arXiv subjects

Aming Li

Publications and source records attributed to Aming Li.

At least 19 recordsLinked to original sources

arXiv2026

Evolution of cooperation with temporal information

Strategy learning governs the evolution of collective cooperation in multi-agent systems. Although evolutionary outcomes depend strongly on the information available to agents during strategy learning, most studies treat both the source and amount of that information as fixed over time. In reality, however, individuals are continually exposed to external information that varies over time. Here we develop a general framework for evolutionary dynamics with temporal information, which uses temporal networks to characterize dynamic changes in information available for strategy learning, with time-varying connections determining each agent's information state. Across synthetic and empirical networks, we find that temporal information consistently promotes cooperation relative to their static counterparts. We further demonstrate that this advantage becomes more pronounced as temporal networks become sparser. This pattern arises because sparsification amplifies information heterogeneity among agents, creating unequal access to learning information that can facilitate the spread of cooperative strategies, in sharp contrast to static information formulations where heterogeneity often suppresses cooperation. Guided by this insight, we develop an interpretable algorithm that substantially enhances cooperation across diverse networks by generating learning networks with tunable heterogeneity. Our results identify temporal information as a realistic and broadly applicable mechanism for promoting collective cooperation.

physics.soc-ph↗

arXiv2026

On Diagonalizable Systems with Random Structure

Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its free entries, are diagonalizable. Structural diagonalizability is useful for the verification and optimization of various structural system properties. In this paper, we study the asymptotic probability distribution of structural diagonalizability for structured systems whose system matrices are represented by directed Erd\H{o}s-R\'{e}nyi random graphs. Leveraging a recently established graph-theoretic characterization of structural diagonalizability, we analyze the distribution of structurally diagonalizable graphs under different edge-density regimes. For dense graphs, we prove that the system is almost always structurally diagonalizable. For graphs of medium density, we derive tight upper and lower bounds on the asymptotic probability of structural diagonalizability. For extremely sparse graphs, we show that this probability approaches 0. The theoretical results are validated through extensive numerical simulations with varying numbers of vertices and connection probabilities.

math.OC↗

arXiv2025

Data-driven functional state estimation of complex networks

The internal state of a dynamical system, a set of variables that defines its evolving configuration, is often hidden and cannot be fully measured, posing a central challenge for real-time monitoring and control. While observers are designed to estimate these latent states from sensor outputs, their classical designs rely on precise system models, which are often unattainable for complex network systems. Here, we introduce a data-driven framework for estimating a targeted set of state variables, known as functional observers, without identifying the model parameters. We establish a fundamental functional observability criterion based on historical trajectories that guarantees the existence of such observers. We then develop methods to construct observers using either input-output data or partial state data. These observers match or exceed the performance of model-based counterparts while remaining applicable even to unobservable systems. The framework incorporates noise mitigation and can be easily extended to nonlinear networks via Koopman embeddings. We demonstrate its broad utility through applications including sensor fault detection in water networks, load-frequency control in power grids, and target estimation in nonlinear neuronal systems. Our work provides a practical route for real-time target state inference in complex systems where models are unavailable.

eess.SY↗

arXiv2025

Modeling and Topology Estimation of Low Rank Dynamical Networks

Conventional topology learning methods for dynamical networks become inapplicable to processes exhibiting low-rank characteristics. To address this, we propose the low rank dynamical network model which ensures identifiability. By employing causal Wiener filtering, we establish a necessary and sufficient condition that links the sparsity pattern of the filter to conditional Granger causality. Building on this theoretical result, we develop a consistent method for estimating all network edges. Simulation results demonstrate the parsimony of the proposed framework and consistency of the topology estimation approach.

cs.GR↗

arXiv2025

Stability of complex communities: A perspective from discrete-time dynamics

Understanding the stability of complex communities is a central focus in ecology, many important theoretical advancements have been made to identify drivers of ecological stability. However, previous results often rely on the continuous-time dynamics, assuming that species have overlapping generations. In contrast, numerous real-world communities consist of species with non-overlapping generations, whose quantitative behavior can only be precisely represented by discrete-time dynamics rather than continuous ones. Here, we develop a theoretical framework and propose a metric to quantify the stability of complex communities characterized by non-overlapping generations and diverse interaction types. In stark contrast to existing results for overlapping generations, we find that increasing self-regulation strength first stabilizes and then destabilizes complex communities. This pattern is further confirmed in both exploitative (E. aerogenes, P. aurantiaca, P. chlororaphis, P. citronellolis) and competitive (P. putida, P. veroni, S. marcescens) soil microbial communities. Moreover, we show that communities with diverse interaction types become the most stable, which is corroborated by empirical mouse microbial networks. Furthermore, we reveal that the prevalence of weak interactions can stabilize communities, which is consistent with findings from existing microbial experiments. Our analyses of complex communities with non-overlapping generations provide a more comprehensive understanding of ecological stability and informs practical strategies for ecological restoration and control.

q-bio.PE↗

arXiv2025

Personalised strategy of allocating social goods in structured populations

Cooperation underlies many aspects of the evolution of human and animal societies, where cooperators produce social goods to benefit others. Explaining the emergence of cooperation among selfish individuals has become a major research interest in evolutionary dynamics. Previous studies typically use complex networks to capture the interactions between individuals, and assume that cooperators distribute benefits equally to their neighbors. In practice, the distribution of social goods is often non-uniform, and individuals may selectively provide benefits to those they interact with based on their personal preferences. Here, we develop an efficient algorithm to optimize the placement of donation structure in any given network to minimize the threshold for the emergence of cooperation. We find when cooperators allocate the benefits preferentially compared to the traditional settings of donating to all neighbors, cooperation tends to be maximally promoted. Furthermore, the optimal donation structure is strongly disassortative -- the low-degree nodes tend to donate to high-degree ones preferentially and vice versa. Based on this finding, we offer a local heuristic strategy based on degree thresholds for personalizing the allocation of social goods and choosing each cooperator's recipient, which we use to prove its effectiveness in empirical datasets. Our findings advance the understanding of mechanisms for promoting cooperation with strategic allocations of social goods.

physics.soc-ph↗

arXiv2025

Transformability reveals the interplay of dynamics across different network orders

Recent studies have investigated various dynamic processes characterizing collective behaviors in real-world systems. However, these dynamics have been studied individually in specific contexts. In this article, we present a holistic analysis framework that bridges the interplays between dynamics across networks of different orders, demonstrating that these processes are not independent but can undergo systematic transformations. Focusing on contagion dynamics, we identify and quantify dynamical and structural factors that explains the interplay between dynamics on higher-order and pairwise networks, uncovering a universal model for system instability governed by these factors. Furthermore, we validate the findings from contagion dynamics to opinion dynamics, highlighting its broader applicability across diverse dynamical processes. Our findings reveal the intrinsic coupling between diverse dynamical processes, providing fresh insights into the distinct role of complex dynamics governed by higher-order interactions.

physics.app-ph↗

arXiv2025

Convergence of time-delayed opinion dynamics with complex interaction types

In opinion dynamics, time delays in agent-to-agent interactions are ubiquitous, which can substantially disrupt the dynamical processes rooted in agents' opinion exchange, decision-making, and feedback mechanisms. However, a thorough comprehension of quantitative impacts of time delays on the opinion evolution, considering diverse interaction types and system dynamics, remains absent. In this paper, we conduct a systematic investigation into the convergence and the associated rate of time-delayed opinion dynamics with diverse interaction types in both discrete-time and continuous-time systems. For the discrete-time system, we commence by establishing sufficient conditions for its convergence on arbitrary signed interaction networks. These conditions show that the convergence is determined solely by the topology of the interaction network and remains impervious to the magnitude of the time delay. Subsequently, we examine the influence of random and other interaction types on the convergence rate and discover that time delays tend to decelerate this rate. Regarding the continuous-time system, we derive the feasible domain of the delay that ensures the convergence of opinion dynamics, revealing that, unlike the discrete-time scenarios, large time delays can instigate the divergence of opinions. Specifically, we prove that for both random and other interaction types, small delays can expedite the convergence of continuous-time system. Finally, we present simulation examples to demonstrate the effectiveness and robustness of our research findings.

math.OC↗

arXiv2025

ARMAX identification of low rank graphical models

In large-scale systems, complex internal relationships are often present. Such interconnected systems can be effectively described by low rank stochastic processes. When identifying a predictive model of low rank processes from sampling data, the rank-deficient property of spectral densities is often obscured by the inevitable measurement noise in practice. However, existing low rank identification approaches often did not take noise into explicit consideration, leading to non-negligible inaccuracies even under weak noise. In this paper, we address the identification issue of low rank processes under measurement noise. We find that the noisy measurement model admits a sparse plus low rank structure in latent-variable graphical models. Specifically, we first decompose the problem into a maximum entropy covariance extension problem, and a low rank graphical estimation problem based on an autoregressive moving-average with exogenous input (ARMAX) model. To identify the ARMAX low rank graphical models, we propose an estimation approach based on maximum likelihood. The identifiability and consistency of this approach are proven under certain conditions. Simulation results confirm the reliable performance of the entire algorithm in both the parameter estimation and noisy data filtering.

cs.LG↗

arXiv2025

Evolutionary game dynamics for higher-order interactions

Cooperative behaviors are deeply embedded in structured biological and social systems. Networks are often employed to portray pairwise interactions among individuals, where network nodes represent individuals and links indicate who interacts with whom. However, it is increasingly recognized that many empirical interactions often involve triple or more individuals instead of the massively oversimplified lower-order pairwise interactions, highlighting the fundamental gap in understanding the evolution of collective cooperation for higher-order interactions with diverse scales of the number of individuals. Here, we develop a theoretical framework of evolutionary game dynamics for systematically analyzing how cooperation evolves and fixates under higher-order interactions. Specifically, we offer a simple condition under which cooperation is favored under arbitrary combinations of different orders of interactions. Compared to pairwise interactions, our findings suggest that higher-order interactions enable lower thresholds for the emergence of cooperation. Surprisingly, we show that higher-order interactions favor the evolution of cooperation in large-scale systems, which is the opposite for lower-order scenarios. Our results offer a new avenue for understanding the evolution of collective cooperation in empirical systems with higher-order interactions.

physics.soc-ph↗

arXiv2024

Promoting collective intelligence: The advantage of temporal star-structures

System structures play an essential role in the emergence of collective intelligence in many natural and engineering systems. In empirical systems, interactions among multiple agents may change over time, forming a temporal network structure, where nodes represent the system's components and links capture who interacts with whom. Recent studies report that temporal networks are more conducive to the emergence of collective cooperation compared to their aggregated static structures. However, the question of which kind of structural characteristics of temporal networks promote collective cooperation still remains elusive. Here we systematically investigate the evolution of cooperation on temporal networks with diverse structural characteristics, such as random, star, and cluster structures. We uncover that temporal networks with single-star structures which lack network clusters are more conducive to collective cooperation than other structures. This counterintuitive result cautions against the common belief that network clusters normally facilitate collective cooperation, revealing the unique advantages of temporal networks over static networks. We further propose an index to quantify the capacity of structural characteristics of temporal networks in promoting collective cooperation. Our findings pave the way for designing the optimal structure of temporal networks to favour collective cooperation.

physics.soc-ph↗

arXiv2024

Convergence rate of opinion dynamics with complex interaction types

The convergence rate is a crucial issue in opinion dynamics, which characterizes how quickly opinions reach a consensus and tells when the collective behavior can be formed. However, the key factors that determine the convergence rate of opinions are elusive, especially when individuals interact with complex interaction types such as friend/foe, ally/adversary, or trust/mistrust. In this paper, using random matrix theory and low-rank perturbation theory, we present a new body of theory to comprehensively study the convergence rate of opinion dynamics. First, we divide the complex interaction types into five typical scenarios: mutual trust $(+/+)$, mutual mistrust $(-/-)$, trust$/$mistrust $(+/-)$, unilateral trust $(+/0)$, and unilateral mistrust $(-/0)$. For diverse interaction types, we derive the mathematical expression of the convergence rate, and further establish the direct connection between the convergence rate and population size, the density of interactions (network connectivity), and individuals' self-confidence level. Second, taking advantage of these connections, we prove that for the $(+/+)$, $(+/-)$, $(+/0)$, and random mixture of different interaction types, the convergence rate is proportional to the population size and network connectivity, while it is inversely proportional to the individuals' self-confidence level. However, for the $(-/-)$ and $(-/0)$ scenarios, we draw the exact opposite conclusions. Third, for the $(+/+,-/-)$ and $(-/-,-/0)$ scenarios, we derive the optimal proportion of different interaction types to ensure the fast convergence of opinions. Finally, simulation examples are provided to illustrate the effectiveness and robustness of our theoretical findings.

math.OC↗

arXiv2024

Dominant strategy in repeated games on networks

Direct reciprocity, stemming from repeated interactions among players, is one of the fundamental mechanisms for understanding the evolution of cooperation. However, canonical strategies for the repeated prisoner's dilemma, such as Win-Stay-Lose-Shift and Tit-for-Tat, fail to consistently dominate alternative strategies during evolution. This complexity intensifies with the introduction of spatial structure or network behind individual interactions, where nodes represent players and edges represent their interactions. Here, we propose a new strategy, ``Cooperate-Stay-Defect-Tolerate" (CSDT), which can dominate other strategies within networked populations by adhering to three essential characteristics. This strategy maintains current behaviour when the opponent cooperates and tolerates defection to a limited extent when the opponent defects. We demonstrate that the limit of tolerance of CSDT can vary with the network structure, evolutionary dynamics, and game payoffs. Furthermore, we find that incorporating the Always Defect strategy (ALLD) can enhance the evolution of CSDT and eliminate strategies that are vulnerable to defection in the population, providing a new interpretation of the role of ALLD in direct reciprocity. Our findings offer a novel perspective on how cooperative strategy evolves on networked populations.

physics.soc-ph↗

arXiv2024

Promoting collective cooperation through temporal interactions

Collective cooperation drives the dynamics of many natural, social, and economic phenomena, making understanding the evolution of cooperation with evolutionary game theory a central question of modern science. Although human interactions are best described as complex networks, current explorations are limited to static networks where interactions represented by network links are permanent and do not change over time. In reality, human activities often involve temporal interactions, where links are impermanent, and understanding the evolution of cooperation on such ubiquitous temporal networks is an open question. Here, we present a general framework for systematically analyzing how collective cooperation evolves on any temporal network, which unifies the study of evolutionary game dynamics with dynamic and static interactions. We show that the emergence of cooperation is facilitated by a simple rule of thumb: hubs (individuals with many social ties) should be temporally deprioritized in interactions. We further provide a quantitative metric capturing the priority of hubs, which we utilize to orchestrate the ordering of interactions to best promote cooperation on empirical temporal networks. Our findings unveil the fundamental advantages conferred by temporal interactions for promoting collective cooperation, which transcends the specific insights gleaned from studying traditional static snapshots.

physics.soc-ph↗

arXiv2023

Temporal networks provide a unifying understanding of the evolution of cooperation

Understanding the evolution of cooperation in structured populations represented by networks is a problem of long research interest, and a most fundamental and widespread property of social networks related to cooperation phenomena is that the node's degree (i.e., number of edges connected to the node) is heterogeneously distributed. Previous results indicate that static heterogeneous (i.e., degree-heterogeneous) networks promote cooperation in stationarity compared to static regular (i.e., degree-homogeneous) networks if equilibrium dynamics starting from many cooperators and defectors is employed. However, the above conclusion reverses if we employ non-equilibrium stochastic processes to measure the fixation probability for cooperation, i.e., the probability that a single cooperator successfully invades a population. Here we resolve this conundrum by analyzing the fixation of cooperation on temporal (i.e., time-varying) networks. We theoretically prove and numerically confirm that on both synthetic and empirical networks, contrary to the case of static networks, temporal heterogeneous networks can promote cooperation more than temporal regular networks in terms of the fixation probability of cooperation. Given that the same conclusion is known for the equilibrium fraction of cooperators on temporal networks, the present results provide a unified understanding of the effect of temporal degree heterogeneity on promoting cooperation across two main analytical frameworks, i.e., equilibrium and non-equilibrium ones.

physics.soc-ph↗

arXiv2023

Generalized Cactus and Structural Controllability of Switched Linear Continuous-Time Systems

This paper explores the structural controllability of switched linear continuous-time systems. It first identifies a gap in the proof for a pivotal criterion for the structural controllability of switched linear systems in the literature. To address this void, we develop novel graph-theoretic concepts, such as multi-layer dynamic graphs, generalized stems/buds, and generalized cacti, and based on them, provide a comprehensive proof for this criterion. Our approach also induces a new, generalized cactus based graph-theoretic criterion for structural controllability. This not only extends Lin's cactus-based graph-theoretic condition to switched systems for the first time, but also provides a lower bound for the generic dimension of controllable subspaces.

eess.SY↗

arXiv2023

Doubly heterogeneous networks facilitate the emergence of collective cooperation

There is growing recognition that the network structures arising from interactions between different entities in physical, social and biological systems fundamentally alter the evolutionary outcomes. Previous paradigm exploring evolutionary game dynamics has assumed that individuals update their strategies at an identical rate, reporting that structurally heterogeneous networks -- despite their ubiquity in real systems -- generally hinder the emergence of collective cooperation compared to their homogeneous counterparts. Here we solve this paradox by creating a new paradigm where individuals on arbitrary networks are allowed to update strategies at arbitrary, personalized rates, and provide the precise condition under which universal collective cooperation is favored. We find that when individuals' update rates vary inversely with their number of connections, heterogeneous networks actually outperform homogeneous ones in promoting cooperation. This surprising property of such "doubly heterogeneous" networks cautions against the conventional wisdom that heterogeneous networks are antagonistic to cooperation. We further develop an efficient protocol for optimizing the promotion of cooperation by tuning individuals' update rates in any structure. Our findings highlight that personalized interaction dynamics, beyond structure, in complex networks are fundamental to understanding and promoting collective cooperation.

physics.soc-ph↗

arXiv2023

Strategy evolution on temporal hypergraphs

Individuals interact and cooperate in structured systems. Many studies represent this structure using static networks, where each link represents a permanent connection between two nodes. However, real interactions are generally not time-invariant and are often not pairwise. Recently, progress has been made in modeling higher-order interactions using hypergraphs, where a link may connect more than two individuals. Here, we study cooperation on temporal hypergraphs, capturing the time-varying, higher-order interactions seen in empirical systems. We find that temporal hypergraphs can promote cooperation compared with static networks, and the latter may even underestimate the cooperation-boosting effects of constrained, local interactions. We further show that cooperation can be facilitated by temporal hypergraphs with sparse components and higher-order interactions. Importantly, when the size of group interactions (hyperedges) is comparable to the population size, relatively small hyperedge sizes best facilitate cooperation. Synthetic and empirical hypergraphs alike affirm our findings, illuminating how temporal, higher-order interactions profoundly shape the evolution of cooperation.

physics.soc-ph↗