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Yuhua Sun

Publications and source records attributed to Yuhua Sun.

At least 19 recordsLinked to original sources
arXiv2026

Flow Decomposition and Sharp Integral Fujita Criteria on Weighted Graphs

We study the Fujita phenomenon for semilinear heat inequalities generated by variable-speed Laplacians on infinite weighted graphs. Assuming that the graph carries a proper adapted path metric, we establish an integral volume-growth criterion forcing every nonnegative global classical supersolution on the open cylinder $(0,\infty)\times V$ to vanish, without assuming an initial value or trace. We prove that a nontrivial supersolution of this kind exists if and only if the equation has a positive global Cauchy solution for some nonzero point-source datum. A complementary heat-kernel construction gives global Cauchy solutions for all sufficiently small point-source data when the same volume integral converges and a matching anchored heat-kernel upper bound is available. This proves sharpness on integer lattices and on a family of logarithmically perturbed weighted half-lines; in the latter examples, even the exponent of an iterated logarithm can determine the existence--nonexistence alternative. A finer nonexistence criterion couples intrinsic volume growth with the capacity of intrinsic annuli. Its proof combines parabolic testing, a Laplace--resolvent reduction, and a pathwise decomposition of resolvent currents. The nonexistence results require no volume-doubling property, Poincar\'e inequality, heat-kernel bound, or stochastic completeness.

math.AP↗
arXiv2026

A sharp integral criterion for the Lane--Emden system of inequalities on weighted graphs

We establish a sharp integral nonexistence criterion for the Lane--Emden system of inequalities \[ -\Delta u\ge v^p,\qquad -\Delta v\ge u^q, \qquad p,q>0,\quad pq>1, \] on arbitrary infinite, connected, locally finite weighted graphs. In the asymmetric case $p\ne q$, set $P=\max\{p,q\}$. If, for some root $o\in V$, \[ \sum_{n=2}^{\infty} \frac{n^{2pq+2P-1}}{\mu(B(o,n))^{pq-1}}=\infty, \] then every nonnegative solution $(u,v)$ satisfies $u\equiv v\equiv0$. The proof combines flow decomposition of the finite Green current with nonlinear testing. In the symmetric case $p=q>1$, the Liouville problem reduces, via the sum $u+v$, to the scalar criterion \[ \sum_{n=2}^{\infty} \frac{n^{2p-1}}{\mu(B(o,n))^{p-1}}=\infty. \] Weighted half-line examples show that the critical logarithmic endpoint in the asymmetric result is sharp.

math.AP↗
arXiv2026

Mixed-Parabolicity and Mixed-Liouville Property for Products of Riemannian Manifolds

Let $p_1,p_2\in(1,\infty)$ and $M=M_1\times M_2$ be the product of two geodesically complete Riemannian manifolds. In this paper, the authors first develop an anisotropic potential-theoretic framework adapted to the Green operator $G^M$ and the mixed-norm Lebesgue space $L^{p_2}(L^{p_1})(M)$, and then demonstrate that the classical equivalence among \emph{parabolicity}, \emph{Green function integrability}, and \emph{Liouville property} persists in this genuinely anisotropic setting. More precisely, the authors establish the following equivalence: $M$ is $L^{p_2}(L^{p_1})$-parabolic if and only if the Green function $G^M(x;\,\cdot\,)$ fails to belong to $L^{p_2'}(L^{p_1'})(M \setminus B(x,\,r))$, which is in turn equivalent to the $L^{p_2'}(L^{p_1'})$-Liouville property, where $p_i'$ denotes the conjugate exponent of $p_i$. Under a weak radial Harnack-type inequality -- in particular, under Li--Yau heat kernel estimates, and hence for products of manifolds with nonnegative Ricci curvature -- these conditions are further equivalent to the divergence of the nonlinear mixed-potential $\mathcal{G}_{p_1,p_2}(f)$ for every nonzero nonnegative $f\in {\mathcal C}_c^\infty(M)$. A key feature of this anisotropic theory is its sensitivity to the geometry of each factor \(M_i\), rather than merely to that of the total manifold \(M\). In contrast to the isotropic case, where parabolicity and the classical Liouville property holds on \(\mathbb{R}^n\) precisely when \(n \le 2\), the anisotropic setting exhibits a refined threshold: the \(L^{p_2}(L^{p_1})\)-parabolicity and the \(L^{p_2'}(L^{p_1'})\)-Liouville property holds on \(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2}\) if and only if $ D_{\mathrm{eff}} := \frac{n_1}{p_1} + \frac{n_2}{p_2} \le 2. $ This effective dimension $D_{\mathrm{eff}}$ captures the anisotropic interplay between the exponents \(p_1, p_2\) and the geometries of \(M_1, M_2\).

math.CA↗
arXiv2026

Rethinking Side-Channel Analysis: Automated Discovery and Analysis of Side-Channel Leakage with LLM-Assisted Agents

Side-channel attacks exploit unintended information leakage from system behavior and continue to pose serious privacy risks in modern platforms. Despite extensive prior work, side-channel analysis remains largely manual and fragmented, typically assuming predefined target events and a fixed set of known channels. As systems and applications grow increasingly complex, several fundamental questions remain unanswered: which user or system events are sensitive in practice, how side channels associated with these events can be systematically discovered without exhaustive manual effort, and how their leakage can be analyzed at scale without prohibitive data collection and model training costs. To address these questions, we present SCAgent, an automated framework for side-channel risk analysis. To identify sensitive targets beyond manually specified events, SCAgent performs agent-driven system exploration guided by LLM-based semantic reasoning. To systematically discover side channels while mitigating the risk of LLM hallucination, it reasons over system documentation and incorporates explicit verification to enforce semantic consistency, threat-model feasibility, and per-channel usability. To enable scalable analysis under limited data, SCAgent adopts a few-shot learning paradigm based on foundation models, avoiding the need to train bespoke models for each channel--event pair. To bridge the gap between raw time-series side-channel signals and tabular foundation models, SCAgent further introduces a time-shift--robust feature extraction layer that enables effective downstream analysis. We instantiate SCAgent on iOS as a first step, focusing on OS-level side channels observable by unprivileged applications. Our evaluation spans standard benchmarks such as foreground app and website fingerprinting, as well as newly identified sensitive in-app activities in popular applications.

cs.CR↗
arXiv2026

A Volume-Growth Criterion for the p-Laplace Inequality on Weighted Graphs

We prove a nonexistence result for nonnegative solutions of the quasi-linear elliptic inequality \[ -\Delta_p u\ge \sigma(x)u^q \] on infinite locally finite connected weighted graphs, where $1 p-1$, $\sigma$ is a nonnegative Radon measure. Under the non-$p$-parabolic setting, we show that every nonnegative solution is identically zero, provided the volume of intrinsic balls satisfy \[ \int_1^\infty \frac{r^{\frac{pq}{p-1}-1}} {\nu(B_\rho(o,r))^{\frac{q-p+1}{p-1}}} \dd r =\infty, \] This criterion recovers the known sharp pointwise critical volume-growth threshold and is strictly more flexible, since it allows irregular growth and does not require uniform upper bounds at every large radius. The proof adapts the finite-network current method to the $p$-Laplace setting, combining a path decomposition with one-dimensional Hardy estimates, $p$-parallel-sum bounds across metric cuts, and the global $p$-Green function furnished by non-$p$-parabolicity.

math.AP↗
arXiv2026

Flow Decomposition, Green Testing, and Lane--Emden Inequalities on Weighted Graphs

We study positive solutions of the superlinear Lane--Emden inequality \[ -\Delta u\ge \sigma u^q,\qquad q>1, \] on infinite locally finite weighted graphs and connected domains. When the Dirichlet Green function is finite, the existence of a positive solution is equivalent to \[ G_\Omega\bigl(\sigma g_\Omega(o,\cdot)^q\bigr)(x) \le C g_\Omega(o,x) \] for some pole \(o\in\Omega\). Under Green function estimates, this yields sharp existence criteria and the Serrin-type exponents on \(\mathbb Z^d\) and orthant domains. For nonexistence, the principal method is flow decomposition. Its basic estimate bounds Green energy from below in terms of the relative capacities of intrinsic balls. %It yields annular conductance, capacity-to-infinity, and Nash--Williams cut-resistance criteria. For \(\sigma>0\), set \(\nu=\sigma\mu\). We show that if \(d_\rho\) is a complete \(\nu\)-adapted path metric and \[ \int_1^\infty \frac{r^{2q-1}}{\nu(B_{d_\rho}(o,r))^{q-1}}\,dr=\infty, \] then every nonnegative solution is identically zero. The proof combines a flow decomposition of the acyclic Green current, a pathwise Hardy estimate, and a relative capacity estimate. It requires none of (VD), (PI), (P$_0$), or the (3G) condition.

math.AP↗
arXiv2026

Liouville Type Results for Quasilinear Elliptic Inequalities Involving Gradient Terms on Weighted Graphs

In this paper, we study the following quasi-linear elliptic inequality $\Delta_m u +u^p |\nabla u|^q \leqslant 0$ on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\mathbb{R}$. According to the ranges of parameters $(m, p, q)$, we establish the non-existence of nontrivial positive solutions under the corresponding sharp volume growth conditions. Our results can be viewed as a discrete generalization of their counterparts on Riemannian manifolds established by [Sun, Yuhua; Xiao, Jie; Xu, Fanheng, Math. Ann. 384 (2022), no. 3-4, 1309--1341.]. However, this generalization is far from trivial, many results exhibit significant differences from the manifold setting, highlighting the distinct behaviors and challenges that arise in the discrete weighted graph framework.

math.AP↗
arXiv2025

GrOCE:Graph-Guided Online Concept Erasure for Text-to-Image Diffusion Models

Concept erasure aims to remove harmful, inappropriate, or copyrighted content from text-to-image diffusion models while preserving non-target semantics. However, existing methods either rely on costly fine-tuning or apply coarse semantic separation, often degrading unrelated concepts and lacking adaptability to evolving concept sets. In this paper, we propose Graph-Guided Online Concept Erasure (GrOCE), a training-free framework that performs precise and context-aware online removal of target concepts. GrOCE constructs dynamic semantic graphs to identify clusters of target concepts and selectively suppress their influence within text prompts. It consists of three synergistic components: (1) dynamic semantic graph construction (Construct) incrementally builds a weighted graph over vocabulary concepts to capture semantic affinities; (2) adaptive cluster identification (Identify) extracts a target concept cluster through multi-hop traversal and diffusion-based scoring to quantify semantic influence; and (3) selective severing (Sever) removes semantic components associated with the target cluster from the text prompt while retaining non-target semantics and the global sentence structure. Extensive experiments demonstrate that GrOCE achieves state-of-the-art performance on the Concept Similarity (CS) and Fr\'echet Inception Distance (FID) metrics, offering efficient, accurate, and stable concept erasure.

cs.CV↗
arXiv2025

Hermitian Self-dual Twisted Generalized Reed-Solomon Codes

Self-dual maximum distance separable (MDS) codes over finite fields are linear codes with significant combinatorial and cryptographic applications. Twisted generalized Reed-Solomon (TGRS) codes can be both MDS and self-dual. In this paper, we study a general class of TGRS codes (A-TGRS), which encompasses all previously known special cases. First, we establish a sufficient and necessary condition for an A-TGRS code to be Hermitian self-dual. Furthermore, we present four constructions of self-dual TGRS codes, which, to the best of our knowledge, nearly cover all the related results previously reported in the literature. More importantly, we also obtain several new classes of Hermitian self-dual TGRS codes with flexible parameters. Based on this framework, we derive a sufficient and necessary condition for an A-TGRS code to be Hermitian self-dual and MDS. In addition, we construct a class of MDS Hermitian self-dual TGRS code by appropriately selecting the evaluation points. This work investigates the Hermitian self-duality of TGRS codes from the perspective of matrix representation, leading to more concise and transparent analysis. More generally, the Euclidean self-dual TGRS codes and the Hermitian self-dual GRS codes can also be understood easily from this point.

cs.IT↗
arXiv2025

Construction of Self-Orthogonal Quasi-Cyclic Codes and Their Application to Quantum Error-Correcting Codes

In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the structure of the dual codes of a class of 2-generator QC codes, we derive necessary and sufficient conditions for the QC codes to be dual-containing under the above three inner products. This class of 2-generator QC codes generalizes many known codes in the literature. Based on the above conditions, we construct several quantum stabilizer codes and quantum synchronizable codes with good parameters, some of which share parameters with certain best-known codes listed in Grassl's code table.

cs.IT↗
arXiv2024

On the equivalence of Lp-parabolicity and Lq-liouville property on weighted graphs

We study the equivalence between the $L^p$-parabolicity, the $L^q$-Liouville property of positive super-harmonic functions, and the existence of nonharmonic positive solutions to the following elliptic differential system \begin{equation*} \left\{ \begin{array}{lr} -\Delta u\geq 0, \Delta(|\Delta u|^{p-2}\Delta u)\geq 0, \end{array} \right. \end{equation*} on weighted graphs, where $1\leq p< \infty$, and $(p, q)$ are H\"{o}lder conjugate exponent pair. Furthermore, by refining a new technique on estimate of heat kernel, we can establish two-sided estimates of Green function on graph, and find the sharp volume growth criteria for the $L^q$-Liouville property on a large class of graphs. As an application, many non-trivial interesting examples are presented.

math.AP↗
arXiv2024

Research on the Construction of Maximum Distance Separable Codes via Arbitrary twisted Generalized Reed-Solomon Codes

Maximum distance separable (MDS) codes have significant combinatorial and cryptographic applications due to their certain optimality. Generalized Reed-Solomon (GRS) codes are the most prominent MDS codes. Twisted generalized Reed-Solomon (TGRS) codes may not necessarily be MDS. It is meaningful to study the conditions under which TGRS codes are MDS. In this paper, we study a general class of TGRS (A-TGRS) codes which include all the known special ones. First, we obtain a new explicit expression of the inverse of the Vandermonde matrix. Based on this, we further derive an equivalent condition under which an A-TGRS code is MDS. According to this, the A-TGRS MDS codes include nearly all the known related results in the previous literatures. More importantly, we also obtain many other classes of MDS TGRS codes with new parameter matrices. In addition, we present a new method to compute the inverse of the lower triangular Toplitz matrix by a linear feedback shift register, which will be very useful in many research fields.

cs.IT↗
arXiv2024

ModelLock: Locking Your Model With a Spell

This paper presents a novel model protection paradigm ModelLock that locks (destroys) the performance of a model on normal clean data so as to make it unusable or unextractable without the right key. Specifically, we proposed a diffusion-based framework dubbed ModelLock that explores text-guided image editing to transform the training data into unique styles or add new objects in the background. A model finetuned on this edited dataset will be locked and can only be unlocked by the key prompt, i.e., the text prompt used to transform the data. We conduct extensive experiments on both image classification and segmentation tasks, and show that 1) ModelLock can effectively lock the finetuned models without significantly reducing the expected performance, and more importantly, 2) the locked model cannot be easily unlocked without knowing both the key prompt and the diffusion model. Our work opens up a new direction for intellectual property protection of private models.

cs.LG↗
arXiv2024

Physical Backdoor: Towards Temperature-based Backdoor Attacks in the Physical World

Backdoor attacks have been well-studied in visible light object detection (VLOD) in recent years. However, VLOD can not effectively work in dark and temperature-sensitive scenarios. Instead, thermal infrared object detection (TIOD) is the most accessible and practical in such environments. In this paper, our team is the first to investigate the security vulnerabilities associated with TIOD in the context of backdoor attacks, spanning both the digital and physical realms. We introduce two novel types of backdoor attacks on TIOD, each offering unique capabilities: Object-affecting Attack and Range-affecting Attack. We conduct a comprehensive analysis of key factors influencing trigger design, which include temperature, size, material, and concealment. These factors, especially temperature, significantly impact the efficacy of backdoor attacks on TIOD. A thorough understanding of these factors will serve as a foundation for designing physical triggers and temperature controlling experiments. Our study includes extensive experiments conducted in both digital and physical environments. In the digital realm, we evaluate our approach using benchmark datasets for TIOD, achieving an Attack Success Rate (ASR) of up to 98.21%. In the physical realm, we test our approach in two real-world settings: a traffic intersection and a parking lot, using a thermal infrared camera. Here, we attain an ASR of up to 98.38%.

cs.CV↗
arXiv2023

Sharp criteria for nonlocal elliptic inequalities on manifolds

Let $M$ be a complete non-compact Riemannian manifold and $σ$ be a Radon measure on $M$, we study the existence and non-existence of positive solutions to a nonlocal elliptic inequality \begin{equation*} (-Δ)^α u\geq u^{q}σ\quad \text{in}\,\,M, \end{equation*} with $q>1$. When the Green function $G^{(α)}$ of the fractional Laplacian $(-Δ)^α$ exists and satisfies the quasi-metric property, we obtain necessary and sufficient criteria for existence of positive solutions. In particular, explicit conditions in terms of volume growth and the growth of $σ$ are given, when $M$ admits Li-Yau Gaussian type heat kernel estimates.

math.AP↗
arXiv2022

Backdoor Attacks on Crowd Counting

Crowd counting is a regression task that estimates the number of people in a scene image, which plays a vital role in a range of safety-critical applications, such as video surveillance, traffic monitoring and flow control. In this paper, we investigate the vulnerability of deep learning based crowd counting models to backdoor attacks, a major security threat to deep learning. A backdoor attack implants a backdoor trigger into a target model via data poisoning so as to control the model's predictions at test time. Different from image classification models on which most of existing backdoor attacks have been developed and tested, crowd counting models are regression models that output multi-dimensional density maps, thus requiring different techniques to manipulate. In this paper, we propose two novel Density Manipulation Backdoor Attacks (DMBA$^{-}$ and DMBA$^{+}$) to attack the model to produce arbitrarily large or small density estimations. Experimental results demonstrate the effectiveness of our DMBA attacks on five classic crowd counting models and four types of datasets. We also provide an in-depth analysis of the unique challenges of backdooring crowd counting models and reveal two key elements of effective attacks: 1) full and dense triggers and 2) manipulation of the ground truth counts or density maps. Our work could help evaluate the vulnerability of crowd counting models to potential backdoor attacks.

cs.CV↗
arXiv2022

A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms

In this article we study local and global properties of positive solutions of $-Δ_mu=|u|^{p-1}u+M|\nabla u|^q$ in a domain $Ω$ of $\mathbb R^N$, with $m>1$, $p,q>0$ and $M\in\mathbb R$. Following some ideas used in \cite{BV,Vron1}, and by using a direct Bernstein method combined with Keller-Osserman's estimate, we obtain several a priori estimates as well as Liouville type theorems. Moreover, we prove a local Harnack inequality with the help of Serrin's classical results.

math.AP↗