arXiv subjects

Jie Wan

Publications and source records attributed to Jie Wan.

At least 19 recordsLinked to original sources

arXiv2026

Piecewise smooth stationary Euler flows with support in a neighborhood of a helix

We construct stationary solutions of the three-dimensional incompressible Euler equations with helical symmetry and support in a neighborhood of a helix. The solutions are piecewise smooth and arise from a nonlinear overdetermined elliptic boundary value problem associated with a stream-function formulation. A distinguishing feature is that the vortex cross-sections are intrinsically anisotropic: after rescaling, the leading-order shape is elliptic rather than radial, and the boundary exhibits a nontrivial third Fourier mode reflecting helical effects absent in previous axisymmetric constructions. A key step in the proof is the analysis of a genuinely anisotropic overdetermined elliptic problem with prescribed Dirichlet and nonconstant Neumann conditions.

math.AP↗

arXiv2025

Co-rotating nearly parallel helical vortices with small cross-section in 3D incompressible Euler equations

In this article, we consider clustered solutions to a semilinear elliptic equation in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in \Omega,\\ u=0,\ \ &x\in\partial \Omega \end{cases} \end{equation*} for small values of $ \varepsilon $. Using Green's function of the elliptic operator $ -\text{div}(K(x)\nabla) $ and finite-dimensional reduction method, we prove that there exist clustered solutions with cluster point $ 0 $ and cluster distance $ |\ln\varepsilon| ^{-\frac{1}{2}} $ whose small-structure is governed by some functional $ H_N $ determined by $ K $ and $ q $. As an application, we prove the existence of traveling-rotating helical vorticity fields to 3D incompressible Euler equations in infinite cylinders, whose support sets consist of helical tubes with small cross-section of radius $ \varepsilon $ and arbitrary circulation $ \kappa $ and concentrates near ``$ 2N $'' and ``$ 2N+1 $'' type of co-rotating helical solutions of nearly parallel vortex filaments model as $ \varepsilon\to0 $, which justifies the result in Klein, Majda and Damodaran [1995, JFM] and generalizes results in Guerra and Musso [arxiv: 2502.01470]. Several kinds of solutions such as ``2 asymmetric'', ``$ 2\times2 $ asymmetric'' and ``$ 2\times2+1 $ asymmetric'' type of co-rotating helical filaments are also considered.

math.AP↗

arXiv2025

Tracing pT-differential radial flow from blast-wave analytics to quark coalescence

The observable $v_0(\pt)$, which quantifies event-by-event fluctuations in the differential transverse-momentum spectrum, is proposed as a direct and penetrating probe of radial flow in heavy-ion collisions. Recent measurements at the LHC exhibit a clear mass ordering for pions, kaons and protons at low \pt and a baryon-meson splitting at intermediate \pt, resembling to the well-known features of elliptic flow ($v_2$). In this letter, we first derive an analytic expression of $v_0(\pt)$ within a Blast-Wave framework incorporating fluctuations of freeze-out temperature and radial expansion velocity, which can naturally explains the experimentally observed mass ordering. The distinct dynamical origins of the mass ordering in $v_0(\pt)$ and $v_2(\pt)$ are discussed. Furthermore, using the AMPT model, we demonstrate that the baryon-meson splitting emerges spontaneously from the quark coalescence. This study provides deeper insight into the $v_0(\pt)$ observable and the collective dynamics of the QGP.

nucl-th↗

arXiv2025

Assessing background effects in search of the chiral vortical effect in relativistic heavy-ion collisions

The search for the Chiral Vortical Effect (CVE) in relativistic heavy-ion collisions is carried out by measuring azimuthal correlators for baryon pairs such as $\Lambda$ and protons. Experimental results from the ALICE collaboration show significant separations in these observables, however, the interpretation remains unclear. It is believed that background contributions from baryon production mechanisms may play an important role. Using three phenomenological models, the Blast Wave, AMPT, and AVFD+UrQMD, we systematically investigate the background effects in Pb--Pb collisions at \snn = 5.02 TeV. We demonstrate that local baryon conservation, as well as hadronic annihilation processes, can significantly influence the correlators. The feed-down contribution from secondary protons is also estimated. Our study provides a foundation for disentangling background mechanisms and further facilitates the search for the CVE.

nucl-th↗

arXiv2025

Federated Fine-Tuning of Sparsely-Activated Large Language Models on Resource-Constrained Devices

Federated fine-tuning of Mixture-of-Experts (MoE)-based large language models (LLMs) is challenging due to their massive computational requirements and the resource constraints of participants. Existing working attempts to fill this gap through model quantization, computation offloading, or expert pruning. However, they cannot achieve desired performance due to impractical system assumptions and a lack of consideration for MoE-specific characteristics. In this paper, we propose FLUX, a system designed to enable federated fine-tuning of MoE-based LLMs across participants with constrained computing resources (e.g., consumer-grade GPUs), aiming to minimize time-to-accuracy. FLUX introduces three key innovations: (1) quantization-based local profiling to estimate expert activation with minimal overhead, (2) adaptive layer-aware expert merging to reduce resource consumption while preserving accuracy, and (3) dynamic expert role assignment using an exploration-exploitation strategy to balance tuning and non-tuning experts. Extensive experiments on LLaMA-MoE and DeepSeek-MoE with multiple benchmark datasets demonstrate that FLUX significantly outperforms existing methods, achieving up to 4.75X speedup in time-to-accuracy.

cs.DC↗

arXiv2025

Particle species dependence of elliptic flow fluctuations in Pb-Pb collisions at LHC energies in a multiphase transport model

The fluctuations of elliptic flow (\vtwo) in relativistic heavy-ion collisions offer a powerful tool to probe the collective behavior and transport properties of the quark-gluon plasma (QGP). The dependence of these fluctuations on particle species further sheds light on the hadronization mechanism. At LHC energies, the ALICE experiment has measured $v_2$ fluctuations for charged pions, kaons, and (anti-)protons via the ratio of \vtwo measured with respect to the spectator plane (\vtwosp) and from the four-particle cumulants (\vtwofour). However, the observed dependencies on transverse momentum and particle type remain not fully understood. In this study, we perform a phenomenological investigation using a multiphase transport (AMPT) model, which allows us to trace the full evolution of flow fluctuations intertwined with the quark coalescence. The results qualitatively reproduce the ALICE measurements and offer deeper insights into the transport dynamics and hadronization of the QGP.

nucl-th↗

arXiv2025

Dynamics and leapfrogging phenomena of multiple helical vortices for 3D incompressible Euler equations

In this paper, we investigate the time evolution of helical vortices without swirl for the incompressible Euler equations in $\mathbb R^3$ under general initial assumptions. Assume the initial helical vorticity is sharply concentrated in $N$ distinct $\ep$-neighborhoods, whose mutual distances vanish as $O(1/|\ln \ep|)$, and each vortex core possesses vorticity mass of order $1/|\ln \ep|^{1+b}$ for an arbitrary fixed $b\in\mathbb R$. We prove that as $\ep\to 0$, the motion of these helical vortices converges uniformly to a dynamical system derived herein over a time interval of order $1/|\ln\varepsilon|^{1-b}$. In the particular case $b=-1$, our results establish the evolution counterpart for interacting vortex helices constructed in [I. Guerra, M. Musso, Ann. Inst. H. Poincar\'e C Anal. Non Lin\'aire, 2025]. Notably, for two interacting helical vortices with initial mutual distance $ \rho_0/|\ln \ep|$, by choosing $\rho_0$ sufficiently small, our analysis extends to timescales covering multiple periods. This result provides the first mathematical justification for the numerically observed phenomenon termed ``leapfrogging of Kelvin waves" reported in [N. Hietala et al., Phys. Rev. Fluids, 2016].

math.AP↗

arXiv2024

On concentrated vortices of 3D incompressible Euler equations under helical symmetry: with swirl

In this paper, we consider the existence of concentrated helical vortices of 3D incompressible Euler equations with swirl. First, without the assumption of the orthogonality condition, we derive a 2D vorticity-stream formulation of 3D incompressible Euler equations under helical symmetry. Then based on this system, we deduce a non-autonomous second order semilinear elliptic equations in divergence form, whose solutions correspond to traveling-rotating invariant helical vortices with non-zero helical swirl. Finally, by using Arnold's variational method, that is, finding maximizers of a properly defined energy functional over a certain function space and proving the asymptotic behavior of maximizers, we construct families of concentrated traveling-rotating helical vortices of 3D incompressible Euler equations with non-zero helical swirl in infinite cylinders. As parameter $ \varepsilon\to0 $, the associated vorticity fields tend asymptotically to a singular helical vortex filament evolved by the binormal curvature flow.

math.AP↗

arXiv2024

On the Lack of Robustness of Binary Function Similarity Systems

Binary function similarity, which often relies on learning-based algorithms to identify what functions in a pool are most similar to a given query function, is a sought-after topic in different communities, including machine learning, software engineering, and security. Its importance stems from the impact it has in facilitating several crucial tasks, from reverse engineering and malware analysis to automated vulnerability detection. Whereas recent work cast light around performance on this long-studied problem, the research landscape remains largely lackluster in understanding the resiliency of the state-of-the-art machine learning models against adversarial attacks. As security requires to reason about adversaries, in this work we assess the robustness of such models through a simple yet effective black-box greedy attack, which modifies the topology and the content of the control flow of the attacked functions. We demonstrate that this attack is successful in compromising all the models, achieving average attack success rates of 57.06% and 95.81% depending on the problem settings (targeted and untargeted attacks). Our findings are insightful: top performance on clean data does not necessarily relate to top robustness properties, which explicitly highlights performance-robustness trade-offs one should consider when deploying such models, calling for further research.

cs.CR↗

arXiv2024

SoK: On the Role and Future of AIGC Watermarking in the Era of Gen-AI

The rapid advancement of AI technology, particularly in generating AI-generated content (AIGC), has transformed numerous fields, e.g., art video generation, but also brings new risks, including the misuse of AI for misinformation and intellectual property theft. To address these concerns, AIGC watermarks offer an effective solution to mitigate malicious activities. However, existing watermarking surveys focus more on traditional watermarks, overlooking AIGC-specific challenges. In this work, we propose a systematic investigation into AIGC watermarking and provide the first formal definition of AIGC watermarking. Different from previous surveys, we provide a taxonomy based on the core properties of the watermark which are summarized through comprehensive literature from various AIGC modalities. Derived from the properties, we discuss the functionality and security threats of AIGC watermarking. In the end, we thoroughly investigate the AIGC governance of different countries and practitioners. We believe this taxonomy better aligns with the practical demands for watermarking in the era of GenAI, thus providing a clearer summary of existing work and uncovering potential future research directions for the community.

cs.CR↗

arXiv2024

Expansion of Green's function and regularity of Robin's function for elliptic operators in divergence form

We consider Green's function $ G_K $ of the elliptic operator in divergence form $ \mathcal{L}_K=-\text{div}(K(x)\nabla ) $ on a bounded smooth domain $ \Omega\subseteq\mathbb{R}^n (n\geq 2) $ with zero Dirichlet boundary condition, where $ K $ is a smooth positively definite matrix-valued function on $ \Omega $. We obtain a high-order asymptotic expansion of $ G_K(x, y) $, which defines uniquely a regular part $ H_K(x, y) $. Moreover, we prove that the associated Robin's function $ R_K(x) = H_K(x, x) $ is smooth in $ \Omega $, despite the regular part $ H_K\notin C^1(\Omega\times\Omega) $ in general.

math.AP↗

arXiv2023

Clustered helical vortices for 3D incompressible Euler equation in infinite cylinders

In this article, we first consider solutions to a semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in \Omega,\\ u=0,\ \ &x\in\partial \Omega \end{cases} \end{equation*} for small values of $ \varepsilon $. We prove that there exists a family of clustered solutions which have arbitrary many bubbles and collapse into given maximum points of $ q^2\sqrt{\det K} $ as $ \varepsilon\to0. $ Then as an application, we construct clustered traveling-rotating helical vortex solutions to Euler equations in infinite cylinders, such that the support set of corresponding vortices consists of several helical tubes concentrating near a single helix.

math.AP↗

arXiv2022

Purifier: Defending Data Inference Attacks via Transforming Confidence Scores

Neural networks are susceptible to data inference attacks such as the membership inference attack, the adversarial model inversion attack and the attribute inference attack, where the attacker could infer useful information such as the membership, the reconstruction or the sensitive attributes of a data sample from the confidence scores predicted by the target classifier. In this paper, we propose a method, namely PURIFIER, to defend against membership inference attacks. It transforms the confidence score vectors predicted by the target classifier and makes purified confidence scores indistinguishable in individual shape, statistical distribution and prediction label between members and non-members. The experimental results show that PURIFIER helps defend membership inference attacks with high effectiveness and efficiency, outperforming previous defense methods, and also incurs negligible utility loss. Besides, our further experiments show that PURIFIER is also effective in defending adversarial model inversion attacks and attribute inference attacks. For example, the inversion error is raised about 4+ times on the Facescrub530 classifier, and the attribute inference accuracy drops significantly when PURIFIER is deployed in our experiment.

cs.LG↗

arXiv2022

LACV-Net: Semantic Segmentation of Large-Scale Point Cloud Scene via Local Adaptive and Comprehensive VLAD

Large-scale point cloud semantic segmentation is an important task in 3D computer vision, which is widely applied in autonomous driving, robotics, and virtual reality. Current large-scale point cloud semantic segmentation methods usually use down-sampling operations to improve computation efficiency and acquire point clouds with multi-resolution. However, this may cause the problem of missing local information. Meanwhile, it is difficult for networks to capture global information in large-scale distributed contexts. To capture local and global information effectively, we propose an end-to-end deep neural network called LACV-Net for large-scale point cloud semantic segmentation. The proposed network contains three main components: 1) a local adaptive feature augmentation module (LAFA) to adaptively learn the similarity of centroids and neighboring points to augment the local context; 2) a comprehensive VLAD module (C-VLAD) that fuses local features with multi-layer, multi-scale, and multi-resolution to represent a comprehensive global description vector; and 3) an aggregation loss function to effectively optimize the segmentation boundaries by constraining the adaptive weight from the LAFA module. Compared to state-of-the-art networks on several large-scale benchmark datasets, including S3DIS, Toronto3D, and SensatUrban, we demonstrated the effectiveness of the proposed network.

cs.CV↗

arXiv2022

Structure of Green's function of elliptic equations and helical vortex patches for 3D incompressible Euler equations

We develop a new structure of the Green's function of a second-order elliptic operator in divergence form in a 2D bounded domain. Based on this structure and the theory of rearrangement of functions, we construct concentrated traveling-rotating helical vortex patches to 3D incompressible Euler equations in an infinite pipe. By solving an equation for vorticity \begin{equation*} w=\frac{1}{\varepsilon^2}f_\varepsilon\left(\mathcal{G}_{K_H}w-\fracα{2}|x|^2|\ln\varepsilon|\right) \ \ \text{in}\ Ω\end{equation*} for small $ \varepsilon>0 $ and considering a certain maximization problem for the vorticity, where $ \mathcal{G}_{K_H} $ is the inverse of an elliptic operator $ \mathcal{L}_{K_H} $ in divergence form, we get the existence of a family of concentrated helical vortex patches, which tend asymptotically to a singular helical vortex filament evolved by the binormal curvature flow. We also get nonlinear orbital stability of the maximizers in the variational problem under $ L^p $ perturbation when $ p\geq 2. $

math.AP↗

arXiv2022

Desingularization of 3D steady Euler equation with helical symmetry

In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady Euler flows with helical symmetry, such that the associated vorticities tend asymptotically to a helical vortex filament. The solutions are obtained by solving a semilinear elliptic problem in divergence form with a parameter. By using the stream-function method, we show the existence and asymptotic behavior of ground state solutions concentrating near a single point as the parameter $ \varepsilon\to 0 $. Qualitative properties of those solutions are also discussed.

math.AP↗

arXiv2022

Helical vortices with small cross-section for 3D incompressible Euler equation

In this article, we construct traveling-rotating helical vortices with small cross-section to the 3D incompressible Euler equations in an infinite pipe, which tend asymptotically to singular helical vortex filament evolved by the binormal curvature flow. The construction is based on studying a general semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in Ω,\\ u=0,\ \ &x\in\partial Ω, \end{cases} \end{equation*} for small values of $ \varepsilon. $ Helical vortex solutions concentrating near several helical filaments with polygonal symmetry are also constructed.

math.AP↗

arXiv2019

Desingularization of steady vortex of perturbation type in the lake equations

In this paper, we study the desingularization of steady lake model of perturbation type with general nonlinearity f. Using the modified vorticity method, we construct a family of steady solutions with vanishing circulation, which constitute a desingularization of a singular vortex. The localization of the singular vortex is determined only by the vanishing rate of the circulation. Some qualitative and asymptotic properties are also established.

math.AP↗