Related papers: A Category-Theoretic Perspective on Higher-Order A…
Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity,…
As an emerging interpretable technique, Generalized Additive Models (GAMs) adopt neural networks to individually learn non-linear functions for each feature, which are then combined through a linear model for final predictions. Although…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
Sequential testing problems involve a complex system with several components, each of which is "working" with some independent probability. The outcome of each component can be determined by performing a test, which incurs some cost. The…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
As sounds carry rich information, environmental sound classification (ESC) is crucial for numerous applications such as rare wild animals detection. However, our world constantly changes, asking ESC models to adapt to new sounds…
This paper introduces the Token Space framework, a novel mathematical construct designed to enhance the interpretability and effectiveness of deep learning models through the application of category theory. By establishing a categorical…
The goal of these notes is to introduce, in a very elementary way, the idea of the anti de-Sitter/Conformal Field Theory (AdS/CFT) correspondence to condensed matter physicists. This theory relates a gravity theory in a (d+1)- dimensional…
We investigate multi-field multicritical scalar theories using CFT constraints on two- and three-point functions combined with the Schwinger-Dyson equation. This is done in general and without assuming any symmetry for the models, which we…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category C with a distinguished object, a symmetric special…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
We investigate the strong coupling problem in modified teleparallel gravity theories using the effective field theory (EFT) approach, demonstrating that it is possible to shift the emergence of new degrees of freedom (DoFs) to lower orders…