arXiv subjects

Zhiqiang Li

Publications and source records attributed to Zhiqiang Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Weak expansion properties and a large deviation principle for coarse expanding conformal systems

Coarse expanding conformal systems were introduced by P. Haïssinsky and K. M. Pilgrim to study the essential dynamical properties of certain rational maps on the Riemann sphere in complex dynamics from the point of view of Sullivan's dictionary. In this paper, we prove that for a metric coarse expanding conformal system $f\colon(\mathfrak{X}_1,X)\rightarrow (\mathfrak{X}_0,X)$ with repellor $X$, the map $f|_X\colon X\rightarrow X$ is asymptotically $h$-expansive. Moreover, we show that $f|_X$ is not $h$-expansive if there exists at least one branch point in the repellor. We also prove that $f|_X$ is forward expansive when there is no branch point in the repellor. Our study of expansion properties does not rely on symbolic codings or Markov partitions, and exploits directly the geometric data. As a consequence of asymptotic $h$-expansiveness, for $f|_X$ and each real-valued continuous potential on $X$, there exists at least one equilibrium state. For such maps, if some additional assumptions are satisfied, we can furthermore establish a level-$2$ large deviation principle for iterated preimages, followed by an equidistribution result.

math.DS↗

arXiv2025

On computability of equilibrium states

Equilibrium states are natural dynamical analogues of Gibbs states in thermodynamic formalism. This paper investigates their computability within the framework of Computable Analysis. We show that the unique equilibrium state for a computable, open, topologically exact, distance-expanding map $T\colon X\rightarrow X$ and a computable Hölder continuous potential $φ\colon X\rightarrow\mathbb{R}$ is always computable. As an application, we establish the computability of equilibrium states for computable hyperbolic rational maps and their respective geometric potentials. Moreover, we develop a constructive method to exhibit the non-uniqueness of equilibrium states for some dynamical systems. We also present some computable dynamical systems whose equilibrium states are all non-computable.

math.DS↗

arXiv2025

Simple smooth modules over the Lie algebras of polynomial vector fields

Let $\mathfrak{g}:={\rm Der}(\mathbb{C}[t_1, t_2,\cdots, t_n])$ and $\mathcal{L}:={\rm Der}(\mathbb{C}[[t_1, t_2,\cdots, t_n]])$ be the Witt Lie algebras. Clearly, $\mathfrak{g}$ is a proper subalegbra of $\mathcal{L}$. Surprisingly, we prove that simple smooth modules over $\mathfrak{g}$ are exactly the simple modules over $\mathcal{L}$ studied by Rodakov (no need to take completion). Then we find an easy and elementary way to classify all simple smooth modules over $\mathfrak{g}$. When the height $\ell_{V}\geq2$ or $n=1$, any nontrivial simple smooth $\mathfrak{g}$-module $V$ is isomorphic to an induced module from a simple smooth $\mathfrak{g}_{\geq0}$-module $V^{(\ell_{V})}$. When $\ell_{V}=1$ and $n\geq2$, any such module $V$ is the unique simple quotient of the tensor module $F(P_{0},M)$ for some simple $\gl_{n}$-module $M$, where $P_0$ is a particular simple module over the Weyl algebra $\mathcal{K}^+_n$. We further show that a simple $\mathfrak{g}$-module $V$ is a smooth module if and only if the action of each of $n$ particular vectors in $\mathfrak{g}$ is locally finite on $V$.

math.RT↗

arXiv2025

EBS-CFL: Efficient and Byzantine-robust Secure Clustered Federated Learning

Despite federated learning (FL)'s potential in collaborative learning, its performance has deteriorated due to the data heterogeneity of distributed users. Recently, clustered federated learning (CFL) has emerged to address this challenge by partitioning users into clusters according to their similarity. However, CFL faces difficulties in training when users are unwilling to share their cluster identities due to privacy concerns. To address these issues, we present an innovative Efficient and Robust Secure Aggregation scheme for CFL, dubbed EBS-CFL. The proposed EBS-CFL supports effectively training CFL while maintaining users' cluster identity confidentially. Moreover, it detects potential poisonous attacks without compromising individual client gradients by discarding negatively correlated gradients and aggregating positively correlated ones using a weighted approach. The server also authenticates correct gradient encoding by clients. EBS-CFL has high efficiency with client-side overhead O(ml + m^2) for communication and O(m^2l) for computation, where m is the number of cluster identities, and l is the gradient size. When m = 1, EBS-CFL's computational efficiency of client is at least O(log n) times better than comparison schemes, where n is the number of clients.In addition, we validate the scheme through extensive experiments. Finally, we theoretically prove the scheme's security.

cs.CR↗

arXiv2025

Learning Unpaired Image Dehazing with Physics-based Rehazy Generation

Overfitting to synthetic training pairs remains a critical challenge in image dehazing, leading to poor generalization capability to real-world scenarios. To address this issue, existing approaches utilize unpaired realistic data for training, employing CycleGAN or contrastive learning frameworks. Despite their progress, these methods often suffer from training instability, resulting in limited dehazing performance. In this paper, we propose a novel training strategy for unpaired image dehazing, termed Rehazy, to improve both dehazing performance and training stability. This strategy explores the consistency of the underlying clean images across hazy images and utilizes hazy-rehazy pairs for effective learning of real haze characteristics. To favorably construct hazy-rehazy pairs, we develop a physics-based rehazy generation pipeline, which is theoretically validated to reliably produce high-quality rehazy images. Additionally, leveraging the rehazy strategy, we introduce a dual-branch framework for dehazing network training, where a clean branch provides a basic dehazing capability in a synthetic manner, and a hazy branch enhances the generalization ability with hazy-rehazy pairs. Moreover, we design a new dehazing network within these branches to improve the efficiency, which progressively restores clean scenes from coarse to fine. Extensive experiments on four benchmarks demonstrate the superior performance of our approach, exceeding the previous state-of-the-art methods by 3.58 dB on the SOTS-Indoor dataset and by 1.85 dB on the SOTS-Outdoor dataset in PSNR. Our code will be publicly available.

cs.CV↗

arXiv2025

Transformers in Protein: A Survey

As protein informatics advances rapidly, the demand for enhanced predictive accuracy, structural analysis, and functional understanding has intensified. Transformer models, as powerful deep learning architectures, have demonstrated unprecedented potential in addressing diverse challenges across protein research. However, a comprehensive review of Transformer applications in this field remains lacking. This paper bridges this gap by surveying over 100 studies, offering an in-depth analysis of practical implementations and research progress of Transformers in protein-related tasks. Our review systematically covers critical domains, including protein structure prediction, function prediction, protein-protein interaction analysis, functional annotation, and drug discovery/target identification. To contextualize these advancements across various protein domains, we adopt a domain-oriented classification system. We first introduce foundational concepts: the Transformer architecture and attention mechanisms, categorize Transformer variants tailored for protein science, and summarize essential protein knowledge. For each research domain, we outline its objectives and background, critically evaluate prior methods and their limitations, and highlight transformative contributions enabled by Transformer models. We also curate and summarize pivotal datasets and open-source code resources to facilitate reproducibility and benchmarking. Finally, we discuss persistent challenges in applying Transformers to protein informatics and propose future research directions. This review aims to provide a consolidated foundation for the synergistic integration of Transformer and protein informatics, fostering further innovation and expanded applications in the field.

cs.LG↗

arXiv2025

Optimizing Personalized Federated Learning through Adaptive Layer-Wise Learning

Real-life deployment of federated Learning (FL) often faces non-IID data, which leads to poor accuracy and slow convergence. Personalized FL (pFL) tackles these issues by tailoring local models to individual data sources and using weighted aggregation methods for client-specific learning. However, existing pFL methods often fail to provide each local model with global knowledge on demand while maintaining low computational overhead. Additionally, local models tend to over-personalize their data during the training process, potentially dropping previously acquired global information. We propose FLAYER, a novel layer-wise learning method for pFL that optimizes local model personalization performance. FLAYER considers the different roles and learning abilities of neural network layers of individual local models. It incorporates global information for each local model as needed to initialize the local model cost-effectively. It then dynamically adjusts learning rates for each layer during local training, optimizing the personalized learning process for each local model while preserving global knowledge. Additionally, to enhance global representation in pFL, FLAYER selectively uploads parameters for global aggregation in a layer-wise manner. We evaluate FLAYER on four representative datasets in computer vision and natural language processing domains. Compared to six state-of-the-art pFL methods, FLAYER improves the inference accuracy, on average, by 5.40\% (up to 14.29\%).

cs.LG↗

arXiv2025

Conformal measures of (anti)holomorphic correspondences

In this paper, we study the existence and properties of conformal measures on limit sets of (anti)holomorphic correspondences. We show that if the critical exponent satisfies $1\leq δ_{\operatorname{crit}}(x) <+\infty,$ the correspondence $F$ is (relatively) hyperbolic on the limit set $Λ_+(x)$, and $Λ_+(x)$ is minimal, then $Λ_+(x)$ admits a non-atomic conformal measure for $F$ and the Hausdorff dimension of $Λ_+(x)$ is strictly less than 2. As a special case, this shows that for a parameter $a$ in the interior of a hyperbolic component of the modular Mandelbrot set, the limit set of the Bullett--Penrose correspondence $F_a$ has a non-atomic conformal measure and its Hausdorff dimension is strictly less than 2. The same results hold for the LLMM correspondences, under some extra assumptions on its defining function $f$.

math.DS↗

arXiv2025

AI-Driven Reinvention of Hydrological Modeling for Accurate Predictions and Interpretation to Transform Earth System Modeling

Traditional equation-driven hydrological models often struggle to accurately predict streamflow in challenging regional Earth systems like the Tibetan Plateau, while hybrid and existing algorithm-driven models face difficulties in interpreting hydrological behaviors. This work introduces HydroTrace, an algorithm-driven, data-agnostic model that substantially outperforms these approaches, achieving a Nash-Sutcliffe Efficiency of 98% and demonstrating strong generalization on unseen data. Moreover, HydroTrace leverages advanced attention mechanisms to capture spatial-temporal variations and feature-specific impacts, enabling the quantification and spatial resolution of streamflow partitioning as well as the interpretation of hydrological behaviors such as glacier-snow-streamflow interactions and monsoon dynamics. Additionally, a large language model (LLM)-based application allows users to easily understand and apply HydroTrace's insights for practical purposes. These advancements position HydroTrace as a transformative tool in hydrological and broader Earth system modeling, offering enhanced prediction accuracy and interpretability.

cs.AI↗

arXiv2025

Gradient polaritonic surface with space-variant switchable light-matter interactions in 2D moire superlattices

Polaritons in two-dimensional (2D) materials provide unique opportunities for controlling light at nanoscales. Tailoring these polaritons via gradient polaritonic surfaces with space-variant response can enable versatile light-matter interaction platforms with advanced functionalities. However, experimental progress has been hampered by the optical losses and poor light confinement of conventionally used artificial nanostructures. Here, we demonstrate natural gradient polaritonic surfaces based on superlattices of solitons-localized structural deformations-in a prototypical moire system, twisted bilayer graphene on boron nitride. We demonstrate on-off switching and continuous modulation of local polariton-soliton interactions, which results from marked modifications of topological and conventional soliton states through variation of local strain direction. Furthermore, we reveal the capability of these structures to spatially modify the near-field profile, phase, and propagation direction of polaritons in record-small footprints, enabling generation and electrical switching of directional polaritons. Our findings open up new avenues toward nanoscale manipulation of light-matter interactions and spatial polariton engineering through gradient moire superlattices.

physics.optics↗

arXiv2024

Ground states and periodic orbits for expanding Thurston maps

Expanding Thurston maps form a class of branched covering maps on the topological $2$-sphere $S^{2}$, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption initially investigated by W. P. Thurston, M. Bonk, D. Meyer, P. Haïssinsky, and K. M. Pilgrim. The measures of maximal entropy and the absolutely continuous invariant measures for these maps have been studied by these authors, and equilibrium states by the first-named author. In this paper, we initiate the investigation on two new classes of invariant measures, namely, the maximizing measures and ground states, and establish the Livšic theorem, a local Anosov closing lemma, and give a positive answer to the Typically Periodic Optimization Conjecture from ergodic optimization for these maps. As an application, we establish these results for Misiurewicz--Thurston rational maps (i.e., postcritically-finite rational maps without periodic critical points) on the Riemann sphere including the Lattès maps with respect to the spherical metric. Our strategy relies on the visual metrics developed by the above authors. In particular, we verify, in a first non-uniformly expanding setting, the Typically Periodic Optimization Conjecture, establishing that for a generic Hölder continuous potential, there exists a unique maximizing measure, moreover, this measure is supported on a periodic orbit, it satisfies the locking property, and it is the unique ground state. The expanding Thurston maps we consider include those that are not topologically conjugate to rational maps; in particular, they can have periodic critical points.

math.DS↗

arXiv2024

Prime orbit theorems for expanding Thurston maps: Lattès maps and split Ruelle operators

We obtain an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, we show that the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In particular, our results apply to postcritically-finite rational maps for which the Julia set is the whole Riemann sphere. Moreover, a stronger result is obtained for Lattès maps.

math.DS↗

arXiv2024

Prime orbit theorems for expanding Thurston maps: Genericity of strong non-integrability condition

In the second paper [LZ24b] of this series, we obtained an analog of the prime number theorem for a class of branched covering maps on the $2$-sphere $S^2$ called expanding Thurston maps, which are topological models of some non-uniformly expanding rational maps without any smoothness or holomorphicity assumption. More precisely, the number of primitive periodic orbits, ordered by a weight on each point induced by a non-constant (eventually) positive real-valued Hölder continuous function on $S^2$ satisfying the $α$-strong non-integrability condition, is asymptotically the same as the well-known logarithmic integral, with an exponential error bound. In this third and last paper of the series, we show that the $α$-strong non-integrability condition is generic in the class of $α$-Hölder continuous functions.

math.DS↗

arXiv2024

Thermodynamic formalism for subsystems of expanding Thurston maps and large deviations asymptotics

Expanding Thurston maps were introduced by M. Bonk and D. Meyer with motivation from complex dynamics and Cannon's conjecture from geometric group theory via Sullivan's dictionary. In this paper, we introduce subsystems of expanding Thurston maps motivated via Sullivan's dictionary as analogs of some subgroups of Kleinian groups. We use thermodynamic formalism to prove the Variational Principle and the existence of equilibrium states for strongly irreducible subsystems and real-valued Hölder continuous potentials. Here, the sphere $S^{2}$ is equipped with a natural metric, called a visual metric, introduced by M. Bonk and D. Meyer. As an application, we establish large deviation asymptotics for expanding Thurston maps.

math.DS↗

arXiv2024

Local optical conductivity of strain solitons in bilayer graphene with arbitrary soliton angle

We theoretically study the electronic band structure and local optical conductivity of domain wall solitons in bilayer graphene (as well as twisted bilayer graphene) with arbitrary soliton angle, which characterizes the local strain direction. We demonstrate that the soliton angle provides an important yet underexplored degree of freedom that can strongly modify the local optical conductivity. The conductivity spectrum features resonance peaks associated with interband transitions involving the topological as well as high-energy soliton states. Two most prominent peaks exhibit continuous suppression and enhancement, respectively, with the soliton angle. The dependence of the peaks on Fermi energy provides important information about the soliton band structure. The local optical conductivity exhibits substantial spatial dependence, which can be used to study the spatial distribution of the soliton states. Furthermore, we show that the conductivity spectra for all soliton angles are broadly tunable by external pressure, which can double the energies of the resonance peaks in experimentally achievable pressure ranges.

cond-mat.mes-hall↗

arXiv2024

Spin-orbit coupling mediated photon-like resonance for a single atom trapped in a symmetric double well

We employ a method involving coherent periodic modulation of Raman laser intensity to induce resonance transitions between energy levels of a spin-orbit coupled atom in a symmetric double-well trap. By integrating photon-assisted tunneling (PAT) technique with spin-orbit coupling (SOC), we achieve resonance transitions between the predefined energy levels of the atom, thereby enabling further precise control of the atom's dynamics. We observe that such photon-like resonance can induce a transition from a localized state to atomic Rabi oscillation between two wells, or effectively reduce tunneling as manifested by a quantum beating phenomenon. Moreover, such resonance transitions have the potential to induce spin flipping in a spin-orbit coupled atom. Additionally, the SOC-mediated transition from multiphoton resonance to fundamental resonance and the SOC-induced resonance suppression are also discovered. In these cases, the analytical results of the effective coupling coefficients of the resonance transition derived from a four-level model can account for the entire dynamics, demonstrating surprisingly good agreement with the numerically exact results based on the realistic continuous model.

quant-ph↗

arXiv2024

SRAS: Self-governed Remote Attestation Scheme for Multi-party Collaboration

Trusted Execution Environments (TEEs), such as Intel Software Guard Extensions (SGX), ensure the confidentiality and integrity of user applications when using cloud computing resources. However, in the multi-party cloud computing scenario, how to select a Relying Party to verify the TEE of each party and avoid leaking sensitive data to each other remains an open question. In this paper, we propose SRAS, an open self-governed remote attestation scheme with attestation and verification functions for verifying the trustworthiness of TEEs and computing assets, achieving decentralized unified trusted attestation and verification platform for multi-party cloud users. In SRAS, we design a Relying Party enclave, which can form a virtual verifiable network, capable of local verification on behalf of other participants relying parties without leaking sensitive data to others. We provide an open-source prototype implementation of SRAS to facilitate the adoption of this technology by cloud users or developers.

cs.CR↗

arXiv2024

Photon-assisted tunneling resonantly controlling spin current of a spin-orbit-coupled atom in a toroidal trap

The periodic flashing potential has proven to be a powerful tool for investigating directed atomic currents. By applying the flashing ring-shaped potential to spin-orbit (SO) coupled, noninteracting Bose-Einstein condensate (BEC) systems, through photon-assisted tunneling (resonance) techniques, we demonstrate the generation of tunable alternating (AC) spin and atomic mass currents that can be precisely controlled in terms of direction and strength. The underlying mechanism behind this phenomenon is that the flashing potential supplies enough photons to induce Rabi oscillations and provides momentum transfer for spin and atomic transport. As the single-particle ground state of the unperturbed SO-coupled BEC depends on the Raman coupling strength, we demonstrate how to generate and control AC spin currents in the cases where the initial state resides in a single-well or double-well phase. In particular, we realize and explain the mechanism of generating a net AC spin current without mass current through single-photon resonance processes. It is shown that these interesting resonance phenomena can be analytically described only by the simple three-level model, which creates the possibility of transparent controls of spin dynamics.

cond-mat.quant-gas↗