介观范畴、自动机与热带几何
The Mesoscopic category, Automata and Tropical Geometry
摘要：
我们首先比较生物学中的层次结构，并将其与量子场论联系起来。因此，我们发现了许多相似之处，并将其转化为丰富的数学对应。基本的联系是通过尺度变换和热带几何学。我们的核心观察之一是，元胞自动机可以自然地引入许多物理模型，并指（广义）介观尺度，因为我们指出它与规范场的基本关系。为了进一步说明我们的框架，我们将其应用于Witten-Kontsevich模型和Miller-Morita-Mumford类，在我们的图片中，它们来自动力系统。
英文摘要：
We start with comparisons of hierarchies in Biology and relate it to Quan- tum Field Theories. Thereby we discover many similarities and translate them into rich mathematical correspondences. The basic connection goes via scale transformations and Tropical geometry. One of our core observations is that Cellular Automata can be naturally introduced in many physical models and refer to a (generalised) mesoscopic scale, as we point it out for the fundamental relation with Gauge Field Theories. To illustrate our framework further, we apply it to the Witten-Kontsevich model and the Miller-Morita-Mumford classes, which in our picture arise from a dynamical system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
