arXiv subjects

Junyan Zhang

Publications and source records attributed to Junyan Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

PhysicsArena: The First Multimodal Physics Reasoning Benchmark Exploring Variable, Process, and Solution Dimensions

Multimodal Large Language Models (MLLMs) have demonstrated remarkable capabilities in diverse reasoning tasks, yet their application to complex physics reasoning remains underexplored. Physics reasoning presents unique challenges, requiring grounding in physical conditions and the interpretation of multimodal information. Current physics benchmarks are limited, often focusing on text-only inputs or solely on problem-solving, thereby overlooking the critical intermediate steps of variable identification and process formulation. To address these limitations, we introduce PhysicsArena, the first multimodal physics reasoning benchmark designed to holistically evaluate MLLMs across three critical dimensions: variable identification, physical process formulation, and solution derivation. PhysicsArena aims to provide a comprehensive platform for assessing and advancing the multimodal physics reasoning abilities of MLLMs.

cs.CL↗

arXiv2025

CoheMark: A Novel Sentence-Level Watermark for Enhanced Text Quality

Watermarking technology is a method used to trace the usage of content generated by large language models. Sentence-level watermarking aids in preserving the semantic integrity within individual sentences while maintaining greater robustness. However, many existing sentence-level watermarking techniques depend on arbitrary segmentation or generation processes to embed watermarks, which can limit the availability of appropriate sentences. This limitation, in turn, compromises the quality of the generated response. To address the challenge of balancing high text quality with robust watermark detection, we propose CoheMark, an advanced sentence-level watermarking technique that exploits the cohesive relationships between sentences for better logical fluency. The core methodology of CoheMark involves selecting sentences through trained fuzzy c-means clustering and applying specific next sentence selection criteria. Experimental evaluations demonstrate that CoheMark achieves strong watermark strength while exerting minimal impact on text quality.

cs.CL↗

arXiv2025

ESDiff: Encoding Strategy-inspired Diffusion Model with Few-shot Learning for Color Image Inpainting

Image inpainting is a technique used to restore missing or damaged regions of an image. Traditional methods primarily utilize information from adjacent pixels for reconstructing missing areas, while they struggle to preserve complex details and structures. Simultaneously, models based on deep learning necessitate substantial amounts of training data. To address this challenge, an encoding strategy-inspired diffusion model with few-shot learning for color image inpainting is proposed in this paper. The main idea of this novel encoding strategy is the deployment of a "virtual mask" to construct high-dimensional objects through mutual perturbations between channels. This approach enables the diffusion model to capture diverse image representations and detailed features from limited training samples. Moreover, the encoding strategy leverages redundancy between channels, integrates with low-rank methods during iterative inpainting, and incorporates the diffusion model to achieve accurate information output. Experimental results indicate that our method exceeds current techniques in quantitative metrics, and the reconstructed images quality has been improved in aspects of texture and structural integrity, leading to more precise and coherent results.

cs.CV↗

arXiv2025

Virtual-mask Informed Prior for Sparse-view Dual-Energy CT Reconstruction

Sparse-view sampling in dual-energy computed tomography (DECT) significantly reduces radiation dose and increases imaging speed, yet is highly prone to artifacts. Although diffusion models have demonstrated potential in effectively handling incomplete data, most existing methods in this field focus on the image do-main and lack global constraints, which consequently leads to insufficient reconstruction quality. In this study, we propose a dual-domain virtual-mask in-formed diffusion model for sparse-view reconstruction by leveraging the high inter-channel correlation in DECT. Specifically, the study designs a virtual mask and applies it to the high-energy and low-energy data to perform perturbation operations, thus constructing high-dimensional tensors that serve as the prior information of the diffusion model. In addition, a dual-domain collaboration strategy is adopted to integrate the information of the randomly selected high-frequency components in the wavelet domain with the information in the projection domain, for the purpose of optimizing the global struc-tures and local details. Experimental results indicated that the present method exhibits excellent performance across multiple datasets.

eess.IV↗

arXiv2025

Stochastic equations for two-type continuous-state branching processes in varying environments

A two-type continuous-state branching process in varying environments is constructed as the pathwise unique solution of a system of stochastic equations driven by time-space noises, where the pathwise uniqueness is derived from a comparison property of solutions. As an application of the main result, we give characterizations of some positive integral functionals of the process in terms of Laplace transforms.

math.PR↗

arXiv2025

Two-type continuous-state branching processes in varying environments

A basic class of two-type continuous-state branching processes in varying environments are constructed by solving the backward equation determining the cumulant semigroup. The parameters of the process are allowed to be càdlàg in time and the difficulty brought about by the bottlenecks are overcome by introducing a suitable moment condition.

math.PR↗

arXiv2025

Incompressible Limit of Compressible Ideal MHD Flows inside a Perfectly Conducting Wall

We prove the incompressible limit of compressible ideal magnetohydrodynamic(MHD) flows in a reference domain where the magnetic field is tangential to the boundary. Unlike the case of transversal magnetic fields, the linearized problem of our case is not well-posed in standard Sobolev space $H^m~(m\geq 2)$, while the incompressible problem is still well-posed in $H^m$. The key observation to overcome the difficulty is a hidden structure contributed by Lorentz force in the vorticity analysis, which reveals that one should trade one normal derivative for two tangential derivatives together with a gain of Mach number weight $\varepsilon^2$. Thus, the energy functional should be defined by using suitable anisotropic Sobolev spaces. The weights of Mach number should be carefully chosen according to the number of tangential derivatives, such that the energy estimates are uniform in Mach number. Besides, part of the proof is similar to the study of compressible water waves, so our result opens the possibility to study the incompressible limit of free-boundary problems in ideal MHD.

math.AP↗

arXiv2025

Exploring Device-Oriented Video Encryption for Hierarchical Privacy Protection in AR Content Sharing

Content sharing across multiple Augmented Reality (AR) displays is becoming commonplace, enhancing team communication and collaboration through devices like smartphones and AR glasses. However, this practice raises significant privacy concerns, especially concerning the physical environment visible in AR, which may include sensitive personal details like facial features and identifiable information. Our research focuses on protecting privacy within AR environments, particularly the physical backgrounds visible during content sharing across three common AR display methods: projection, smartphone, and AR glasses. We analyze the potential privacy risks associated with each method and employ a Region Of Interest (ROI) video encryption system to hierarchically encrypt the physical backdrop based on its safety rating. This study pioneers the integration of ROI video encryption at the bitstream level within AR contexts, providing a more efficient solution than traditional pixel-level encryption by enhancing encryption speed and reducing the required space. Our adaptive system dynamically adjusts the encryption intensity based on the AR display method, ensuring tailored privacy protection.

cs.HC↗

arXiv2024

Uniform Anisotropic Regularity and Low Mach Number Limit of Non-isentropic Ideal MHD Equations with a Perfectly Conducting Boundary

We prove the low Mach number limit of non-isentropic ideal magnetohydrodynamic (MHD) equations with general initial data in the half-space whose boundary satisfies the perfectly conducting wall condition. By observing a special structure contributed by Lorentz force in vorticity analysis, we establish uniform estimates in suitable anisotropic Sobolev spaces with weights of Mach number determined by the number of material derivatives. We also observe that the entropy has the enhanced regularity in the direction of the magnetic field. These two observations help us get rid of the loss of derivatives and weights of Mach number in vorticity analysis caused by the simultaneous appearance of entropy, general initial data and the magnetic field, which is one of the major difficulties that do not appear in Euler equations or the isentropic problems. By utilizing the technique of Alinhac good unknowns, the anti-symmetric structure is preserved in the tangential estimates for the system differenetiated by high-order material derivatives.

math.AP↗

arXiv2023

Local Well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension

We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the ideas developed in the remarkable paper [11] by Coutand and Shkoller to generate an approximate problem with artificial viscosity indexed by $κ>0$ whose solution converges to that of the MHD equations as $κ\to 0$. However, the local well-posedness of the MHD equations is no easy consequence of Euler equations thanks to the strong coupling between the velocity and magnetic fields. This paper is the continuation of the second and third authors' previous work [38] in which the a priori energy estimate for incompressible free-boundary MHD with surface tension is established. But the existence is not a trivial consequence of the a priori estimate as it cannot be adapted directly to the approximate problem due to the loss of the symmetric structure.

math.AP↗

arXiv2023

Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics

We consider 3D free-boundary compressible ideal magnetohydrodynamic (MHD) system under the Rayleigh-Taylor sign condition. It describes the motion of a free-surface perfect conducting fluid in an electro-magnetic field. A local existence and uniqueness result was recently proved by Trakhinin and Wang [64] by using Nash-Moser iteration. However, that result loses regularity going from data to solution. In this paper, we show that the Nash-Moser iteration scheme in [64] can be improved such that the local-in-time smooth solution exists and is unique when the initial data is smooth and satisfies the compatibility condition up to infinite order. Second, we prove the a priori estimates without loss of regularity for the free-boundary compressible MHD system in Lagrangian coordinates in anisotropic Sobolev space, with more regularity tangential to the boundary than in the normal direction. It is based on modified Alinhac good unknowns, which take into account the covariance under the change of coordinates to avoid the derivative loss; full utilization of the cancellation structures of MHD system, to turn normal derivatives into tangential ones; and delicate analysis in anisotropic Sobolev spaces. As a result, we can prove the uniqueness and the continuous dependence on initial data provided the local existence, and a continuation criterion for smooth solution. Finally, we extend the local well-posedness theorem to the case of initial data only satisfying compatibility conditions up to finite order, assuming these can be approximated by data satisfying infinitely many compatibility conditions.

math.AP↗

arXiv2023

Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics

We prove the local well-posedness in Sobolev spaces of the free-boundary problem for compressible inviscid resistive isentropic MHD system under the Rayleigh-Taylor physical sign condition, which describes the motion of a free-boundary compressible plasma in an electro-magnetic field with magnetic diffusion. We use Lagrangian coordinates and apply the tangential smoothing method introduced by Coutand-Shkoller to construct the approximation solutions. One of the key observations is that the Christodoulou-Lindblad type elliptic estimate together with magnetic diffusion not only gives the common control of magnetic field and fluid pressure directly, but also controls the Lorentz force which is a higher order term in the energy functional.

math.AP↗

arXiv2022

Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics

We show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the Rayleigh-Taylor sign condition holds true initially. This result is a continuation of the authors' previous works [17,32,16]. Our proof is based on the combination of the techniques developed in our previous works [17,32,16], Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.

math.AP↗

arXiv2022

Local Well-posedness for the Motion of a Compressible Gravity Water Wave with Vorticity

In this paper we prove the local well-posedness (LWP) for the 3D compressible Euler equations describing the motion of a liquid in an unbounded initial domain with moving boundary. The liquid is under the influence of gravity but without surface tension, and it is not assumed to be irrotational. We apply the tangential smoothing method introduced in [10,11] to construct the approximation system with energy estimates uniform in the smooth parameter. It should be emphasized that, when doing the nonlinear a priori estimates, we need neither the higher order wave equation of the pressure and delicate elliptic estimates, nor the higher regularity on the flow-map or initial vorticity. Instead, we adapt the Alinhac's good unknowns to the estimates of full spatial derivatives.

math.AP↗

arXiv2022

Local Well-posedness and Incompressible Limit of the Free-Boundary Problem in Compressible Elastodynamics

We consider 3D free-boundary compressible elastodynamic system under the Rayleigh-Taylor sign condition. It describes the motion of an isentropic inviscid elastic medium with moving boundary. The deformation tensor satisfies the neo-Hookean linear elasticity. The local well-posedness was proved by Trakhinin [84] by Nash-Moser iteration. In this paper, we give a new proof of the local well-posedness by the combination of classical energy method and hyperbolic approach and also establish the incompressible limit. We apply the tangential smoothing method to define the approximation system. The key observation is that the structure of the wave equation of pressure together with Christodoulou-Lindblad elliptic estimates reduces the energy estimates to the control of tangentially-differentiated wave equations in spite of a potential loss of derivative in the source term. We first establish the nonlinear energy estimate without loss of regularity for the free-boundary compressible elastodynamic system. The energy estimate is also uniform in sound speed which yields the incompressible limit. It is worth emphasizing that our method is completely applicable to compressible Euler equations. Our observation also shows that it is not necessary to include the full time derivatives in boundary energy and analyze higher order wave equations as in the previous works of compressible Euler equations (cf. Lindblad-Luo [59] and Luo [61]) even if we require the energy is uniform in sound speed. Moreover, the enhanced regularity for compressible Euler equations obtained in [59,61] can still be recovered for a slightly compressible elastic medium by further delicate analysis which is completely different from Euler equations.

math.AP↗

arXiv2021

PairConnect: A Compute-Efficient MLP Alternative to Attention

Transformer models have demonstrated superior performance in natural language processing. The dot product self-attention in Transformer allows us to model interactions between words. However, this modeling comes with significant computational overhead. In this work, we revisit the memory-compute trade-off associated with Transformer, particularly multi-head attention, and show a memory-heavy but significantly more compute-efficient alternative to Transformer. Our proposal, denoted as PairConnect, a multilayer perceptron (MLP), models the pairwise interaction between words by explicit pairwise word embeddings. As a result, PairConnect substitutes self dot product with a simple embedding lookup. We show mathematically that despite being an MLP, our compute-efficient PairConnect is strictly more expressive than Transformer. Our experiment on language modeling tasks suggests that PairConnect could achieve comparable results with Transformer while reducing the computational cost associated with inference significantly.

cs.LG↗

arXiv2021

A priori Estimates for the Free-Boundary problem of Compressible Resistive MHD Equations and Incompressible Limit

In this paper, we prove the a priori estimates in Sobolev spaces for the free-boundary compressible inviscid magnetohydrodynamics equations with magnetic diffusion under the Rayleigh-Taylor physical sign condition. Our energy estimates are uniform in the sound speed. As a result, we can prove the convergence of solutions of the free-boundary compressible resistive MHD equations to the solution of the free-boundary incompressible resistive MHD equations, i.e., the incompressible limit. The key observation is that the magnetic diffusion together with elliptic estimates directly controls the Lorentz force, magnetic field and pressure wave simultaneously.

math.AP↗

arXiv2021

A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension

We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish a priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result focusing on the incompressible ideal free-boundary MHD equations with surface tension. It is worth pointing out that the $1/2$-extra spatial regularity for the flow map $η$ is no longer required in this manuscript thanks to the presence of the surface tension on the boundary.

math.AP↗