Zobrazeno 1 - 10
of 327
pro vyhledávání: '"Douglas, Michael R."'
We numerically study whether there exist nowhere vanishing harmonic $1$-forms on the real locus of some carefully constructed examples of Calabi-Yau manifolds, which would then give rise to potentially new examples of $G_2$-manifolds and an explicit
Externí odkaz:
http://arxiv.org/abs/2405.19402
Autor:
Douglas, Michael R., McAllister, Liam
We give a mathematical perspective on string compactifications. Submitted as a chapter in the Encyclopedia of Mathematical Physics.
Comment: 27 pages. Chapter prepared for the Encyclopedia of Mathematical Physics 2nd edition
Comment: 27 pages. Chapter prepared for the Encyclopedia of Mathematical Physics 2nd edition
Externí odkaz:
http://arxiv.org/abs/2310.20118
Autor:
Douglas, Michael R.
Artificial intelligence is making spectacular progress, and one of the best examples is the development of large language models (LLMs) such as OpenAI's GPT series. In these lectures, written for readers with a background in mathematics or physics, w
Externí odkaz:
http://arxiv.org/abs/2307.05782
Tame geometry originated in mathematical logic and implements strong finiteness properties by defining the notion of tame sets and functions. In part I we argued that observables in a wide class of quantum field theories are tame functions and that t
Externí odkaz:
http://arxiv.org/abs/2302.04275
We propose a generalized finiteness principle for physical theories, in terms of the concept of tameness in mathematical logic. A tame function or space can only have a finite amount of structure, in a precise sense which we explain. Tameness general
Externí odkaz:
http://arxiv.org/abs/2210.10057
Autor:
Douglas, Michael R., Simkin, Michael, Ben-Eliezer, Omri, Wu, Tianqi, Chin, Peter, Dang, Trung V., Wood, Andrew
A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph with edge types. KGs are an important primitive in modern machine learning and artificial intelligence. Embedding-based m
Externí odkaz:
http://arxiv.org/abs/2110.09978
Publikováno v:
Phys. Rev. Research 5, 023042 (2023)
We study four-dimensional fractional quantum Hall states on CP2 geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of the Jastro
Externí odkaz:
http://arxiv.org/abs/2109.11522
Autor:
Douglas, Michael R.
Publikováno v:
Pure and Applied Mathematics Quarterly, volume 17, number 2, 605-617, 2021
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career at several
Externí odkaz:
http://arxiv.org/abs/2107.14387
Autor:
Douglas, Michael R.
A very popular model in machine learning is the feedforward neural network (FFN). The FFN can approximate general functions and mitigate the curse of dimensionality. Here we introduce FFNs which represent sections of holomorphic line bundles on compl
Externí odkaz:
http://arxiv.org/abs/2105.03991
We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat K\"ahler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with
Externí odkaz:
http://arxiv.org/abs/2012.04797