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Zhiqiang Li

Publications and source records attributed to Zhiqiang Li.

At least 19 recordsLinked to original sources
arXiv2026

Explicit exposure of Haar measure

We solve the problem of explicitly constructing a continuous function whose unique maximizing measure for the doubling map is Lebesgue measure. More generally, given a nontrivial compact metrizable abelian group and a continuous surjective endomorphism for which normalised Haar measure is ergodic, we explicitly construct a continuous function on the group for which Haar measure is the unique invariant maximizing measure. The function is the uniform limit of a recursively defined sequence of trigonometric polynomials with rational coefficients; every parameter of the recursion is given by a closed formula, every step is exact, and the rate of convergence is explicit. In specific cases, we further obtain a uniformly convergent Fourier expansion in the classical frequency order, each of whose coefficients is rational and computable exactly, by a finite procedure.

math.DS↗
arXiv2026

Clarity Contrast and Similarity Selection for Multi-Focus Image Fusion

Multi-focus image fusion (MFIF) aims to generate an all-in-focus image from multiple images of the same scene focused at different regions. Most existing deep learning-based methods lack explicit interaction between the source images, which limits their performance and interpretability. This paper presents a novel Clarity Contrast and Similarity Selection Network (CSNet), to bridge direct information exchange for MFIF. Specifically, by contrasting the clarity differences between source images within our proposed Clarity Contrast Attention Module (CCAM), we mutually enhance sharp features while suppressing blurry ones. This allows us to identify the exactly focused regions in each source and locate the focused-defocused boundaries. Moreover, the Defocus Spread Effect (DSE) degrades pixels in all source images around the boundaries. To further refine these ambiguous areas, we introduce a Similarity Selection Strategy, which reconstructs an initial clear image from source images and selects optimal pixels by comparing the similarity among them. Through this interactive approach, CSNet effectively preserves focused regions as well as recovering natural boundaries to fuse an all-in-focus output. Extensive experiments demonstrate that our method achieves state-of-the-art performance both quantitatively and qualitatively. Our code is available on Github: https://github.com/ZYC-HUST/CSNet.

cs.CV↗
arXiv2026

How Your Credentials Are Leaked by LLM Agent Skills: An Empirical Study

Large Language Model (LLM) agents increasingly rely on third-party skills that operate within privileged execution environments and routinely handle sensitive credentials, yet how these credentials are leaked remains largely unexplored. To fill this gap, we present the first large-scale empirical study on credential leakage in agent skills. From 170,226 artifacts on SkillsMP, the largest open-source skill marketplace, we sampled 17,022 skills via stratified random sampling and analyzed each through static secret extraction (regex and AST parsing), dynamic sandbox testing with mock credentials, and cross-referencing developer intent against runtime behavior. Our analysis identifies 520 affected skills containing 1,708 security issues, and yields a taxonomy of 10 leakage patterns. Three findings stand out. First, 76.3% of cases require jointly analyzing natural-language descriptions and programming logic, showing that credential exposure in skills is fundamentally cross-modal. Second, debug logging accounts for 73.5% of vulnerabilities because agent frameworks feed stdout into the LLM context window, turning routine debugging into a credential exposure vector. Third, 89.6% of leaked credentials are immediately exploitable -- 92.5% during routine execution without elevated privileges -- and the fork-based distribution model defeats remediation, as secrets removed from 107 upstream repositories persist across 50+ independent forks. Following responsible disclosure, all malicious skills have been removed and 91.6% of hardcoded cases remediated. We release our dataset, taxonomy, and detection pipeline to support future agent security research.

cs.CR↗
arXiv2026

Quasi-isometric rigidity for random subsets in products of trees

In this article, we prove a rigidity result for quasi-isometric embeddings from a random subset $D$ of the product $\mathbb{X}$ of two regular trees into $\mathbb{X}$ itself. This can be seen as an extension of Eskin's quasi-isometric rigidity of higher-rank nonuniform lattices to random subsets. As a consequence, we give a description of the self-quasi-isometric embeddings of a random sample. We also show that two independent samples are almost surely non-quasi-isometric, confirming that such a phenomenon occurs in the higher-rank setting, as suggested by Abért. This result contrasts with the result on quasi-isometric equivalence between random sequences by Basu and Sly.

math.MG↗
arXiv2026

Joint typical periodic optimization: systems with stable hyperbolicity

The framework of joint typical periodic optimization, in which both the dynamical system and the potential function are allowed to vary simultaneously, was introduced in [HHJL25], in a direction motivated by the work of Yang, Hunt & Ott [YHO00]. For certain classes of hyperbolic systems, it was shown there that optimizing periodic orbits persist under simultaneous perturbation, yielding joint locking sets that contain open dense subsets of the relevant product spaces. In the present article we broaden the scope of this theory, by developing an axiomatic joint perturbation framework that accommodates a wider class of stably hyperbolic systems, and by establishing new joint typical periodic optimization results for several natural and important families: Axiom A diffeomorphisms with the no-cycle property, hyperbolic rational maps on the Riemann sphere, real quadratic polynomials, and $C^r$ maps in one dimension.

math.DS↗
arXiv2026

Joint typical periodic optimization

We prove a generalised Yuan--Hunt--Mañé Conjecture: if $\mathcal{F}$ is the Banach space of $α$-Hölder functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of beta-transformations on the interval, there is an open dense subset of $\mathcal{T}\times\mathcal{F}$ consisting of map-function pairs whose maximizing invariant measure is unique and supported on a periodic orbit.

math.DS↗
arXiv2026

Dual-stream Spatio-Temporal GCN-Transformer Network for 3D Human Pose Estimation

3D human pose estimation is a classic and important research direction in the field of computer vision. In recent years, Transformer-based methods have made significant progress in lifting 2D to 3D human pose estimation. However, these methods primarily focus on modeling global temporal and spatial relationships, neglecting local skeletal relationships and the information interaction between different channels. Therefore, we have proposed a novel method,the Dual-stream Spatio-temporal GCN-Transformer Network (MixTGFormer). This method models the spatial and temporal relationships of human skeletons simultaneously through two parallel channels, achieving effective fusion of global and local features. The core of MixTGFormer is composed of stacked Mixformers. Specifically, the Mixformer includes the Mixformer Block and the Squeeze-and-Excitation Layer ( SE Layer). It first extracts and fuses various information of human skeletons through two parallel Mixformer Blocks with different modes. Then, it further supplements the fused information through the SE Layer. The Mixformer Block integrates Graph Convolutional Networks (GCN) into the Transformer, enhancing both local and global information utilization. Additionally, we further implement its temporal and spatial forms to extract both spatial and temporal relationships. We extensively evaluated our model on two benchmark datasets (Human3.6M and MPI-INF-3DHP). The experimental results showed that, compared to other methods, our MixTGFormer achieved state-of-the-art results, with P1 errors of 37.6mm and 15.7mm on these datasets, respectively.

cs.CV↗
arXiv2025

Ergodic optimization for Gauss's continued fraction map

The theory of ergodic optimization for distance-expanding maps is extended to Gauss's continued fraction map. Since the set of invariant probability measures is not weak$^*$ closed, we establish a characterisation of the closure of this set, and investigate limit-maximizing measures for Hölder continuous functions. Although a Mañé cohomology lemma is shown to hold, the typical periodic optimization conjecture is shown to fail, as a consequence of the typical finite optimization property established for a certain class of (rationally maximized) functions. The typical periodic optimization (TPO) property is shown to hold, however, for the class of $α$-Hölder essentially compact functions.

math.DS↗
arXiv2025

Thermodynamic formalism for correspondences

In this article, we investigate the Variational Principle and develop thermodynamic formalism for correspondences. We define the measure-theoretic entropy for transition probability kernels and topological pressure for correspondences. Based on these two notions, we establish the following results: The Variational Principle holds and equilibrium states exist for continuous potential functions, provided that the correspondence satisfies some expansion property called forward expansiveness. If, in addition, the correspondence satisfies the specification property and the potential function is Bowen summable, then the equilibrium state is unique. On the other hand, for a distance-expanding, open, strongly transitive correspondence and a Hölder continuous potential function, there exists a unique equilibrium state, and the backward orbits are equidistributed. Furthermore, we investigate the Variational Principle for general correspondences. In complex dynamics, we establish the Variational Principle for the Lee-Lyubich-Markorov-Mukherjee anti-holomorphic correspondences, which are matings of some anti-ho\-lo\-mor\-phic rational maps with anti-Hecke groups and are not forward expansive. We also show a Ruelle-Perron-Frobenius theorem for a family of hyperbolic holomorphic correspondences of the form $\boldsymbol{f}_c (z)= z^{q/p}+c$.

math.DS↗
arXiv2025

Breaking the 800 mV open-circuit voltage barrier in antimony sulfide photovoltaics

Sb2S3 is a promising material for low-toxicity, high-stability next-generation photovoltaics. Despite high optical limits in efficiency, progress in improving its device performance has been limited by severe voltage losses. Recent spectroscopic investigations suggest that self-trapping occurs in Sb2S3, limiting the open-circuit voltage (Voc) to a maximum of approximately 800 mV, which is the level the field has asymptotically approached. In this work, we surpass this voltage barrier through reductions in the defect density in Sb2S3 thin films by modulating the growth mechanism in chemical bath deposition using citrate ligand additives. Deep level transient spectroscopy identifies two deep traps 0.4-0.7 eV above the valence band maximum, and, through first-principles calculations, we identify these to likely be S vacancies, or Sb on S anti-sites. The concentrations of these traps are lowered by decreasing the grain boundary density from 1114+/-52 nm/um2 to 585+/-10 nm/um2, and we achieve a Voc of 824 mV, the record for Sb2S3 solar cells. This work addresses the debate in the field around whether Sb2S3 is limited by defects or self-trapping, showing that it is possible to improve the performance towards the radiative limit through careful defect engineering.

cond-mat.mtrl-sci↗
arXiv2025

Computable thermodynamic formalism

We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the computability of equilibrium states for nonuniformly expanding computable dynamical systems. The first approach applies to dynamical systems whose topological pressure functions admit effective approximations and whose measure-theoretic entropy functions are upper semicontinuous. As a concrete application, we establish the computability of the equilibrium states for Misiurewicz-Thurston rational maps with Hölder continuous potentials. The second approach exploits prescribed Jacobians of equilibrium states through a local analysis and applies to settings where the measure-theoretic entropy functions may lack upper semicontinuity.

math.DS↗
arXiv2025

Rigidity and quasisymmetric uniformization of Thurston-type maps

We prove the No Invariant Line Fields conjecture for a class of generalized postcritically-finite branched covers on higher-dimensional Riemannian manifolds. Moreover, we establish a quasisymmetric uniformization theorem for this class of generalized postcritically-finite maps.

math.DS↗
arXiv2025

A class of Lattès maps with cellular structures

We show that a class of quasiregular Lattès maps, called orthotopic Lattès maps, are cellular Markov maps. This provides examples of expanding Thurston-type maps that are also uniformly quasiregular, and whose visual metrics are quasisymmetrically equivalent to the Riemannian distance.

math.DS↗
arXiv2025

Counting prime orbits in shrinking intervals for expanding Thurston maps

We establish a local central limit theorem for primitive periodic orbits of expanding Thurston maps, providing a fine-scale refinement of the Prime Orbit Theorem in the context of non-uniformly expanding dynamics. Specifically, we count the number of primitive periodic orbits whose Birkhoff sums for a given potential lie within a family of shrinking intervals. For eventually positive, real-valued \holder continuous potentials that satisfy the strong non-integrability condition, we derive precise asymptotic estimates. In particular, our results apply to postcritically-finite rational maps whose Julia set is the whole Riemann sphere.

math.DS↗
arXiv2025

High-resolution Photo Enhancement in Real-time: A Laplacian Pyramid Network

Photo enhancement plays a crucial role in augmenting the visual aesthetics of a photograph. In recent years, photo enhancement methods have either focused on enhancement performance, producing powerful models that cannot be deployed on edge devices, or prioritized computational efficiency, resulting in inadequate performance for real-world applications. To this end, this paper introduces a pyramid network called LLF-LUT++, which integrates global and local operators through closed-form Laplacian pyramid decomposition and reconstruction. This approach enables fast processing of high-resolution images while also achieving excellent performance. Specifically, we utilize an image-adaptive 3D LUT that capitalizes on the global tonal characteristics of downsampled images, while incorporating two distinct weight fusion strategies to achieve coarse global image enhancement. To implement this strategy, we designed a spatial-frequency transformer weight predictor that effectively extracts the desired distinct weights by leveraging frequency features. Additionally, we apply local Laplacian filters to adaptively refine edge details in high-frequency components. After meticulously redesigning the network structure and transformer model, LLF-LUT++ not only achieves a 2.64 dB improvement in PSNR on the HDR+ dataset, but also further reduces runtime, with 4K resolution images processed in just 13 ms on a single GPU. Extensive experimental results on two benchmark datasets further show that the proposed approach performs favorably compared to state-of-the-art methods. The source code will be made publicly available at https://github.com/fengzhang427/LLF-LUT.

cs.CV↗
arXiv2025

Whittaker modules over the loop Virasoro algebra

In this paper, we first study two classes of Whittaker modules over the loop Witt algebra ${\mathfrak g}:=\mathcal{W}\otimes\mathcal{A}$, where $\mathcal{W}=\text{Der}({\mathbb{C}}[t])$, $\mathcal{A}={\mathbb{C}}[t,t^{-1}]$. The necessary and sufficient conditions for these Whittaker modules being simple are determined. Furthermore, we study a family of Whittaker modules over the loop Virasoro algebra $\mathfrak{L}:=Vir\otimes\mathcal{A}$, where $Vir$ is the Virasoro algebra. The irreducibility criterion for these Whittaker modules are obtained. As an application, we give the irreducibility criterion for universal Whittaker modules of the affine Lie algebra $\widehat{\mathfrak{sl}_{2}}$.

math.RT↗
arXiv2025

Tropical thermodynamic formalism

We investigate the zero-temperature large deviation principle for equilibrium states in the context of distance-expanding maps. The logarithmic-type zero-temperature limit in the large deviation principle induces a tropical algebra structure, which motivates our study of the tropical adjoint Bousch operator $\mathcal{L}_A^{*}$ since the Bousch operator $\mathcal{L}_A$ is tropical linear and corresponds to the Ruelle operator $\mathcal{R}_A$. We extend tropical functional analysis, define the adjoint operator $\mathcal{L}_A^{*}$ corresponding to $\mathcal{R}_A^{*}$, and establish the existence and generic uniqueness of tropical eigen-densities of $\mathcal{L}_A^{*}$. The Aubry set and the Mañé potential, both originating from weak KAM theory, serve as important tools in the representation of tropical eigen-densities. We derive a sufficient condition for the large deviation principle which holds for a generic Hölder potential and establish a characterization theorem for the large deviation principle.

math.DS↗