论文标题
Mahler测量变形虫的遗传密码
Mahler Measuring the Genetic Code of Amoebae
论文作者
论文摘要
来自热带几何形状和Mahler量度的变形虫在数字理论中起着重要作用在颤抖的理论和二聚体模型中。他们对牛顿多项式系数的依赖性彼此紧密相似，并且通过Ronkin函数连接。遗传符号回归方法用于提取2D和3D Amoebae组分与Mahler度量之间的数值关系。我们发现，D维变形虫的有界补体的体积与通过d = 2和3的气相对Mahler测量的气相贡献有关。然后将这些方法进一步扩展到非反省性Mahler量度的数值分析。此外，机器学习方法用于直接学习3D Amoebae的拓扑结构，并具有很强的性能。另外，给出了某些变形虫边界的分析表达式。
Amoebae from tropical geometry and the Mahler measure from number theory play important roles in quiver gauge theories and dimer models. Their dependencies on the coefficients of the Newton polynomial closely resemble each other, and they are connected via the Ronkin function. Genetic symbolic regression methods are employed to extract the numerical relationships between the 2d and 3d amoebae components and the Mahler measure. We find that the volume of the bounded complement of a d-dimensional amoeba is related to the gas phase contribution to the Mahler measure by a degree-d polynomial, with d = 2 and 3. These methods are then further extended to numerical analyses of the non-reflexive Mahler measure. Furthermore, machine learning methods are used to directly learn the topology of 3d amoebae, with strong performance. Additionally, analytic expressions for boundaries of certain amoebae are given.
