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Guohua Zhang

Publications and source records attributed to Guohua Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Dimensional entropy of amenable group actions over stable sets and fibres

This paper is devoted to the study of Bowen's dimensional entropy on subsets for actions of amenable groups. We prove three main results. (1) First, topological conditional entropy is characterized by the dimensional entropy of stable sets (Theorem 1.1), answering a question of Dou, Wang and the second author of the present paper raised in [Fund. Math., 2025]. We remark that our Theorem 1.1 is the first characterization of topological conditional entropy via Bowen's dimensional entropy of stable sets even for $\mathbb{Z}$-actions. (2) Second, we establish a dimensional entropy inequality for factor maps (Theorem 1.2). It relates dimensional entropy of a set to that of its image and topological entropy of fibres, and may be viewed as the dimensional-entropy counterpart of the factor-map inequality for packing topological entropy due to Dou, Zheng, and Zhou proved as Theorem 1.4 in [Ergodic Theory Dynam. Systems, 2023]. (3) Third, the relative topological entropy of a factor map is determined by the dimensional entropy of the fibres (Theorem 1.3). Notably, our proof of this formula (Theorem 1.3) is purely topological, in contrast to the recent measure-theoretic approach of Dou, Wang and Zhou based on relative Shannon--McMillan--Breiman theorems. These results (Theorem 1.2 and 1.3) not only generalize the work of Oprocha and the second author of the present paper [Nonlinearity, 2011] from single transformations to amenable group actions, but also provide a purely topological and self-contained proof of a fibre entropy characterization recently obtained through measure-theoretic arguments.

math.DS↗
arXiv2026

Metric mean dimension of amenable group actions: localization and non-uniformity

In this paper, we extend Tsukamoto's recent localization formula for metric mean dimension to actions of countable discrete amenable groups, which previously applied only to $\mathbb{R}^k$- and $\mathbb{Z}^k$-actions -- by proving that the global metric mean dimension is characterized by the asymptotic entropy of pointwise $\varepsilon$-stable sets (Theorem 2.3). To achieve this generalization, we introduce equivalent definitions of the invariant using topological entropy, packing topological entropy, and Bowen's dimensional entropy, respectively. A key technical contribution is our replacement of tiling arguments with Lindenstrauss's combinatorial covering lemma, which enables us to handle the general structure of amenable groups. Furthermore, we resolve all three questions regarding uniformity raised in Section 6 of a recent paper by Yang, Chen, and Zhou by constructing counterexamples (Theorem 2.6 and Proposition 5.8), which demonstrates that the supremum and limit superior in the localization formula cannot generally be interchanged, thereby highlighting the heterogeneous nature of the convergence. These results clarify the uniformity issue and offer insights into the link between local dynamics and global invariants, while our equivalent definitions provide flexible tools for computing metric mean dimension in concrete settings.

math.DS↗
arXiv2026

QD-PCQA: Quality-Aware Domain Adaptation for Point Cloud Quality Assessment

No-Reference Point Cloud Quality Assessment (NR-PCQA) still struggles with generalization, primarily due to the scarcity of annotated point cloud datasets. Since the Human Visual System (HVS) drives perceptual quality assessment independently of media types, prior knowledge on quality learned from images can be repurposed for point clouds. This insight motivates adopting Unsupervised Domain Adaptation (UDA) to transfer quality-relevant priors from labeled images to unlabeled point clouds. However, existing UDA-based PCQA methods often overlook key characteristics of perceptual quality, such as sensitivity to quality ranking and quality-aware feature alignment, thereby limiting their effectiveness. To address these issues, we propose a novel Quality-aware Domain adaptation framework for PCQA, termed QD-PCQA. The framework comprises two main components: i) a Rank-weighted Conditional Alignment (RCA) strategy that aligns features under consistent quality levels and adaptively emphasizes misranked samples to reinforce perceptual quality ranking awareness; and ii) a Quality-guided Feature Augmentation (QFA) strategy, which includes quality-guided style mixup, multi-layer extension, and dual-domain augmentation modules to augment perceptual feature alignment. Extensive cross-domain experiments demonstrate that QD-PCQA significantly improves generalization in NR-PCQA tasks.

cs.CV↗
arXiv2026

GT-PCQA: Geometry-Texture Decoupled Point Cloud Quality Assessment with MLLM

With the rapid advancement of Multi-modal Large Language Models (MLLMs), MLLM-based Image Quality Assessment (IQA) methods have shown promising generalization. However, directly extending these MLLM-based IQA methods to PCQA remains challenging. On the one hand, existing PCQA datasets are limited in scale, which hinders stable and effective instruction tuning of MLLMs. On the other hand, due to large-scale image-text pretraining, MLLMs tend to rely on texture-dominant reasoning and are insufficiently sensitive to geometric structural degradations that are critical for PCQA. To address these gaps, we propose a novel MLLM-based no-reference PCQA framework, termed GT-PCQA, which is built upon two key strategies. First, to enable stable and effective instruction tuning under scarce PCQA supervision, a 2D-3D joint training strategy is proposed. This strategy formulates PCQA as a relative quality comparison problem to unify large-scale IQA datasets with limited PCQA datasets. It incorporates a parameter-efficient Low-Rank Adaptation (LoRA) scheme to support instruction tuning. Second, a geometry-texture decoupling strategy is presented, which integrates a dual-prompt mechanism with an alternating optimization scheme to mitigate the inherent texture-dominant bias of pre-trained MLLMs, while enhancing sensitivity to geometric structural degradations. Extensive experiments demonstrate that GT-PCQA achieves competitive performance and exhibits strong generalization.

cs.CV↗
arXiv2026

On Existence of Girth-8 QC-LDPC Code with Large Column Weight: Combining Mirror-sequence with Classification Modulo Ten

Quasi-cyclic (QC) LDPC codes with large girths play a crucial role in several research and application fields, including channel coding, compressed sensing and distributed storage systems. A major challenge in respect of the code construction is how to obtain such codes with the shortest possible length (or equivalently, the smallest possible circulant size) using algebraic methods instead of search methods. The greatest-common-divisor (GCD) framework we previously proposed has algebraically constructed QC-LDPC codes with column weights of 5 and 6, very short lengths, and a girth of 8. By introducing the concept of a mirror sequence and adopting a new row-regrouping scheme, QC-LDPC codes with column weights of 7 and 8, very short lengths, and a girth of 8 are proposed for arbitrary row weights in this article via an algebraic manner under the GCD framework. Thanks to these novel algebraic methods, the lower bounds (for column weights 7 and 8) on consecutive circulant sizes are both improved by asymptotically about 20%, compared with the existing benchmarks. Furthermore, these new constructions can also offer circulant sizes asymptotically about 25% smaller than the novel bounds.

cs.IT↗
arXiv2025

Smooth surface systems may contain smooth curves which have no measure of maximal entropy

In this paper, we study Borel probability measures of maximal entropy for analytic subsets in a dynamical system. It is well known that higher smoothness of the map over smooth space plays important role in the study of invariant measures of maximal entropy. A famous theorem of Newhouse states that smooth diffeomorphisms on compact manifolds without boundary have invariant measures of maximal entropy. However, we show that the situation becomes completely different when we study measures of maximal entropy for analytic subsets. Namely, we construct a smooth surface system which contains a smooth curve having no Borel probability measure of maximal entropy. Another evidence to show this difference is that, once an analytic set has one measure of maximal entropy, then the set has many measures of maximal entropy (no matter if we consider packing or Bowen entropy). For a general dynamical system with positive entropy $h_\mathrm{top}(T)$, we shall show that the system contains not only a Borel subset which has Borel probability measures of maximal entropy and has entropy sufficiently close to $h_\mathrm{top}(T)$, but also a Borel subset which has no Borel probability measures of maximal entropy and has entropy equal to the arbitrarily given positive real number which is at most $h_\mathrm{top}(T)$. We also provide in all $h$-expansive systems a full characterization for analytic subsets which have Borel probability measures of maximal entropy. Consequently, if let $Z\subset \mathbb{R}^n$ be any analytic subset with positive Hausdorff dimension in Euclidean space, then the set $Z$ either has a measure of full lower Hausdorff dimension, or it can be partitioned into a union of countably many analytic sets $\{Z_i\}_{i\in \mathbb{N}}$ with $\dim_{\mathcal{H}}(Z_i) < \dim_{\mathcal{H}}(Z)$ for each $i$.

math.DS↗
arXiv2025

NTIRE 2025 Challenge on Short-form UGC Video Quality Assessment and Enhancement: Methods and Results

This paper presents a review for the NTIRE 2025 Challenge on Short-form UGC Video Quality Assessment and Enhancement. The challenge comprises two tracks: (i) Efficient Video Quality Assessment (KVQ), and (ii) Diffusion-based Image Super-Resolution (KwaiSR). Track 1 aims to advance the development of lightweight and efficient video quality assessment (VQA) models, with an emphasis on eliminating reliance on model ensembles, redundant weights, and other computationally expensive components in the previous IQA/VQA competitions. Track 2 introduces a new short-form UGC dataset tailored for single image super-resolution, i.e., the KwaiSR dataset. It consists of 1,800 synthetically generated S-UGC image pairs and 1,900 real-world S-UGC images, which are split into training, validation, and test sets using a ratio of 8:1:1. The primary objective of the challenge is to drive research that benefits the user experience of short-form UGC platforms such as Kwai and TikTok. This challenge attracted 266 participants and received 18 valid final submissions with corresponding fact sheets, significantly contributing to the progress of short-form UGC VQA and image superresolution. The project is publicly available at https://github.com/lixinustc/KVQE- ChallengeCVPR-NTIRE2025.

eess.IV↗
arXiv2025

Universality of G-subshifts with specification

Let $G$ be an infinite countable amenable group and let $(X,G)$ be a $G$-subshift with specification, containing a free element. We prove that $(X,G)$ is universal, i.e., has positive topological entropy and for any free ergodic $G$-action on a standard probability space, $(Y,ν,G)$, with $h(ν)<h_{top}(X)$, there exists a shift-invariant measure $μ$ on $X$ such that the systems $(Y,ν,G)$ and $(X,μ,G)$ are isomorphic. In particular, any $K$-shift (consisting of the indicator functions of all maximal $K$-separated sets) containing a free element is universal.

math.DS↗
arXiv2024

Short Regular Girth-8 QC-LDPC Codes From Exponent Matrices with Vertical Symmetry

To address the challenge of constructing short girth-8 quasi-cyclic (QC) low-density parity-check (LDPC) codes, a novel construction framework based on vertical symmetry (VS) is proposed. Basic properties of the VS structure are presented. With the aid of these properties, existing explicit constructions for column weights from three to five which can be transformed into the VS structure are sorted out. Then two novel explicit constructions with the VS structure which guarantee short codes are presented for column weights of three and six. Moreover, an efficient search-based method is also proposed to find short codes with the VS structure. Compared with the state-of-the-art benchmarks, both the explicit constructions and the search-based method presented in this paper can provide shorter codes for most cases. Simulation results show that the new shorter codes can perform almost the same as or better than the longer existing counterparts. Thus, the new shorter codes can fit better with the low-latency requirement for modern communication systems.

cs.IT↗
arXiv2023

Multiorders in amenable group actions

The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a~{\em multiorder} on a~countable group we mean any probability measure $ν$ on the collection $\tilde{\mathcal{O}}$ of linear orders of type $\mathbb Z$ on $G$, invariant under the natural action of $G$ on such orders. Every free measure-preserving $G$-action $(X,μ,G)$ has a~multiorder $(\tilde{\mathcal{O}},ν,G)$ as a factor and has the same orbits as the $\mathbb Z$-action $(X,μ,S)$, where $S$ is the \emph{successor map} determined by the multiorder factor. Moreover, the sub-sigma-algebra $Σ_{\tilde{\mathcal{O}}}$ associated with the multiorder factor is invariant under $S$, which makes the corresponding $\mathbb Z$-action $(\tilde{\mathcal{O}},ν,\tilde S)$ a factor of $(X,μ,S)$. We prove that the entropy of any $G$-process generated by a finite partition of $X$, conditional with respect to $Σ_{\tilde{\mathcal{O}}}$, is preserved by the orbit equivalence with $(X,μ,S)$. Furthermore, this entropy can be computed in terms of the so-called random past, by a formula analogous to $ h(μ,T,\mathcal P)=H(μ,\mathcal P|\mathcal{P}^-)$ known for $\mathbb Z$-actions. The above fact is then applied to prove a variant of a result by Rudolph and Weiss. The original theorem states that orbit equivalence between free actions of countable amenable groups preserves conditional entropy with respect to a~sub-sigma-algebra $Σ$, as soon as the ``orbit change'' is measurable with respect to $Σ$. In our variant, we replace the measurability assumption by a~simpler one: $Σ$ should be invariant under both actions and the actions on the resulting factor should be free. In conclusion we provide a characterization of the Pinsker sigma-algebra of any $G$-process in terms of an appropriately defined remote past arising from a multiorder.

math.DS↗
arXiv2021

Quasi-graphs, zero entropy and measures with discrete spectrum

In this paper, we study dynamics of maps on quasi-graphs characterizing their invariant measures. In particular, we prove that every invariant measure of quasi-graph map with zero topological entropy has discrete spectrum. Additionally, we obtain an analog of Llibre-Misiurewicz's result relating positive topological entropy with existence of topological horseshoes. We also study dynamics on dendrites and show that if a continuous map on a dendrite, whose set of all endpoints is closed and has only finitely many accumulation points, has zero topological entropy, then every invariant measure supported on an orbit closure has discrete spectrum.

math.DS↗
arXiv2020

The comparison property of amenable groups

Let a countable amenable group $G$ act on a \zd\ compact metric space $X$. For two clopen subsets $\mathsf A$ and $\mathsf B$ of $X$ we say that $\mathsf A$ is \emph{subequivalent} to $\mathsf B$ (we write $\mathsf A\preccurlyeq \mathsf B$), if there exists a finite partition $\mathsf A=\bigcup_{i=1}^k \mathsf A_i$ of $\mathsf A$ into clopen sets and there are elements $g_1,g_2,\dots,g_k$ in $G$ such that $g_1(\mathsf A_1), g_2(\mathsf A_2),\dots, g_k(\mathsf A_k)$ are disjoint subsets of $\mathsf B$. We say that the action \emph{admits comparison} if for any clopen sets $\mathsf A, \mathsf B$, the condition, that for every $G$-invariant probability measure $μ$ on $X$ we have the sharp inequality $μ(\mathsf A)<μ(\mathsf B)$, implies $\mathsf A\preccurlyeq \mathsf B$. Comparison has many desired consequences for the action, such as the existence of tilings with arbitrarily good Følner properties, which are factors of the action. Also, the theory of symbolic extensions, known for $\mathbb z$-actions, extends to actions which admit comparison. We also study a purely group-theoretic notion of comparison: if every action of $G$ on any zero-dimensional compact metric space admits comparison then we say that $G$ has the \emph{comparison property}. Classical groups $\mathbb z$ and $\mathbb z^d$ enjoy the comparison property, but in the general case the problem remains open. In this paper we prove this property for groups whose every finitely generated subgroup has subexponential growth.

math.DS↗
arXiv2020

Optimal Resource Allocation in Ground Wireless Networks Supporting Unmanned Aerial Vehicle Transmissions

We consider a fully-loaded ground wireless network supporting unmanned aerial vehicle (UAV) transmission services. To enable the overload transmissions to a ground user (GU) and a UAV, two transmission schemes are employed, namely non-orthogonal multiple access (NOMA) and relaying, depending on whether or not the GU and UAV are served simultaneously. Under the assumption of the system operating with infinite blocklength (IBL) codes, the IBL throughputs of both the GU and the UAV are derived under the two schemes. More importantly, we also consider the scenario in which data packets are transmitted via finite blocklength (FBL) codes, i.e., data transmission to both the UAV and the GU is performed under low-latency and high reliability constraints. In this setting, the FBL throughputs are characterized again considering the two schemes of NOMA and relaying. Following the IBL and FBL throughput characterizations, optimal resource allocation designs are subsequently proposed to maximize the UAV throughput while guaranteeing the throughput of the cellular user.Moreover, we prove that the relaying scheme is able to provide transmission service to the UAV while improving the GU's performance, and that the relaying scheme potentially offers a higher throughput to the UAV in the FBL regime than in the IBL regime. On the other hand, the NOMA scheme provides a higher UAV throughput (than relaying) by slightly sacrificing the GU's performance.

cs.IT↗
arXiv2019

Analysis and Optimization of Tail-Biting Spatially Coupled Protograph LDPC Codes for BICM-ID Systems

As a typical example of bandwidth-efficient techniques, bit-interleaved coded modulation with iterative decoding (BICM-ID) provides desirable spectral efficiencies in various wireless communication scenarios. In this paper, we carry out a comprehensive investigation on tail-biting (TB) spatially coupled protograph (SCP) low-density parity-check (LDPC) codes in BICM-ID systems. Specifically, we first develop a two-step design method to formulate a novel type of constellation mappers, referred to as labeling-bit-partial-match (LBPM) constellation mappers, for SC-P-based BICM-ID systems. The LBPM constellation mappers can be seamlessly combined with high-order modulations, such as M-ary phase-shift keying (PSK) and M-ary quadrature amplitude modulation (QAM). Furthermore, we conceive a new bit-level interleaving scheme, referred to as variable node matched mapping (VNMM) scheme, which can substantially exploit the structure feature of SC-P codes and the unequal protection-degree property of labeling bits to trigger the wave-like convergence for TB-SC-P codes. In addition, we propose a hierarchical extrinsic information transfer (EXIT) algorithm to predict the convergence performance (i.e., decoding thresholds) of the proposed SC-P-based BICM-ID systems. Theoretical analyses and simulation results illustrate that the LBPM-mapped SC-P-based BICM-ID systems are remarkably superior to the state-of-the-art mapped counterparts. Moreover, the proposed SC-P-based BICM-ID systems can achieve even better error performance with the aid of the VNMM scheme. As a consequence, the proposed LBPM constellation mappers and VNMM scheme make the SC-P-based BICM-ID systems a favorable choice for the future-generation wireless communication systems.

cs.IT↗
arXiv2019

Discrete spectrum for amenable group actions

In this paper, we study discrete spectrum of invariant measures for countable discrete amenable group actions. We show that an invariant measure has discrete spectrum if and only if it has bounded measure complexity. We also prove that, discrete spectrum can be characterized via measure-theoretic complexity using names of a partition and the Hamming distance, and it turns out to be equivalent to both mean equicontinuity and equicontinuity in the mean.

math.DS↗