arXiv subjects

Juntao Wu

Publications and source records attributed to Juntao Wu.

8 recordsLinked to original sources

arXiv2026

Pullback Measure Attractors, Zero-Noise Limits, and Moderate Deviations for 2D Stochastic Primitive Equations with Multiplicative Lévy Noise

We study the long-term distributional dynamics and small-noise asymptotics of two-dimensional nonautonomous stochastic primitive equations driven by Gaussian and multiplicative Lévy noise, together with moderate deviations for the purely jump model. For sufficiently small noise, uniform moment bounds and an exponentially weighted terminal estimate yield a pullback absorbing family and tightness, while a lower semicontinuous vertical-moment functional preserves admissibility under weak limits. We prove the existence and uniqueness of a pullback measure attractor in the weak topology of probability measures and establish its upper semicontinuity as both noise components vanish. For the jump-driven equation, we establish a moderate deviation principle in $\mathcal D([0,T];H)\cap L^2(0,T;V)$ with speed $a^2(ε)/ε$. The proof combines continuity of the skeleton map with controlled stochastic convergence based on entropy bounds, truncation, martingale estimates, and direct vertical estimates, avoiding Lipschitz continuity of the vertical derivative of the jump coefficient.

math.PR↗

arXiv2026

Commutator Estimates Uniform in the Screening Parameter and Mean-Field Limits for Yukawa Interactions

We study quantitative mean-field limits for classical particles with Yukawa (screened Coulomb) interactions in every fixed dimension $d\ge2$, uniformly as the screening parameter $κ$ tends to zero. Our main result is a first-order commutator estimate in the natural Yukawa modulated energy, with an additive error of order $N^{-2/d}$ for $d\ge3$ and $(1+\log N)/N$ for $d=2$. It requires only a bounded reference density and a Lipschitz transport field, with no uniform lower bound on interparticle distances and no negative power of $κ$. The modified Helmholtz operator $-Δ+κ^2$ creates the main new difficulty. Truncating the potential to a constant inside each truncation ball produces a surface charge and a positive volume charge whose total mass is strictly less than one. We keep the reference density unchanged and control this loss of mass through an exact Green function representation and renormalized energy identities. A stress-energy identity with interface terms and averaging over the truncation radii then give the uniform commutator estimate. Combined with the modulated energy dissipation identity and a normalized quadratic transport cost, this estimate yields weak--strong stability, propagation of chaos, and time-integrated control of the mean-square difference between empirical and mean-field forces. We also prove a quantitative Yukawa-to-Coulomb limit. For smooth product data, $N\to\infty$ and $κ\downarrow0$ may be taken simultaneously with no relation between their rates; in dimension three, a direct comparison at the particle level also holds for general symmetric initial laws with finite initial error.

math.AP↗

arXiv2026

Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability

We establish quantitative mean-field convergence and propagation of chaos for repulsive Coulomb gradient flows at the bounded-density regularity of the limiting equation. The argument couples the dissipative modulated-energy identity with the normalized quadratic transport cost of the full $N$-particle law. The remaining negative mean-square force-error term is used through an exact completion of squares after mollification: the non-Lipschitz remainder is absorbed by this negative term, while a sharp first-order commutator estimate is applied to the mollified Lipschitz field. For the Coulomb equation, the sharp $L^\infty$ decay gives the density envelope $m(t)=\|ρ_0\|_{L^\infty}/(1+t\|ρ_0\|_{L^\infty})$. A density-adapted transport weight and mollification scale $m(t)^{-1/d}$ yield an Osgood comparison. Thus, for every $d\ge2$ and $ρ_0\in\mathcal P_2(\mathbb R^d)\cap L^\infty(\mathbb R^d)$, we obtain quantitative comparison with the global bounded-density Coulomb solution on every prescribed finite interval. For tensorized initial data, the normalized squared Wasserstein distance of the full $N$-particle law, the expected modulated energy, and the time-integrated mean-square force error are bounded by $N^{-2γ_{T,d}/d}$ for $d\ge3$ and $((1+\log N)/N)^{γ_{T,2}}$ for $d=2$, where $γ_{T,d}=(1+T\|ρ_0\|_{L^\infty})^{-c_d}$. For $d-2<s<d$, we also prove Riesz weak--strong stability for prescribed reference solutions in $L^\infty(0,T;B^{s-d+2}_{\infty,q})$, with Gronwall, Bihari, and Osgood comparisons according to $q$, together with uniqueness in the stated Besov class. Finally, an outlier construction separates modulated-energy convergence and Kac chaos from normalized Wasserstein convergence of the full $N$-particle law.

math.AP↗

arXiv2026

Event-based vision sensing and its application to pedestrian detection for intelligent transportation and surveillance

Pedestrian detection in conventional frame-based imaging often suffers from limited temporal responsiveness and substantial data redundancy. Inspired by the biological retina, event-based vision sensing (EVS) offers ultra-low latency, high temporal resolution, wide dynamic range, and low power consumption, making it highly attractive for pedestrian perception in complex environments. This paper provides a comprehensive review of EVS and its application to pedestrian detection in intelligent transportation and surveillance scenarios. We first summarize the sensing principles, historical development, and key advantages of event-based vision in comparison with conventional frame-based imaging. We then review the major methodological components of event-based pedestrian detection, including sensing inputs, event representations, preprocessing strategies, feature extraction, detection models, datasets, and evaluation metrics. In addition, representative methods are comparatively analyzed in terms of temporal fidelity, detection accuracy, computational efficiency, and deployment complexity. Finally, we discuss the major open challenges in current EB-PD research, including benchmark standardization, event-native model design, multimodal fusion, and real-world deployment, and outline several promising directions for future development. This review aims to provide a structured and up-to-date reference for researchers working on event-based pedestrian perception and related intelligent vision systems.

cs.CV↗

arXiv2026

Breaking the Evaluation Paradox: Evaluating High-Entropy Search with Computationally Irreducible Constraints

Evaluating the exhaustive search capabilities of large language models (LLMs) is plagued by a fundamental paradox: verifying completeness requires complete ground truth, yet high-entropy enumeration tasks make such ground truth impossible for humans to create. This causes benchmarks to systematically penalize models for outperforming their human annotators. Despite rapid progress in web-search and deep research agents -- which now issue hundreds of queries, traverse diverse sites, and synthesize long reports -- evaluation still largely relies on partially annotated answer sets, LLM-based judges, or single-answer questions that avoid genuinely exhaustive search scenarios. We break this paradox by shifting the evaluation paradigm from simulating a messy reality to constructing computationally pure challenges. We introduce VERITAS (Verifiable Traversal Assessment for Search), a framework built on the principle of computationally irreducible constraints. By introducing novel, non-optimizable constraints, we create verifiable, sparse-answer search tasks that are computationally equivalent to exhaustive enumeration. These constraints are easy to verify but impossible for LLMs or search engines to optimize, forcing agents to genuinely traverse the entire search space. VERITAS can automatically generate a virtually infinite number of test cases with perfect ground truth and precise difficulty control, with marginal instance cost dominated by hash computations. This provides not only a robust benchmark for evaluating systematic exploration under uncertainty but also a scalable method for generating training data to improve these crucial, yet underdeveloped, capabilities.

cs.IR↗

arXiv2026

Uniform measure attractors of the distribution-dependent 2D stochastic Navier-Stokes equations driven by nonlinear noise

In this paper, we investigate the uniform measure attractors of the distribution-dependent nonautonomous 2D stochastic Navier-Stokes equations driven by nonlinear noise and subject to almost periodic external forcing. Owing to the distribution-dependent structure and the almost periodicity of the external forcing, the resulting solution process becomes an inhomogeneous Markov process, presenting significant analytical challenges. To overcome these difficulties, we propose sufficient conditions on the time-dependent external forcing and distribution-dependent nonlinear terms, and develop novel analytical estimates. As a result, we establish the existence and uniqueness of uniform measure attractors for the system. Notably, the joint continuity of the family of processes is achieved without relying on the Feller property of the distribution law operators.

math.DS↗

arXiv2026

Well-posedness, mean attractors and invariant measures of stochastic discrete long-wave-short-wave resonance equations driven by locally Lipschitz nonlinear noise

This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: $(1)$ the equations contain locally Lipschitz nonlinear coupling terms $u_mv_m$ and $(B(|u(t)|^2))_m$ for $m\in \mathbb{Z}$; $(2)$ the nonlinear coefficients of noises satisfy local Lipschitz conditions; and $(3)$ the system couples real and complex equations and is infinite-dimensional. These inherent structural properties prevent the analysis from being carried out in a standard Bochner product space of the same order and make it difficult to directly verify the tightness of the distribution family of solutions. To address these challenges, we adopt a higher-order Bochner product space $L^4(Ω,\ell_c^2)\times L^2(Ω,\ell^2)$ as the phase space and employ the technique of uniform tail-end estimates. The main results include: establishing the global well-posedness of the nonautonomous stochastic discrete long-wave-short-wave resonance equations driven by nonlinear noise in $L^4(Ω,\ell_c^2)\times L^2(Ω,\ell^2)$; based on this, defining the mean random dynamical system and proving the existence and uniqueness of weak $\mathscr{D}$-pullback mean random attractors. When the external forcing terms are independent of time and sample, we investigate the existence of invariant measures for the corresponding autonomous system and examine the limiting behavior of the invariant measure as the noise intensity tends to zero.

math.PR↗

arXiv2024

AppPoet: Large Language Model based Android malware detection via multi-view prompt engineering

Due to the vast array of Android applications, their multifarious functions and intricate behavioral semantics, attackers can adopt various tactics to conceal their genuine attack intentions within legitimate functions. However, numerous learning-based methods suffer from a limitation in mining behavioral semantic information, thus impeding the accuracy and efficiency of Android malware detection. Besides, the majority of existing learning-based methods are weakly interpretive and fail to furnish researchers with effective and readable detection reports. Inspired by the success of the Large Language Models (LLMs) in natural language understanding, we propose AppPoet, a LLM-assisted multi-view system for Android malware detection. Firstly, AppPoet employs a static method to comprehensively collect application features and formulate various observation views. Then, using our carefully crafted multi-view prompt templates, it guides the LLM to generate function descriptions and behavioral summaries for each view, enabling deep semantic analysis of the views. Finally, we collaboratively fuse the multi-view information to efficiently and accurately detect malware through a deep neural network (DNN) classifier and then generate the human-readable diagnostic reports. Experimental results demonstrate that our method achieves a detection accuracy of 97.15% and an F1 score of 97.21%, which is superior to the baseline methods. Furthermore, the case study evaluates the effectiveness of our generated diagnostic reports.

cs.CR↗