arXiv subjects

Chengqing Li

Publications and source records attributed to Chengqing Li.

At least 19 recordsLinked to original sources

arXiv2026

When Do Markets Work? Multiplex Networks and Efficiency

We study an Arrow-Debreu economy with externalities generated by multiplex networks. Market equilibrium prices reflect both the preferences and scarcity of goods, consumers' network centralities arising from goods' externalities, as well as linkages across goods (layers) through the budget constraint. Despite the presence of externalities, competitive markets can still be efficient: the First and Second Welfare Theorems hold if either all networks are regular or all layers share the same network structure. When markets allocate goods inefficiently, a Lindahl equilibrium-implemented through personalized prices-can restore efficiency, but may leave some consumers worse off.

econ.TH↗

arXiv2026

Graph Structure of Chebyshev Permutation Polynomials over Binary and Ternary Adic Rings

Understanding the functional graph of a nonlinear map over a finite domain is crucial for analyzing its dynamical complexity and potential applications in cryptography and pseudorandom generation. In this paper, we investigate the graph structure of Chebyshev permutation polynomials over the ring $\mathbb{Z}_{2^{k_1}3^{k_2}}$, where $k_1$ and $k_2$ are positive integers and $0\in\{k_1, k_2\}$. Each element of the ring is regarded as a vertex, and the mapping relation defined by the polynomial corresponds to a directed edge. Building on new properties of Chebyshev polynomials modulo powers of $2$ and $3$, we provide an explicit characterization of path lengths and cycle structures in the functional graph. We show that, despite the complexities introduced by the binary and ternary components, the graph exhibits strong regularities, including a constant number of cycles of a given length and predictable branching patterns as $k_1$ and $k_2$ increase. Our results extend previous studies over prime-power rings, offering insights into the emergence of complexity in digital nonlinear maps and supporting the security analysis of their cryptographic applications.

cs.CR↗

arXiv2025

IVCR-200K: A Large-Scale Multi-turn Dialogue Benchmark for Interactive Video Corpus Retrieval

In recent years, significant developments have been made in both video retrieval and video moment retrieval tasks, which respectively retrieve complete videos or moments for a given text query. These advancements have greatly improved user satisfaction during the search process. However, previous work has failed to establish meaningful "interaction" between the retrieval system and the user, and its one-way retrieval paradigm can no longer fully meet the personalization and dynamic needs of at least 80.8\% of users. In this paper, we introduce the Interactive Video Corpus Retrieval (IVCR) task, a more realistic setting that enables multi-turn, conversational, and realistic interactions between the user and the retrieval system. To facilitate research on this challenging task, we introduce IVCR-200K, a high-quality, bilingual, multi-turn, conversational, and abstract semantic dataset that supports video retrieval and even moment retrieval. Furthermore, we propose a comprehensive framework based on multi-modal large language models (MLLMs) to help users interact in several modes with more explainable solutions. The extensive experiments demonstrate the effectiveness of our dataset and framework.

cs.CV↗

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

Price Regulation and Network Spillovers

We study price regulation for a monopolist operating in networked markets with demand spillovers. Achieving efficiency requires price reductions proportional to consumers' Katz-Bonacich centralities, which generally cannot be implemented by commonly used price regulations. Moreover, these regulations become asymptotically welfare neutral as spillovers grow. Nevertheless, some price regulations may still benefit consumers. In particular, average-price regulation robustly increases consumer surplus. By contrast, banning price discrimination increases consumer surplus only when more central consumers have higher intrinsic willingness to pay.

econ.TH↗

arXiv2025

The Graph Structure of a Class of Permutation Maps over Ring $\mathbb{Z}_{p^k}$

Understanding the periodic and structural properties of permutation maps over residue rings such as $\mathbb{Z}_{p^k}$ is a foundational challenge in algebraic dynamics and pseudorandom sequence analysis. Despite notable progress in characterizing global periods, a critical bottleneck remains: the lack of explicit tools to analyze local cycle structures and their evolution with increasing arithmetic precision. In this work, we propose a unified analytical framework to systematically derive the distribution of cycle lengths for a class of permutation maps over $\mathbb{Z}_{p^k}$. The approach combines techniques from generating functions, minimal polynomials, and lifting theory to track how the cycle structure adapts as the modulus $p^k$ changes. To validate the generality and effectiveness of our method, we apply it to the well-known Cat map as a canonical example, revealing the exact patterns governing its cycle formation and transition. This analysis not only provides rigorous explanations for experimentally observed regularities in fixed-point implementations of such maps but also lays a theoretical foundation for evaluating the randomness and dynamical behavior of pseudorandom number sequences generated by other nonlinear maps. The results have broad implications for secure system design, computational number theory, and symbolic dynamics.

math.NT↗

arXiv2025

Graph Structure of the Generalized Tent Map over Ring $\mathbb{Z}_{2^e}$

The structure of functional graphs of nonlinear systems provides one of the most intuitive methods for analyzing their properties in digital domain. The generalized Tent map is particularly suitable for studying the degradation of dynamic behaviors in the digital domain due to its significantly varied dynamical behaviors across different parameters in the continuous domain. This paper quantifies the generalized Tent map under various parameters to investigate the dynamic degradation that occurs when implemented in fixed-precision arithmetic. Additionally, the small period problem caused by the indeterminate point in the fixed-point domain is addressed by transforming the parameters. The period of the mapping in the fixed-point domain is optimized by introducing disturbances, resulting in an optimized mapping that is a permutation mapping. Furthermore, the paper reveals the dynamic degradation of analogous one-dimensional maps in fixed-precision domains and provides a more orderly design for this map.

nlin.CD↗

arXiv2024

The Graph Structure of Baker's maps Implemented on a Computer

The complex dynamics of baker's map and its variants in an infinite-precision mathematical domain have been extensively analyzed in the past five decades. However, their real structure implemented in a finite-precision computer remains unclear. This paper gives an explicit formulation for the quantized baker's map and its extension into higher dimensions. Our study reveals certain properties, such as the in-degree distribution in the state-mapping network approaching a constant with increasing precision, and a consistent maximum in-degree across various levels of fixed-point arithmetic precision. We also observe a fractal pattern in baker's map functional graph as precision increases, characterized by fractal dimensions. We then thoroughly examine the structural nuances of functional graphs created by the higher-dimensional baker's map (HDBM) in both fixed-point and floating-point arithmetic domains. An interesting aspect of our study is the use of interval arithmetic to establish a relationship between the HDBM's functional graphs across these two computational domains. A particularly intriguing discovery is the emergence of a semi-fractal pattern within the functional graph of a specific baker's map variant, observed as the precision is incrementally increased. The insights gained from our research offer a foundational understanding for the dynamic analysis and application of baker's map and its variants in various domains.

nlin.CD↗

arXiv2024

Graph Structure of an Inversive Pseudorandom Number Generator over Ring $\mathbb{Z}_{p^{e}}$

Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have been designed as attractive alternatives to those based on the classical linear congruential method. This paper discloses the least period of sequences generated by iterating an inversive pseudorandom number generator over the ring $\mathbb{Z}_e$ by transforming it into a two-order linear congruential recurrence relation. Depending on whether the sequence is periodic or ultimately periodic, all states in the domain can be attributed to two types of objects: some cycles of different lengths and one unilateral connected digraph whose structure remains unchanged concerning parameter $e$. The graph structure of the generator over the ring $\mathbb{Z}_e$ is precisely disclosed with rigorous theoretical analysis and verified experimentally. The adopted analysis methodology can be extended to study the graph structure of other nonlinear maps.

cs.DM↗

arXiv2024

Adjusting Dynamics of Hopfield Neural Network via Time-variant Stimulus

As a paradigmatic model for nonlinear dynamics studies, the Hopfield Neural Network (HNN) demonstrates a high susceptibility to external disturbances owing to its intricate structure. This paper delves into the challenge of modulating HNN dynamics through time-variant stimuli. The effects of adjustments using two distinct types of time-variant stimuli, namely the Weight Matrix Stimulus (WMS) and the State Variable Stimulus (SVS), along with a Constant Stimulus (CS) are reported. The findings reveal that deploying four WMSs enables the HNN to generate either a four-scroll or a coexisting two-scroll attractor. When combined with one SVS, four WMSs can lead to the formation of an eight-scroll or four-scroll attractor, while the integration of four WMSs and multiple SVSs can induce grid-multi-scroll attractors. Moreover, the introduction of a CS and an SVS can significantly disrupt the dynamic behavior of the HNN. Consequently, suitable adjustment methods are crucial for enhancing the network's dynamics, whereas inappropriate applications can lead to the loss of its chaotic characteristics. To empirically validate these enhancement effects, the study employs an FPGA hardware platform. Subsequently, an image encryption scheme is designed to demonstrate the practical application benefits of the dynamically adjusted HNN in secure multimedia communication. This exploration into the dynamic modulation of HNN via time-variant stimuli offers insightful contributions to the advancement of secure communication technologies.

cs.NE↗

arXiv2024

Recovering Sign Bits of DCT Coefficients in Digital Images as an Optimization Problem

Recovering unknown, missing, damaged, distorted, or lost information in DCT coefficients is a common task in multiple applications of digital image processing, including image compression, selective image encryption, and image communication. This paper investigates the recovery of sign bits in DCT coefficients of digital images, by proposing two different approximation methods to solve a mixed integer linear programming (MILP) problem, which is NP-hard in general. One method is a relaxation of the MILP problem to a linear programming (LP) problem, and the other splits the original MILP problem into some smaller MILP problems and an LP problem. We considered how the proposed methods can be applied to JPEG-encoded images and conducted extensive experiments to validate their performances. The experimental results showed that the proposed methods outperformed other existing methods by a substantial margin, both according to objective quality metrics and our subjective evaluation.

cs.CV↗

arXiv2023

Recovering the Block-wise Relationship in an Encryption-Then-Compression System

Joint encryption and compression is an ideal solution for protecting security and privacy of image data in a real scenario, e.g. storing them on an existing cloud-based service like Facebook. Recently, some block-wise encryption-then-compression (ETC) schemes compatible with JPEG were proposed to provide a reasonably high level of security without compromising compression ratio much. This paper investigates recovering the block-wise relationship in an ETC scheme exerting on single-color blocks of size $8\times 8$ in the scenarios of ciphertext-only attack, known-plaintext attack and chosen-plaintext attack. Then, the attacking targets are extended to the other conventional ETC schemes exerting on multiple color channels and blocks of various sizes. Especially, an elaborate jigsaw puzzle solver is designed to recover enough visual information from multiple cipher-images encrypted by the same secret key. Moreover, the nice attacking performance was verified over two social media platforms, Facebook and Weibo.

cs.CR↗

arXiv2023

Periodicity Analysis of the Logistic Map over Ring $\mathbb{Z}_{3^n}$

Periodicity analysis of sequences generated by a deterministic system is a long-standing challenge in both theoretical research and engineering applications. To overcome the inevitable degradation of the Logistic map on a finite-precision circuit, its numerical domain is commonly converted from a real number field to a ring or a finite field. This paper studies the period of sequences generated by iterating the Logistic map over ring $\mathbb{Z}_{3^n}$ from the perspective of its associate functional network, where every number in the ring is considered as a node, and the existing mapping relation between any two nodes is regarded as a directed edge. The complete explicit form of the period of the sequences starting from any initial value is given theoretically and verified experimentally. Moreover, conditions on the control parameter and initial value are derived, ensuring the corresponding sequences to achieve the maximum period over the ring. The results can be used as ground truth for dynamical analysis and cryptographical applications of the Logistic map over various domains.

cs.IT↗

arXiv2022

Few-shot Fine-grained Image Classification via Multi-Frequency Neighborhood and Double-cross Modulation

Traditional fine-grained image classification typically relies on large-scale training samples with annotated ground-truth. However, some sub-categories have few available samples in real-world applications, and current few-shot models still have difficulty in distinguishing subtle differences among fine-grained categories. To solve this challenge, we propose a novel few-shot fine-grained image classification network (FicNet) using multi-frequency neighborhood (MFN) and double-cross modulation (DCM). MFN focuses on both spatial domain and frequency domain to capture multi-frequency structural representations, which reduces the influence of appearance and background changes to the intra-class distance. DCM consists of bi-crisscross component and double 3D cross-attention component. It modulates the representations by considering global context information and inter-class relationship respectively, which enables the support and query samples respond to the same parts and accurately identify the subtle inter-class differences. The comprehensive experiments on three fine-grained benchmark datasets for two few-shot tasks verify that FicNet has excellent performance compared to the state-of-the-art methods. Especially, the experiments on two datasets, "Caltech-UCSD Birds" and "Stanford Cars", can obtain classification accuracy 93.17\% and 95.36\%, respectively. They are even higher than that the general fine-grained image classification methods can achieve.

cs.CV↗

arXiv2022

The Graph Structure of Chebyshev Permutation Polynomials over Ring $\mathbb{Z}_{p^k}$

Understanding the underlying graph structure of a nonlinear map over a particular domain is essential in evaluating its potential for real applications. In this paper, we investigate the structure of the associated \textit{functional graph} of Chebyshev permutation polynomials over a ring $\mathbb{Z}_{p^k}$, with $p$ being a prime number greater than three, where every number in the ring is considered as a vertex and the existing mapping relation between two vertices is regarded as a directed edge. Based on some new properties of Chebyshev polynomials and their derivatives, we disclose how the basic structure of the functional graph evolves with respect to parameter $k$. First, we present a complete and explicit form of the length of a path starting from any given vertex. Then, we show that the strong patterns of the functional graph that the number of cycles of any given length always remains constant as $k$ increases. Moreover, we rigorously prove the rules on the elegant structure of the functional graph and verify them experimentally. Our results could be useful for studying the emergence of the complexity of a nonlinear map in digital computers and security analysis of its cryptographic applications.

nlin.CD↗

arXiv2022

Cryptanalyzing an Image Encryption Algorithm Underpinned by 2D Lag-Complex Logistic Map

This paper analyzes security performance of an image encryption algorithm using 2D lag-complex Logistic map (LCLM), which adopts it as a pseudo-random number generator, and uses the sum of all pixel values of the plain-image as its initial value to control the random combination of the basic encryption operations. However, multiple factors make the final pseudo-random sequences controlling the encryption process may be the same for different plain-images. Based on this point, we proposed a chosen-plaintext attack by attacking the six encryption steps with a strategy of divide and conquer. Using the pitfalls of 2D-LCLM, the number of required chosen plain-images is further reduced to $5\cdot\log_2(MN)+95$, where $\mathit{MN}$ is the number of pixels of the plain-image.

cs.CR↗

arXiv2022

Multi-Channel Deep Networks for Block-Based Image Compressive Sensing

Incorporating deep neural networks in image compressive sensing (CS) receives intensive attentions in multimedia technology and applications recently. As deep network approaches learn the inverse mapping directly from the CS measurements, the reconstruction speed is significantly faster than the conventional CS algorithms. However, for existing network based approaches, a CS sampling procedure has to map a separate network model. This may potentially degrade the performance of image CS with block-wise sampling because of blocking artifacts, especially when multiple sampling rates are assigned to different blocks within an image. In this paper, we develop a multichannel deep network for block-based image CS by exploiting inter-block correlation with performance significantly exceeding the current state-of-the-art methods. The significant performance improvement is attributed to block-wise approximation but full image removal of blocking artifacts. Specifically, with our multichannel structure, the image blocks with a variety of sampling rates can be reconstructed in a single model. The initially reconstructed blocks are then capable of being reassembled into a full image to improve the recovered images by unrolling a hand-designed block based CS recovery algorithm. Experimental results demonstrate that the proposed method outperforms the state-of-the-art CS methods by a large margin in terms of objective metrics and subjective visual image quality. Our source codes are available at https://github.com/siwangzhou/DeepBCS.

eess.IV↗

arXiv2022

Security measurement of a medical communication scheme based on chaos and DNA coding

To encrypt sensitive information existing in a color DICOM images, a medical privacy protection scheme (called as MPPS) based on chaos and DNA coding was proposed by using two coupled chaotic systems to produce cryptographic primitives. Relying on some empirical analyses and experimental results, the designers of MPPS claimed that it can withstand a chosen-plaintext attack and some other classic attacking models. However, this statement is groundless. In this paper, we investigate the essential properties of MPPS and DNA coding, and we then propose an efficient chosen-plaintext attack to disclose its equivalent secret-key. The attack only needs $\lceil \log_{256}(3\cdot M\cdot N)\rceil+4$ pair of chosen plain-images and the corresponding cipher-images, where $M \times N$ and ``3" are the size of the RGB color image and the number of color channels, respectively. In addition, the other claimed superiorities are questioned from the perspective of modern cryptography. Both theoretical and experimental results are presented to support the efficiency of the proposed attack and the other reported security faults. The proposed cryptanalysis results will promote the proper application of DNA encoding to protect multimedia privacy data, especially that in a DICOM image.

cs.CR↗