1 citations · 2 across the 13 of their papers we have counts for
14 papers
Wolfram Model and the Technological Architecture of the Fourth Industrial Revolution
José Manuel Rodríguez Caballero
In this essay, we will defend the thesis that the multi-computational paradigm is a natural way of thinking about the fourth industrial revolution. This will be done considering th…
Renormalized Wolfram model exhibiting non-relativistic quantum behavior
José Manuel Rodríguez Caballero
We show a Wolfram model whose renormalization generates a sequence of approximations of a wave function having the Pauli-x matrix as Hamiltonian.
Incompatibility between 't Hooft's and Wolfram's models of quantum mechanics
José Manuel Rodríguez Caballero
Stephen Wolfram and Gerard 't Hooft developed classical models of quantum mechanics. We show that the descriptive complexity grows differently as a function of time in each model.…
Homophilic networks evolving by mimesis
Jose Manuel Rodriguez Caballero
We provide a mathematical model for networks based on similarities (homophily) and evolving by mutual imitation (mimesis). We show that such social networks will converge to a stat…
Brainstorming about the geometric structures in the Wolfram model of fundamental physics
Jose Manuel Rodriguez Caballero
In this essay, we explore the geometric structures involved in the Wolfram model of fundamental physics. Furthermore, we propose some directions of research aiming to get the boson…
The Thue-Morse substitutions and self-similar groups and algebras
Laurent Bartholdi, José Manuel Rodríguez Caballero, Ahmed Tanbir
We introduce self-similar algebras and groups closely related to the Thue-Morse sequence, and begin their investigation by describing a character on them, the "spread" character.
A -analog of Jacobi's two squares formula and its applications
José Manuel Rodríguez Caballero
We consider a -analog of the number of representations of an integer as a sum of two squares . This -analog is generated by the expansion of a product tha…
Elementary number-theoretical statements proved by Language Theory
José Manuel Rodríguez Caballero
We introduce a method to derive theorems from Elementary Number Theory by means of relationships among formal languages. Using -algebras, we define what a proof of a number-theo…
On a function introduced by Erdös and Nicolas
José Manuel Rodríguez Caballero
Erdös and Nicolas [erdos1976methodes] introduced an arithmetical function related to divisors of in short intervals . The aim of this note…
Divisors on overlapped intervals and multiplicative functions
José Manuel Rodríguez Caballero
Consider the real numbers and the intervals $\mathcal{L}_{n,k} = \left]\ell_{n,k}…
Self-Similar Algebras with connections to Run-length Encoding and Rational Languages
José Manuel Rodríguez Caballero, Tanbir Ahmed
A self-similar algebra is an associative algebra with a morphism of algebras $ψ: \mathfrak{A} \longrightarrow M_d \left( \mathfrak{A}\…
Factorization of Dyck words and the distribution of the divisors of an integer
José Manuel Rodríguez Caballero
In [CaballeroHooleyDelta], we associated a Dyck word to any pair consisting of an integer and a real number . Th…
A relationship between the ideals of and the Fibonacci numbers
José Manuel Rodríguez Caballero
Let be the number of ideals of codimension of , where is the finite field with elements. Kassel and…
On prime numbers of the form
José Manuel Rodríguez Caballero
Consider the set of integers for which there are infinitely many primes such that is a power of . The aim of this paper is to show a relationship bet…