arXiv subjects

Ting Zhou

Publications and source records attributed to Ting Zhou.

At least 19 recordsLinked to original sources

arXiv2026

Logarithmic Stability for an Inverse Source Problem in a Coupled Nonlinear Helmholtz System

We study an inverse source problem for a two-mode nonlinear Helmholtz system motivated by second-harmonic generation. The datum is the full first Fr\'{e}chet derivative of the nonlinear Dirichlet-to-Neumann map at one fixed, common, small boundary state, which need not be zero. For real-valued small data, a known susceptibility bounded away from zero, and sources supported in a fixed compact subset of the domain, we prove uniqueness and a conditional single-logarithmic stability estimate. The first boundary variation is the Dirichlet-to-Neumann map of a symmetric $2\times2$ matrix Schr\"odinger operator. Absorbing the two known Helmholtz energies into its matrix potential permits the use of standard zero-energy complex geometrical optics solutions with a common null phase geometry. A bilinear Alessandrini identity then gives a uniform Fourier estimate for the two entries containing the background fields. Zero extension below the exponent $3/2$, a low/high frequency splitting, and interpolation between $H^{-2}$ and the a priori $H^s$ source bound yield the stated stability modulus.

math.AP↗

arXiv2026

An Inverse Random Source Problem for the Moore-Gibson-Thompson Equation Driven by Fractional Brownian Motion

In this paper, we consider an inverse random source problem for the stochastic Moore-Gibson-Thompson equation driven by fractional Brownian motion with Hurst index $H \in (0, 1)$ of the form $f_1(x)g_1(t)\dot{B}^H(t)+f_2(x)g_2(t)$. Given the random source, existence and uniqueness of mild solutions are verified. For the inverse problem, the uniqueness of recovering the strength $f_i(x)$ if the time functions $g_i$ are known and $g_i(t)$ if the spatial functions $f_i$ are known when $H \in(0,1)$ from the boundary flux on a special nonempty open subset is proved.

math.AP↗

arXiv2026

Beyond Solvability: Task Learnability as a Static Prior for LLM RL Post-Training

Reinforcement learning (RL) has become a central post-training paradigm for eliciting reasoning capabilities in large language models, yet uniform task sampling allocates compute without regard to differences in how tasks respond to optimization. Existing task-valuation methods mostly rely on snapshot-based signals such as current pass rate or reward, which estimate how solvable a task is under the current policy. However, tasks with similar current solvability can still differ substantially in how positively they respond to further training. We study this residual axis as task learnability: a regime-conditional measure of expected positive response to continued training under a fixed RL post-training regime. By analyzing per-task reward trajectories, we find that learnability is reproducible across independently sampled training contexts and predictive of downstream utility. To make this signal practical before training begins, we propose TrajVal, a lightweight probe-based estimator that approximates per-task learnability from a short probe run and two endpoint evaluations. TrajVal can be used either as a standalone static prior for task sampling or as a multiplicative prior for existing online schedulers. Experiments on mathematical and logical reasoning benchmarks across multiple model scales show that TrajVal improves data efficiency over uniform sampling and provides complementary gains when combined with online scheduling methods.

cs.LG↗

arXiv2026

Partial data Calder\'{o}n problem for quasilinear conductivities in dimension 2

In this paper, we prove a uniqueness result for the partial data Calder\'{o}n problem with quasilinear conductivity in two dimensions. The proof is based on higher-order linearization and the use of CGO solutions in dimension two that vanish on part of the boundary. Since derivatives of the solutions appear in the integral identity, we need improved remainder estimates, for which we introduce a modification in the choice of the phase, analogous to limiting Carleman weights. We also analyze how combinations of phases produce specific patterns in the products of solutions, which allows us to apply both stationary and nonstationary phase arguments to recover the conductivity.

math.AP↗

arXiv2026

Semantic Noise Aided Secure Image Transmission over MIMO Fading Channels

Existing semantic communications have exhibited satisfactory performance in many tasks, but secure image transmission remains insufficiently explored. We propose a novel secure image semantic communication (SISC) framework over multiple-input multiple-output (MIMO) fading channels. To ensure high-quality image reconstruction for the legitimate semantic user (SU) and simultaneously interfere with the eavesdropper (Eve), we design a semantic noise generation (SNG) network. This network generates a beneficial semantic noise map based on both the source features and the SU channel state information (CSI). An efficient channel estimation enhanced network is incorporated to obtain the accurate CSI and enhance the system performance. Furthermore, to improve the secure image reconstruction quality, we develop an efficient transceiver beamformer optimization algorithm, where the formulated problem is solved using the constrained stochastic successive convex approximation method. In the proposed SISC framework, semantic noise generation and beamforming optimization work together to ensure secure and high-quality image transmission. Numerical results demonstrate that the proposed semantic noise aided transmission scheme effectively protects image information from leakage to Eve while maintaining high-fidelity image reconstruction at SU.

cs.IT↗

arXiv2026

GEOALIGN: Geometric Rollout Curation for Robust LLM Reinforcement Learning

Online reinforcement learning is widely used to align large language models (LLMs) with reward signals, yet training can be unstable under noisy or misspecified rewards. We identify a failure mode we call directional inconsistency: within a batch, a small set of high-reward rollouts induces representation-space preference directions that sharply disagree with the batch majority, resulting in high-variance and destabilizing updates. We propose geoalign, a lightweight plug-in for rollout curation in iterative policy optimization. Geoalign (i) forms within-prompt preference pairs, (ii) learns an online projector on per-rollout hidden states to concentrate reward-ordered displacement directions, and (iii) detects directionally inconsistent rollouts via their angular deviation from a batch consensus prototype and rectifies them with within-prompt stable alternatives. Geoalign is forward-pass only and adds negligible overhead. Across dialogue alignment with a learned reward model and mathematical reasoning with binary verified rewards, Geoalign improves final performance and reduces training oscillation, outperforming PF-PPO, PAR, PODS, and Seed-GRPO. These results suggest latent directional consensus as an effective reliability signal for online LLM RL.

cs.LG↗

arXiv2026

Gauge symmetry and uniqueness in inverse problems for the JMGT equation

In this paper, we study an inverse boundary value problem for the Jordan--Moore--Gibson--Thompson equation on a simple Riemannian manifold. We consider an all boundary measurement map that maps Dirichlet boundary data and initial data to the corresponding Neumann-type boundary data and final-time data. Our main result shows that the nonlinear acoustic coefficient $\beta$ is uniquely determined by this measurement map, and the linear damping coefficients $\alpha$ and $q$, along with the internal source term $F$, can be recovered up to a gauge symmetry. As a corollary, we also establish a specific case in which all coefficients are uniquely recovered. The proof relies on the method of first-order and second-order linearization and on the construction of geometric optics solutions. In the intermediate step, we establish the unique recovery of the lower-order coefficients in the linearized MGT equation.

math.AP↗

arXiv2026

Inverse boundary value problems of determining nonlinear coefficients for the JMGT equation

We consider inverse boundary value problems for the Jordan-Moore-Gibson-Thompson (JMGT) equation in nonlinear acoustics with quadratic nonlinearities of Kuznetsov-type and Westervelt-type. We show that the associated boundary Dirichlet-to-Neumann map uniquely determines the nonlinear coefficients $\beta$ in the Westervelt-type model, and the pair $(\beta,\kappa)$ in the Kuznetsov-type model, provided that the observation time is greater than the maximal boundary-to-boundary geodesic travel time. The results are obtained in both the Euclidean setting and on compact Riemannian manifolds with proper geometric assumptions. The proof is based on the idea of second order linearization combined with the construction of geometric optics and Gaussian beam solutions, reducing the inverse problem of uniqueness to the injectivity of associated geodesic ray transforms.

math.AP↗

arXiv2025

Uniqueness Result For Semi-linear Wave Equations With Sources

This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general semilinear term and an internal source. The inverse problem is to determine the nonlinear coefficients (potentials), the source term, and the initial data from the Dirichlet-to-Neumann (DtN) map. Our approach combines higher-order linearization and the construction of complex geometrical optics (CGO) solutions. The main results establish that while unique recovery is not always possible, we can precisely characterize the gauge equivalence classes in the solutions to this inverse problem. For a wave equation with a polynomial nonlinearity of degree $n$, we prove that only the highest-order coefficient can be uniquely determined from the DtN map; the lower-order coefficients and the source can only be recovered up to a specific gauge transformation involving a function $\psi$. Furthermore, we provide sufficient conditions under which unique determination of all parameters is guaranteed. We also extend these results to various specific non-polynomial nonlinearities, demonstrating that the nature of the nonlinearity critically influences whether unique recovery or a gauge symmetry is obtained.

math.AP↗

arXiv2025

Bridging BCI and Communications: A MIMO Framework for EEG-to-ECoG Wireless Channel Modeling

As a method to connect human brain and external devices, Brain-computer interfaces (BCIs) are receiving extensive research attention. Recently, the integration of communication theory with BCI has emerged as a popular trend, offering potential to enhance system performance and shape next-generation communications. A key challenge in this field is modeling the brain wireless communication channel between intracranial electrocorticography (ECoG) emitting neurons and extracranial electroencephalography (EEG) receiving electrodes. However, the complex physiology of brain challenges the application of traditional channel modeling methods, leaving relevant research in its infancy. To address this gap, we propose a frequency-division multiple-input multiple-output (MIMO) estimation framework leveraging simultaneous macaque EEG and ECoG recordings, while employing neurophysiology-informed regularization to suppress noise interference. This approach reveals profound similarities between neural signal propagation and multi-antenna communication systems. Experimental results show improved estimation accuracy over conventional methods while highlighting a trade-off between frequency resolution and temporal stability determined by signal duration. This work establish a conceptual bridge between neural interfacing and communication theory, accelerating synergistic developments in both fields.

eess.SP↗

arXiv2025

Exploring Constraints on Axion-like Particles with the Observations for blazar Mrk 501

Oscillations between axion-like particles (ALPs) and photons in astrophysical magnetic fields can lead to irregularities in the high energy gamma ray spectra of blazars. The magnetic field within the blazar jet plays a crucial role in shaping these effects, with its strength in the emission region being an important parameter determined by multi-wavelength observations. However, the origin of the high energy bump observed in the spectral energy distribution of some blazars is a topic of debate, with both leptonic and hadronic scenarios providing plausible explanations that result in different magnetic field strengths in the emission region. In this study, we investigate the impact of magnetic field configurations on the constraints of ALP parameters. We consider both leptonic and hadronic emission scenarios for the blazar Mrk 501 and derive the corresponding jet magnetic field strengths. Additionally, we explore two jet magnetic field models: one with a toroidal component and the other with helical and tangled components. By analyzing the spectra of Mrk 501 observed by MAGIC and Fermi-LAT from 2017-06-17 to 2019-07-23, which are well-described by both emission scenarios, we derive constraints on the ALP parameters. Our results demonstrate that both the emission scenario and the magnetic field structure play a significant role in deriving these constraints, with the hadronic model leading to much more stringent limits compared to the leptonic model.

astro-ph.HE↗

arXiv2025

Computational fluid dynamics-based structure optimization of ultra-high-pressure water-jet nozzle using approximation method

Since the geometry structure of ultra-high-pressure (UHP) water-jet nozzle is a critical factor to enhance its hydrodynamic performance, it is critical to obtain a suitable geometry for a UHP water jet nozzle. In this study, a CFD-based optimization loop for UHP nozzle structure has been developed by integrating an approximate model to optimize nozzle structure for increasing the radial peak wall shear stress. In order to improve the optimization accuracy of the sparrow search algorithm (SSA), an enhanced version called the Logistic-Tent chaotic sparrow search algorithm (LTC-SSA) is proposed. The LTC-SSA algorithm utilizes the Logistic-Tent Chaotic (LTC) map, which is designed by combining the Logistic and Tent maps. This new approach aims to overcome the shortcoming of "premature convergence" for the SSA algorithm by increasing the diversity of the sparrow population. In addition, to improve the prediction accuracy of peak wall shear stress, a data prediction method based on LTC-SSA-support vector machine (SVM) is proposed. Herein, LTC-SSA algorithm is used to train the penalty coefficient C and parameter gamma g of SVM model. In order to build LTC-SSA-SVM model, optimal Latin hypercube design (Opt LHD) is used to design the sampling nozzle structures, and the peak wall shear stress (objective function) of these nozzle structures are calculated by CFD method. For the purpose of this article, this optimization framework has been employed to optimize original nozzle structure. The results show that the optimization framework developed in this study can be used to optimize nozzle structure with significantly improved its hydrodynamic performance.

physics.flu-dyn↗

arXiv2024

HumanVBench: Probing Human-Centric Video Understanding in MLLMs with Automatically Synthesized Benchmarks

Evaluating the nuanced human-centric video understanding capabilities of Multimodal Large Language Models (MLLMs) remains a great challenge, as existing benchmarks often overlook the intricacies of emotion, behavior, and cross-modal alignment. We introduce HumanVBench, a comprehensive video benchmark designed to rigorously probe these capabilities across 16 fine-grained tasks. A cornerstone of our work is a novel and scalable benchmark construction methodology, featuring two automated pipelines that synthesize high-quality video annotations and challenging multiple-choice questions with minimal human labor. By leveraging state-of-the-art models for annotation and systematically converting model-induced errors into plausible distractors, our framework provides a generalizable ``machine'' for creating nuanced evaluation suites. Our extensive evaluation of 30 leading MLLMs on HumanVBench reveals critical deficiencies, particularly in perceiving subtle emotions and aligning speech with visual cues, with even top proprietary models falling short of human performance. We open-source HumanVBench and our synthesis pipelines to catalyze the development of more socially intelligent and capable video MLLMs.

cs.CV↗

arXiv2024

Comprehensive Optimization of Interferometric Diffusing Wave Spectroscopy (iDWS)

It has been shown that light speckle fluctuations provide a means for noninvasive measurements of cerebral blood flow index (CBFi). While conventional Diffuse Correlation Spectroscopy (DCS) provides marginal brain sensitivity for CBFi in adult humans, new techniques have recently emerged to improve diffuse light throughput and thus, brain sensitivity. Here we further optimize one such approach, interferometric diffusing wave spectroscopy (iDWS), with respect to number of independent channels, camera duty cycle and full well capacity, incident power, noise and artifact mitigation, and data processing. We build the system on a cart and define conditions for stable operation. We show pulsatile CBFi monitoring at 4-4.5 cm source-collector separation in adults with moderate pigmentation (Fitzpatrick 4). We also report preliminary clinical measurements in the Neuro Intensive Care Unit (Neuro ICU). These results push the boundaries of iDWS CBFi monitoring performance beyond previous reports.

physics.med-ph↗

arXiv2024

CKGFuzzer: LLM-Based Fuzz Driver Generation Enhanced By Code Knowledge Graph

In recent years, the programming capabilities of large language models (LLMs) have garnered significant attention. Fuzz testing, a highly effective technique, plays a key role in enhancing software reliability and detecting vulnerabilities. However, traditional fuzz testing tools rely on manually crafted fuzz drivers, which can limit both testing efficiency and effectiveness. To address this challenge, we propose an automated fuzz testing method driven by a code knowledge graph and powered by an LLM-based intelligent agent system, referred to as CKGFuzzer. We approach fuzz driver creation as a code generation task, leveraging the knowledge graph of the code repository to automate the generation process within the fuzzing loop, while continuously refining both the fuzz driver and input seeds. The code knowledge graph is constructed through interprocedural program analysis, where each node in the graph represents a code entity, such as a function or a file. The knowledge graph-enhanced CKGFuzzer not only effectively resolves compilation errors in fuzz drivers and generates input seeds tailored to specific API usage scenarios, but also analyzes fuzz driver crash reports, assisting developers in improving code quality. By querying the knowledge graph of the code repository and learning from API usage scenarios, we can better identify testing targets and understand the specific purpose of each fuzz driver. We evaluated our approach using eight open-source software projects. The experimental results indicate that CKGFuzzer achieved an average improvement of 8.73% in code coverage compared to state-of-the-art techniques. Additionally, CKGFuzzer reduced the manual review workload in crash case analysis by 84.4% and successfully detected 11 real bugs (including nine previously unreported bugs) across the tested libraries.

cs.SE↗

arXiv2024

Bridging Design and Development with Automated Declarative UI Code Generation

Declarative UI frameworks have gained widespread adoption in mobile app development, offering benefits such as improved code readability and easier maintenance. Despite these advantages, the process of translating UI designs into functional code remains challenging and time-consuming. Recent advancements in multimodal large language models (MLLMs) have shown promise in directly generating mobile app code from user interface (UI) designs. However, the direct application of MLLMs to this task is limited by challenges in accurately recognizing UI components and comprehensively capturing interaction logic. To address these challenges, we propose DeclarUI, an automated approach that synergizes computer vision (CV), MLLMs, and iterative compiler-driven optimization to generate and refine declarative UI code from designs. DeclarUI enhances visual fidelity, functional completeness, and code quality through precise component segmentation, Page Transition Graphs (PTGs) for modeling complex inter-page relationships, and iterative optimization. In our evaluation, DeclarUI outperforms baselines on React Native, a widely adopted declarative UI framework, achieving a 96.8% PTG coverage rate and a 98% compilation success rate. Notably, DeclarUI demonstrates significant improvements over state-of-the-art MLLMs, with a 123% increase in PTG coverage rate, up to 55% enhancement in visual similarity scores, and a 29% boost in compilation success rate. We further demonstrate DeclarUI's generalizability through successful applications to Flutter and ArkUI frameworks.

cs.SE↗

arXiv2024

Oxygen vacancies modulated VO2 for neurons and Spiking Neural Network construction

Artificial neuronal devices are the basic building blocks for neuromorphic computing systems, which have been motivated by realistic brain emulation. Aiming for these applications, various device concepts have been proposed to mimic the neuronal dynamics and functions. While till now, the artificial neuron devices with high efficiency, high stability and low power consumption are still far from practical application. Due to the special insulator-metal phase transition, Vanadium Dioxide (VO2) has been considered as an idea candidate for neuronal device fabrication. However, its intrinsic insulating state requires the VO2 neuronal device to be driven under large bias voltage, resulting in high power consumption and low frequency. Thus in the current study, we have addressed this challenge by preparing oxygen vacancies modulated VO2 film(VO2-x) and fabricating the VO2-x neuronal devices for Spiking Neural Networks (SNNs) construction. Results indicate the neuron devices can be operated under lower voltage with improved processing speed. The proposed VO2-x based back-propagation SNNs (BP-SNNs) system, trained with the MNIST dataset, demonstrates excellent accuracy in image recognition. Our study not only demonstrates the VO2-x based neurons and SNN system for practical application, but also offers an effective way to optimize the future neuromorphic computing systems by defect engineering strategy.

cs.NE↗

arXiv2023

Partial Data Inverse Problems for the Nonlinear Schr\"odinger Equation

In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient $\beta(t, x)$ in the Schr\"odinger equation $(i\partial_t + \Delta + q(t, x))u + \beta u^2 = 0$, from the boundary Dirichlet-to-Neumann (DN) map. In particular, we are interested in the partial data problem, in which the DN-map is measured on a proper subset of the boundary. We show two results: a local uniqueness of the coefficient at the points where certain type of geometric optics (GO) solutions can reach; and a stability estimate based on the unique continuation property for the linear equation.

math.AP↗