Special Session 42: High-order complex systems structure and modeling

On Poles and Zeros of Linear Quantum Systems

Zhiyuan Dong Harbin Institute of Technology, Shenzhen Peoples Rep of China Co-Author(s):    Guofeng Zhang, Heung-wing Joseph Lee

Abstract: The non-commutative nature of quantum mechanics imposes fundamental constraints on system dynamics, which in the linear realm are manifested by the physical realizability conditions on system matrices. These restrictions endow system matrices with special structure. The purpose of this paper is to study such structure by investigating zeros and poses of linear quantum systems. In particular, we show that $-s_0^\ast$ is a transmission zero if and only if $s_0$ is a pole, and which is further generalized to the relationship between system eigenvalues and invariant zeros. Additionally, we study left-invertibility and fundamental tradeoff for linear quantum systems in terms of their zeros and poles.

Complex network-based information fusion theory and its applications

Zhongke Gao Tianjin University Peoples Rep of China Co-Author(s):    Xinlin Sun, Gavin Gao, Mengyu Li, Zhongke Gao

Abstract: Multi-source information fusion is a multidisciplinary research field. Complex network-based information fusion explores the evolutionary relationships between units within the complex systems, providing a fresh perspective for real complex system analysis through the lens of topological dynamics. This report mainly introduces the development and application of this theory in two typical complex scenarios: the petroleum industry and human-machine hybrid intelligence. In the petroleum industry, by integrating multi-source sensor information through complex network, the challenges of high water cut, high gas void fraction, and non-steady-state flow in oil well output fluids are addressed. This technology enables effective monitoring of oil well output status, aiding in reservoir management and enhancing oil recovery rates. In the human-machine hybrid intelligence scenario, the focus is on tasks such as fatigue monitoring, emotional computing, and motor imagery rehabilitation. By constructing brain functional networks to integrate multi-source physiological data, the brain`s cognitive differences under various tasks are analyzed from a topological perspective, leading to more accurate and efficient brain state decoding. These advancements have been implemented in several tertiary hospitals.

Chinese Font Generation Algorithm Integrating Coordinate and Channel and Spatial Attention

Xiaoqi Guo Dalian Minzu University Peoples Rep of China Co-Author(s):    Cunrui Wang, Yu Liu, Guodong Zhan

Abstract: This paper proposes a Chinese font generation algorithm that addresses common issues in existing methods, including structural imbalance, stroke errors, and character blending. The proposed algorithm integrates Coordinate Attention (CA) with the Convolutional Block Attention Module (CBAM). To mitigate structural imbalance, CA is utilized to incorporate positional information into channel features, generating direction-aware and position-sensitive attention maps that enhance the stability of font structures. To address stroke errors and character blending, the CBAM module is introduced to improve the generator`s focus on stylistic features while preserving critical information such as glyph style, structure, and stroke details, and suppressing noise and irrelevant data. The CA and CBAM attention mechanisms are combined within a Generative Adversarial Network (GAN). Experiments were conducted using four types of Hanyi character databases, each with 6763 samples. The proposed algorithm was compared with Pix2pix, CycleGAN, Zi2zi, MX-Font and DG-Font. The experimental results indicate that the proposed method outperforms existing approaches in terms of structural stability and stroke detail style, with improvements observed in PSNR, SSIM, and LPIPS metrics.

Variable Convergence Rate Control of Nonlinear Impulsive Systems: A Fully Actuated System Approach

Xuefang Li Sun Yat-sen University Peoples Rep of China Co-Author(s):    Yuanen Li, Xuefang Li, Wanquan Liu, Xiao-Dong Li

Abstract: This paper investigates the variable convergence rate stability of nonlinear impulsive systems utilising the fully actuated system (FAS) method. Different from most of the existing methods, this work eliminates the nonlinearities by using the full-actuation property of the system, based on which the idea of generalized pole assignment is employed to ensure the convergence of the target system with regulable convergence rate. According to the definition of global exponential stability, a variable convergence rate stability theorem for nonlinear impulsive systems is given using the FAS approach. Finally, the validity and feasibility of the method are verified by numerical simulations of a single-link flexible joint robotic system.

A Large-Population Stochastic Differential Game with Terminal State Constraint and Common Noise

Shujun Wang Shandong University Peoples Rep of China Co-Author(s):    Pengyan HUANG, Guangchen WANG

Abstract: In this paper, we focus on a type of linear-quadratic (LQ) mean-field game of stochastic differential equation (SDE) with terminal state constraint and common noise, where a coupling structure enters state equation, cost functional and constraint condition. First, by virtue of mean-field method, we introduce an auxiliary problem of the original game, which is a constrained optimal control problem. Second, by virtue of Lagrangian multiplier method and stochastic maximum principle, a decentralized control strategy depending on the optimal Lagrangian multiplier is derived. Finally, we prove that the decentralized control strategy obtained is an $\epsilon$-Nash equilibrium of the LQ mean-field game. As an application, we solve a financial problem and give some numerical results.

The SIQRS propagation model with quarantine on simplicial complexes

Chengyi Xia Tiangong University Peoples Rep of China Co-Author(s):    Jiaxing Chen

Abstract: Simplicial complexes successfully resolve the limitation of social networks to describe the spread of infectious diseases in group interactions. However, the effects of quarantines in the context of group interactions remain largely unaddressed. In this paper, we therefore propose a SIQRS model with quarantines and study its evolution on simplicial complexes. In the model, a fraction of infected individuals is subject to quarantine, but individuals leaving quarantine may still be contagious. Using mean-field methods, we derive the propagation threshold and the steady-state infection densities as well as conditions for their stability. Numerical simulations moreover show that longer quarantine times and higher quarantine ratios tend to disrupt discontinuous phase transition and bistable phenomena that are commonly due to group interactions. Additionally, when epidemic outbreaks are recurrent, although quarantine measures can reduce the peak of the first wave and delay the onset of future waves, they may also lead to an increase in subsequent peak infected densities. This highlights the need to prepare sufficient resources to deal with periodic infections after the initial wave is over.

Higher-order Community Detection by Motif-based Modularity Optimization

Xiaoke Xu Beijing Normal University Peoples Rep of China Co-Author(s):    Ye Wu, Lun Zhang, and Zengru Di

Abstract: Recently higher-order community detection based on network motifs has received increasing attention, because motif-based communities reflect not only mesoscale structures but also functional characteristics of real-life networks. In this study, we propose a Modularity Optimization method for Motif-based Community Detection (MOMCD). In order to approximate the global optimum in modularity optimization, an improved nature-inspired metaheuristic algorithm is proposed as optimization strategy. In addition, by comprehensively utilizing motif-based (higher-order) and edge-based (lower-order) structural information, a neighbor community modification operation and a local search operation are also designed to improve the quality of individuals and promote the convergence of MOMCD. Experimental results show that MOMCD is promising and competitive in identifying motif-based communities from synthetic and real-life networks, which outperforms state-of-the-art approaches in terms of quality and accuracy, and deepens our understanding of network structural and functional characteristics.

A higher-order dynamical model based on simplicial complexes

Yi Zhao Harbin Institute of Technology, Shenzhen Peoples Rep of China Co-Author(s):

Abstract: The introduction of higher-order structures results in two significant changes in propagation dynamics: non-linear effects and discontinuous mechanisms. Non-linearity arises because group behaviors exhibit emergent properties that are not merely the sum of individual actions. Discontinuity refers to abrupt changes in system dynamics, where minor perturbations can lead to large-scale shifts in behavior, especially when critical thresholds are crossed. To address these complex dynamics, this report develops a higher-order dynamical model based on simplicial complexes. Simplicial complexes allow for the representation of multi-body interactions, extending the modeling framework beyond traditional graph-based approaches. This model captures the non-linear propagation dynamics observed in complex systems and provides insights into how these interactions influence the overall spread of phenomena across networks. Additionally, to manage the discontinuous nature of higher-order interactions, the report proposes a threshold-based control model using differential complementarity systems. This model is designed to describe the discontinuous behaviors emerging from higher-order interactions, enabling the evaluation of intervention strategies aimed at controlling the spread. By incorporating threshold dynamics, the model can assess the effectiveness of various control measures and optimize intervention strategies.

Synchronization of a high-dimensional Kuramoto model with nonidentical oscillators

Jiandong Zhu Nanjing Normal University Peoples Rep of China Co-Author(s):

Abstract: For a high-dimensional Kuramoto model with nonidentical oscillators, a necessary and sufficient condition for complete phase synchronization is presented. Matrix differential equations describing the synchronisation errors are constructed for commutative oscillators and a class of non-commutative oscillators, respectively. Exponential synchronization and the exponential synchronization rate are obtained.structed. Exponential synchronization and the exponential synchronization rate are achieved.

Prescribed-time stabilization of a class of nonlinear systems based on fully actuated system approach

Yingqi Zhu Harbin Institute of Technology, Shenzhen Peoples Rep of China Co-Author(s):    Zhiyuan Dong,Yuzhong wang

Abstract: This article investigates the prescribed-time control problem for a class of nonlinear systems with disturbances. Using general backstepping and state scaling techniques to deal with high-order systems with disturbances may lead to differential explosion and complicate stability analysis. To avoid these problems, this paper proposes a prescribed-time control scheme based on fully actuated system (FAS) approach. Transform the nonlinear system into FAS with disturbances, giving the system a more concise structure, and then use a state scaling function to transform the original system state. Using strictly bounded robust controllers to achieve asymptotic stability of new FAS with amplified disturbances, thereby achieving prescribed-time stability of the original system. Finally, the effectiveness of the algorithm was verified through numerical examples.