the ability to learn human-like expressions through self-training. To address this challenge, we have designed a highly biomimetic robotic face with physical-electronic animated facial units and developed an end-to-end learning framework based on KAN (Kolmogorov-Arnold Network) and attention mechanisms. Unlike previous humanoid social robots, we have also meticulously designed an automated data collection system based on expert strategies of facial motion primitives to construct the dataset. Notably, to the best of our knowledge, this is the first open-source facial dataset for humanoid social robots. Comprehensive evaluations indicate that our approach achieves accurate and diverse facial mimicry across different test subjects.

cs.RO↗

arXiv2025

Trends in porous media laboratory imaging and open science practices

Understanding processes in porous media is fundamental to a broad spectrum of environmental, energy, and geoscience applications. These processes include multiphase fluid transport, interfacial dynamics, reactive transformations, and interactions with solids or microbial components, all governed by wettability, capillarity, and reactive transport at fluid-fluid and fluid-solid interfaces. Laboratory-based multiscale imaging provides critical insights into these phenomena, enabling direct visualization and quantitative characterization from the nanometer to meter scale. It is essential for advancing predictive models and optimizing the design of subsurface and engineered porous systems. This review presents an integrated overview of imaging techniques relevant to porous media research, emphasizing the type of information each method can provide, their applicability to porous media systems, and their inherent limitations. We highlight how imaging data are combined with quantitative analyses and modeling to bridge pore-scale mechanisms with continuum-scale behavior, and we critically discuss current challenges such as limited spatio-temporal resolution, sample representativity, and restricted data accessibility. We conduct an in-depth analysis on open-science trends in experimental and computational porous media research and find that, while open-access publishing has become widespread, the availability of imaging data and analysis code remains limited, often restricted to 'upon request'. Finally, we underscore the importance of open sharing of imaging datasets to enable reproducibility, foster cross-disciplinary integration, and support the development of robust predictive frameworks for porous media systems.

physics.flu-dyn↗

arXiv2025

Model Order Reduction for Large-scale Circuits Using Higher Order Dynamic Mode Decomposition

Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical modes directly from time-domain simulation data without requiring explicit system equations. This paper first deduces the DMD algorithm and then proposes high order dynamic mode decomposition (HODMD) incorporating delayed embedding technique, specifically targeting computational efficiency in large-scale circuit simulations. Compared with the DMD method, the HODMD method overcomes the problem that the output signal cannot be reconstructed when the spatial resolution is insufficient. The proposed HODMD algorithm is applicable to general circuits and does not impose any constraints on the topology of the pertinent circuit or type of the components. Three representative numerical test cases are presented to systematically validate both the computational efficiency and accuracy of the proposed HODMD method.

eess.SP↗

arXiv2025

MARS: Radio Map Super-resolution and Reconstruction Method under Sparse Channel Measurements

Radio maps reflect the spatial distribution of signal strength and are essential for applications like smart cities, IoT, and wireless network planning. However, reconstructing accurate radio maps from sparse measurements remains challenging. Traditional interpolation and inpainting methods lack environmental awareness, while many deep learning approaches depend on detailed scene data, limiting generalization. To address this, we propose MARS, a Multi-scale Aware Radiomap Super-resolution method that combines CNNs and Transformers with multi-scale feature fusion and residual connections. MARS focuses on both global and local feature extraction, enhancing feature representation across different receptive fields and improving reconstruction accuracy. Experiments across different scenes and antenna locations show that MARS outperforms baseline models in both MSE and SSIM, while maintaining low computational cost, demonstrating strong practical potential.

cs.CV↗

arXiv2025

Measurements and Modeling of Air-Ground Integrated Channel in Forest Environment Based on OFDM Signals

Forests are frequently impacted by climate conditions, vegetation density, and intricate terrain and geology, which contribute to natural disasters. Personnel engaged in or supporting rescue operations in such environments rely on robust communication systems to ensure their safety, highlighting the criticality of channel measurements in forest environments. However, according to current research, there is limited research on channel detection and modeling in forest areas in the existing literature. This paper describes the channel measurements campaign of air and ground in the Arxan National Forest Park of Inner Mongolia. It presents measurement results and propagation models for ground-to-ground (G2G) and air-to-ground (A2G) scenarios. The measurement campaign uses orthogonal frequency division multiplexing signals centered at 1.4 GHz for channel sounding. In the G2G measurement, in addition to using omnidirectional antennas to record data, we also use directional antennas to record the arrival angle information of the signal at the receiver. In the A2G measurement, we pre-plan the flight trajectory of the unmanned aerial vehicle so that it can fly at a fixed angle relative to the ground. We present path loss models suitable for G2G and A2G in forest environments based on the analysis of measurement results. The results indicate that the proposed model reduces error margins compared with other path loss models. Furthermore, we derive the multipath model expression specific to forest environments and conduct statistical analysis on key channel parameters e.g., shadow fading factor, root mean square delay spread, and Rician K factor. Our findings reveal that signal propagation obstruction due to tree crowns in A2G communication is more pronounced than tree trunk obstructions in G2G communication. Adjusting the elevation angle between air and ground can enhance communication quality.

cs.IT↗

arXiv2025

Transformable Plasmonic Helix with Swinging Gold Nanoparticles

Control over multiple optical elements that can be dynamically rearranged to yield substantial three-dimensional structural transformations is of great importance to realize reconfigurable plasmonic nanoarchitectures with sensitive and distinct optical feedback. In this work, we demonstrate a transformable plasmonic helix system, in which multiple gold nanoparticles (AuNPs) can be directly transported by DNA swingarms to target positions without undergoing consecutive stepwise movements. The swingarms allow for programmable AuNP translocations in large leaps within plasmonic nanoarchitectures, giving rise to tailored circular dichroism spectra. Our work provides an instructive bottom-up solution to building complex dynamic plasmonic systems, which can exhibit prominent optical responses through cooperative rearrangements of the constituent optical elements with high fidelity and programmability.

physics.bio-ph↗

arXiv2025

Recent advances in DNA origami-engineered nanomaterials and applications

DNA nanotechnology is a unique field, where physics, chemistry, biology, mathematics, engineering, and materials science can elegantly converge. Since the original proposal of Nadrian Seeman, significant advances have been achieved in the past four decades. During this glory time, the DNA origami technique developed by Paul Rothemund further pushed the field forward with a vigorous momentum, fostering a plethora of concepts, models, methodologies, and applications that were not thought of before. This review focuses on the recent progress in DNA origami-engineered nanomaterials in the past five years, outlining the exciting achievements as well as the unexplored research avenues. We believe that the spirits and asset that Seeman left for scientists will continue to bring inter-disciplinary innovations and useful applications to this field in the next decade.

physics.bio-ph↗

arXiv2025

Modulating lipid membrane morphology by dynamic DNA origami networks

Membrane morphology and its dynamic adaptation regulate many cellular functions, which are often mediated by membrane proteins. Advances in DNA nanotechnology have enabled the realization of various protein-inspired structures and functions with precise control at the nanometer level, suggesting a viable tool to artificially engineer the membrane morphology. In this work, we demonstrate a DNA origami cross (DOC) structure that can be anchored onto giant unilamellar vesicles (GUVs) and subsequently polymerized into micron-scale reconfigurable one-dimensional (1D) chains or two-dimensional (2D) lattices. Such DNA origami-based networks can be switched between left-handed (LH) and right-handed (RH) conformations by DNA fuels and exhibit potent efficacy in remodeling the membrane curvatures of GUVs. This work sheds light on designing hierarchically-assembled dynamic DNA systems for the programmable modulation of synthetic cells for useful applications.

physics.bio-ph↗