The principal objective of this article is a brief overview of the main parts of p-adic
mathematics, which have already had valuable applications and may have a significant …

Understanding how deep learning architectures work is a central scientific problem.
Recently, a correspondence between neural networks (NNs) and Euclidean quantum field …

We construct a family of quantum scalar fields over ap-adic spacetime which satisfy p-adic
analogues of the Gårding–Wightman axioms. Most of the axioms can be formulated in the …

A class of heat operators over non-archimedean local fields acting on L 2-function spaces
on holed discs in the local field are developed and seen as being operators previously …

We establish rigorously the regularization of the p-adic open string amplitudes, with Chan-
Paton rules and a constant B-field, introduced by Ghoshal and Kawano. In this study we use …

The purpose of this article is to study new non-Archimedean pseudo-differential operators
whose symbols are determined from the behavior of two functions defined on the p-adic …

This article aims to study the Coulomb gas model over the d-dimensional p-adic space. We
establish the existence of equilibrium measures and the Γ-limit for the Coulomb energy …

In this article we introduce the ultrametric networks which are p-adic continuous analogs of
the standard Markov state models constructed using master equations. A p-adic transition …

The p-adic cellular neural networks (CNNs) are mathematical generalizations of the neural
networks introduced by Chua and Yang in the 80s. In this work we present two new types of …

In this work we initiate the study of the correspondence between p-adic statistical field
theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic …