Boolean Networks and Their Applications in Science and Engineering

Jose C. Valverde, Henning S. Mortveit, Carlos Gershenson, Yongtang Shi
2020 Complexity  
In recent decades, Boolean networks (BN) have emerged as an effective mathematical tool to model not only computational processes, but also several phenomena in science and engineering. For this reason, the development of the theory of such models has become a compelling need that has attracted the interest of many research groups in recent years. Dynamics of BN are traditionally associated with complexity, since they are composed of many elemental units whose behavior is relatively simple in
more » ... mparison with the behavior of the entire system. BN are a generalization of other relevant mathematical models, which appeared previously as cellular automata (CA), inspired by von Neumann and studied by Wolfram and others to explore the computational universe, or Kauffman networks (KN), proposed by Kauffman in 1969 for modeling gene regulatory networks. This gives an idea of the versatility of this new paradigm in applications to several branches of science (mathematics, physics chemistry, biology, ecology, etc.) and engineering (computing, artificial intelligence, electronics, circuits, etc.). The aim of this special issue was to collect cuttingedge research on the different models of BN (deterministic and nondeterministic, synchronous and asynchronous, homogenous and non-homogenous, directed and undirected, regular and non-regular, etc.). Thus, several research groups in this field submitted their recent developments and future research directions concerning new models. In addition, original research articles showing some applications of BN in science and engineering were received. Although fifteen manuscripts were submitted to the special issue, only nine of them were finally accepted for publication after the review process. These contributions are briefly described below. In the paper "Predecessors Existence Problems and Gardens of Eden in Sequential Dynamical Systems", Aledo et al. deal with network models which are deterministic, asynchronously updated, homogeneous and defined over arbitrary (non-regular) undirected graphs, so extending the work on the synchronous case [1]. In particular, the local functions are restrictions of a global operator, given by a maxterm or minterm Boolean function; and the update order is a vertex indexed permutation. For these kinds of models, which are usually known as sequential dynamical systems (SDS) on maxterm and minterm Boolean functions, the authors solve the predecessor-existence problems algebraically. In addition, they give a characterization of the Garden-of-Eden configurations and provide the best upper bound for the number of such configurations. The article "A Boolean network approach to estrogen transcriptional regulation" by Anda-Jáuregui et al. presents a dynamical model of gene regulation of the Estrogen receptor transcription network based on known regulatory interactions, to better understand the implications of deregulation of the Estrogen and Estrogen receptor regulatory networks. By using an adaptation to classical Boolean Networks dynamics, Hindawi Complexity Volume 2020, Article ID 6183798, 3 pages https://doi.
doi:10.1155/2020/6183798 fatcat:a2kdkdc4dndmdfzy4qnhiximhy