Related papers: Machine Learning for Hilbert Series
We consider modules $M$ over Lie algebroids ${\mathfrak g}_A$ which are of finite type over a local noetherian ring $A$. Using ideals $J\subset A$ such that ${\mathfrak g}_A \cdot J\subset J $ and the length $\ell_{{\mathfrak g}_A}(M/JM)<…
Machine learning is a novel and powerful technology and has been widely used in various science topics. We demonstrate a machine-learning based approach built by a set of general metrics and rules inspired by physics. Taking advantages of…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Finding all the mutually unbiased bases in various dimensions is a problem of fundamental interest in quantum information theory and pure mathematics. The general problem formulated in finite-dimensional Hilbert spaces is open. In the…
This entry introduces the topic of machine learning and provides an overview of its relevance for applied linguistics and language learning. The discussion will focus on giving an introduction to the methods and applications of machine…
The areas of machine learning and communication technology are converging. Today's communications systems generate a huge amount of traffic data, which can help to significantly enhance the design and management of networks and…
Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of…
The numerical Hilbert series combinatorics and the comodule Hilbert series combinatorics are introduced, and some applications are presented, including the MacMahon Master Theorem.
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
First-principle simulations are at the heart of the high-energy physics research program. They link the vast data output of multi-purpose detectors with fundamental theory predictions and interpretation. This review illustrates a wide range…
Time series data is being used everywhere, from sales records to patients' health evolution metrics. The ability to deal with this data has become a necessity, and time series analysis and forecasting are used for the same. Every Machine…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
Machine Learning is a powerful tool for astrophysicists, which has already had significant uptake in the community. But there remain some barriers to entry, relating to proper understanding, the difficulty of interpretability, and the lack…
Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily…
Depending on the point of view, modern machine learning is either providing an unprecedented boost to the numerical methods of particle physics, or it is transforming the way we do science with vast amounts of complex data. In any case, it…
A method of induction the distances with Hilbert structure is proposed. Some properties of the method are studied. Typical examples of corresponding metric spaces are discussed. Key words: Hilbert spaces; metric spaces; isometric embedding…
We review machine learning methods employing positive definite kernels. These methods formulate learning and estimation problems in a reproducing kernel Hilbert space (RKHS) of functions defined on the data domain, expanded in terms of a…
In this paper, we study the linear dynamical properties of shift operators on some classes of Segal algebras. Moreover, we characterize hypercyclic generalized bilateral shift operators on the standard Hilbert module.
Modern machine learning is driving a paradigm shift in particle physics phenomenology at the Large Hadron Collider. This short review examines the transformative role of machine learning across the entire theoretical prediction pipeline,…