论文标题
间歇性作为亚稳定性：在无序环境中进化的预测方法
Intermittency as metastability: a predictive approach to evolution in disordered environments
论文作者
论文摘要
整个科学的许多系统通过乘法生长和扩散运输的结合而发展。在存在障碍的情况下，这些系统倾向于形成局部结构，这些结构在相对停滞和短暂的活动爆发之间交替。这种行为很难预测，这种行为被称为物理学的间歇性和进化论的标点平衡。特别是没有一般原则可以找到系统将定居的区域，它将停留多长时间或接下来会跳跃的地方。在这里，我介绍了线性间歇性的预测理论，该理论缩小了这些差距。我表明，任何正线性系统都可以映射到“最大熵随机步行”的概括上，这是一个非本地过渡速率的图表上的马尔可夫过程。这种结构揭示了本地化岛是有效潜力的当地岛屿，并且间歇性跳跃是该潜力的障碍交叉口。我的结果统一了线性系统和马尔可夫竞争性中间歇性的概念，并提供了一种通常适用的方法来减少和预测无序线性系统的动力学。应用涵盖物理学，进化动力学和流行病学。
Many systems across the sciences evolve through a combination of multiplicative growth and diffusive transport. In the presence of disorder, these systems tend to form localized structures which alternate between long periods of relative stasis and short bursts of activity. This behaviour, known as intermittency in physics and punctuated equilibrium in evolutionary theory, is difficult to forecast; in particular there is no general principle to locate the regions where the system will settle, how long it will stay there, or where it will jump next. Here I introduce a predictive theory of linear intermittency that closes these gaps. I show that any positive linear system can be mapped onto a generalization of the "maximal entropy random walk", a Markov process on graphs with non-local transition rates. This construction reveals the localization islands as local minima of an effective potential, and intermittent jumps as barrier crossings in that potential. My results unify the concepts of intermittency in linear systems and Markovian metastability, and provide a generally applicable method to reduce, and predict, the dynamics of disordered linear systems. Applications span physics, evolutionary dynamics and epidemiology.
