Accessible Percolation with Crossing Valleys on n-ary Trees

In this paper we study a variation of the accessibility percolation model, this is also motivated by evolutionary biology and evolutionary computation. Consider a tree whose vertices are labeled with random numbers. We study the probability of having a monotone subsequence of a path from the root to a leaf, where any k consecutive vertices in the path contain at least one vertex of the subsequence. An n-ary tree, with height h, is a tree whose vertices at distance at most h − 1 to the root have n children. For the case of n-ary trees, we prove that, as h tends to infinity the probability of having such subsequence: tends to 1, if n grows significantly faster than ek ; and tends to 0, if n grows significantly slower than

• Autores: Duque Patiño, Frank Rodrigo; Roldan Correa, Alejandro; Valencia, Leon
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2019
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/45968
• Acceso en línea: https://hdl.handle.net/10495/45968
• Palabra clave: Percolación; Percolation; Biología evolutiva; Developmental biology; Programación evolutiva (computación); Evolutionary programming (Computer science); Dynamics of evolution
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/