Maxwells Demon: Controlling Entropy via Discrete Ricci Flow Over Networks
Maxwells Demon: Controlling Entropy via Discrete Ricci Flow Over Networks
复制标题
麦克斯韦妖：通过网络上的离散里奇流控制熵
DOI：
10.1007/978-3-030-38965-9_9
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Ji Liu
中科院分区：
文献类型：
--
作者：
Romeil Sandhu;Ji Liu
在这项工作中，我们提出利用离散图Ricci流通过反馈控制来改变网络熵。鉴于这种反馈输入可以“逆转”熵的变化，我们采用了麦克斯韦妖的绰号来激励我们的方法。特别是，最近已经表明，几何中的里奇曲率与玻尔兹曼熵以及网络的功能鲁棒性或在随机波动存在下保持功能的能力具有内在联系。由此，离散的Ricci流提供了一个自然的途径来“重新布线”特定网络的底层几何结构，以提高整体和弹性。由于在现实世界中，人们可能会对在特定代理之间施加非线性约束以理解网络动态演化感兴趣，因此控制离散里奇流可能是必要的（例如，我们可能会寻求理解两个网络之间的熵动力学和曲率“流”，而不仅仅是曲率收缩）。反过来，这可以被表述为一个自然控制问题，我们对离散的ricci流采用反馈控制，并表明在一定的离散化下，即奥利维-里奇曲率，可以通过李雅普诺夫分析显示稳定性。最后，我们给出了初步结果，并对潜在的应用进行了评论，这将是未来工作的一个主题。
In this work, we propose to utilize discrete graph Ricci flow to alter network entropy through feedback control. Given such feedback input can “reverse” entropic changes, we adapt the moniker of Maxwell’s Demon to motivate our approach. In particular, it has been recently shown that Ricci curvature from geometry is intrinsically connected to Boltzmann entropy as well as functional robustness of networks or the ability to maintain functionality in the presence of random fluctuations. From this, the discrete Ricci flow provides a natural avenue to “rewire” a particular network’s underlying geometry to improve throughout and resilience. Due to the real-world setting for which one may be interested in imposing nonlinear constraints amongst particular agents to understand the network dynamic evolution, controlling discrete Ricci flow may be necessary (e.g., we may seek to understand the entropic dynamics and curvature “flow” between two networks as opposed to solely curvature shrinkage). In turn, this can be formulated as a natural control problem for which we employ feedback control towards discrete Ricci-based flow and show that under certain discretization, namely Ollivier-Ricci curvature, one can show stability via Lyapunov analysis. We conclude with preliminary results with remarks on potential applications that will be a subject of future work.
DOI：
10.1090/gsm/077
发表时间：
2018
期刊：
--
影响因子：
--
作者：
B. Chow;P. Lu;Lei Ni
通讯作者：
B. Chow;P. Lu;Lei Ni