Mahler Measuring the Genetic Code of Amoebae - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Mahler Measuring the Genetic Code of Amoebae

Siqi Chen
  • Fonction : Auteur
Yang-Hui He
  • Fonction : Auteur
Edward Hirst
  • Fonction : Auteur
Andrew Nestor
  • Fonction : Auteur

Résumé

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.

Dates et versions

hal-03921154 , version 1 (03-01-2023)

Identifiants

Citer

Siqi Chen, Yang-Hui He, Edward Hirst, Andrew Nestor, Ali Zahabi. Mahler Measuring the Genetic Code of Amoebae. 2023. ⟨hal-03921154⟩
11 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More