Title: Diffusion in dynamic networks with time-varying inputs to allocate responsibility Show Chinese title

Title: 动态网络中的扩散与随时间变化的输入以分配责任

Abstract: Responsibility in complex networks extends beyond direct actions: players should also bear responsibility for the indirect effects within their supply chains or network. We introduce a novel framework to allocate responsibility for indirect environmental, social, and economic impacts across a dynamic network. Unlike static approaches, our framework accounts for the evolving structure of supply chains, financial systems, and other interconnected systems, where relationships change over time. We use the time-dependent Laplacian matrix to capture how responsibility propagates through the network, revealing a diffusion process that aligns with key axioms of fairness: linearity, efficiency, symmetry, and the independent player property. We show that approximating the responsibility measure preserves these properties, supporting the use of our framework as a rigorous method to allocate responsibility in real-world networks. Show Chinese abstract

Abstract: 责任在复杂网络中不仅限于直接行为：参与者还应对其供应链或网络中的间接影响负责。 我们引入了一个新的框架，以在动态网络中分配间接环境、社会和经济影响的责任。 与静态方法不同，我们的框架考虑了供应链、金融系统和其他相互关联系统的演变结构，其中关系随时间变化。 我们使用时变拉普拉斯矩阵来捕捉责任如何在网络中传播，揭示了一个与公平的关键公理相一致的扩散过程：线性、效率、对称性和独立参与者属性。 我们表明，近似责任度量保留了这些性质，支持将我们的框架作为一种严格的方法，在现实世界的网络中分配责任。