标题： 关于经济活动循环流动的数学及其在疫情期间照顾弱势群体主题的应用 显示英文标题

标题： On the mathematics of the circular flow of economic activity with applications to the topic of caring for the vulnerable during pandemics

摘要： 我们从基本层面探讨“为什么”、“何时”以及“如何”在缺乏政府机构的情况下，应主动接触贫困和脆弱人群以支持他们的问题。 我们提供了一种简单且新的方法，该方法基于线性代数和基础图论，用于捕捉经济代理之间收入循环的动力学。 引入了一种新的线性代数模型来描述收入循环，基于此，我们能够将社会分类为碎片化或凝聚型。 我们表明，在碎片化社会中，说服社会等级顶端的富裕代理支持穷人和脆弱群体将非常困难。 我们还强调了线性代数和简单的图论方法如何从基本角度解释碎片化社会中阶级斗争的一些机制。 然后，我们直观地解释并数学上证明了为何在凝聚型社会中，社会等级顶端的富裕代理倾向于通过支持其社会中的弱势群体而受益。 我们的数学分析自然地产生了一些新概念，用于描述社会的凝聚力水平、商业（而非社交）网络中的分离度数量以及整体经济的慷慨程度，这些因素都会影响顶层富裕阶层收回其支持资金的速度。 在对未来前景的讨论中，强调了所提出的矩阵模型与统计物理概念之间的联系。 显示英文摘要

摘要： We investigate, at the fundamental level, the questions of `why', `when' and `how' one could or should reach out to poor and vulnerable people to support them in the absence of governmental institutions. We provide a simple and new approach that is rooted in linear algebra and basic graph theory to capture the dynamics of income circulation among economic agents. A new linear algebraic model for income circulation is introduced, based on which we are able to categorize societies as fragmented or cohesive. We show that, in the case of fragmented societies, convincing wealthy agents at the top of the social hierarchy to support the poor and vulnerable will be very difficult. We also highlight how linear-algebraic and simple graph-theoretic methods help explain, from a fundamental point of view, some of the mechanics of class struggle in fragmented societies. Then, we explain intuitively and prove mathematically why, in cohesive societies, wealthy agents at the top of the social hierarchy tend to benefit by supporting the vulnerable in their society. A number of new concepts emerge naturally from our mathematical analysis to describe the level of cohesiveness of the society, the number of degrees of separation in business (as opposed to social) networks, and the level of generosity of the overall economy, which all tend to affect the rate at which the top wealthy class recovers its support money back. In the discussion on future perspectives, the connections between the proposed matrix model and statistical physics concepts are highlighted.