Related papers: Symbolic representation and classification of inte…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
Developing robust representations of chemical structures that enable models to learn topological inductive biases is challenging. In this manuscript, we present a representation of atomistic systems. We begin by proving that our…
In this paper, we present a compositional methodology for constructing symbolic models of nonlinear interconnected impulsive systems. Our approach relies on the concept of "alternating simulation function" to establish a relationship…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We study representations of wreath product analogues of categories of finite sets. This includes the category of finite sets and injections (studied by Church, Ellenberg, and Farb) and the opposite of the category of finite sets and…
The distributed representations currently used are dense and uninterpretable, leading to interpretations that themselves are relative, overcomplete, and hard to interpret. We propose a method that transforms these word vectors into reduced…
In this paper, we are devoted to define p symphonic morphism and characterize it partially as in the case of harmonic morphism.
Research on integrated neural-symbolic systems has made significant progress in the recent past. In particular the understanding of ways to deal with symbolic knowledge within connectionist systems (also called artificial neural networks)…
This is a written version of the invited lecture at the 9th European Congress of Mathematics in July 2024 in Sevilla. We review certain new symmetries of Grothendieck rings that have emerged in representation theory.
Discrete abstractions of continuous and hybrid systems have recently been the topic of great interest from both the control systems and the computer science communities, because they provide a sound mathematical framework for analysing and…
We investigate the convergence properties of a perturbation method proposed some time ago and reveal some of it most interesting features. Anharmonic oscillators in the strong--coupling limit prove to be appropriate illustrative examples…
Survey article on representation stability and examples in algebraic geometry and topology, written for the Notices of the AMS.
We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…
The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to…
The aim of this work is to show how symbolic computation can be used to perform multivariate Lagrange, Hermite and Birkhoff interpolation and help us to build more realistic interpolating functions. After a theoretical introduction in which…
We characterize continuous, symmetric and homogeneous means $M$ that can be represented in the form \begin{equation*} \frac{1}{M(x,y)}=\int_0^1 \frac{dt}{N\left(\tfrac{x+y}{2}-t\tfrac{x-y}{2},\tfrac{x+y}{2}+t\tfrac{x-y}{2}\right)}.…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear…
This paper presents a compositional framework for the construction of symbolic models for a network composed of a countably infinite number of finite-dimensional discrete-time control subsystems. We refer to such a network as infinite…
Despite significant progress in the development of neural-symbolic frameworks, the question of how to integrate a neural and a symbolic system in a \emph{compositional} manner remains open. Our work seeks to fill this gap by treating these…