Special Issue "Boolean Networks Models in Science and Engineering"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: 31 January 2021.

Special Issue Editors

Prof. Dr. Jose C. Valverde
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Guest Editor
Department of Mathematics, University of Castilla‐La Mancha, Avda. de Espana, s/n, 02071‐Albacete, Spain
Interests: dynamical systems; discrete mathematics; biomathematics
Prof. Dr. Juan A. Aledo
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Guest Editor
Department of Mathematics, University of Castilla‐La Mancha, Avda. de Espana, s/n, 02071‐Albacete, Spain
Interests: Boolean networks; discrete mathematics; computational mathematics
Prof. Dr. Silvia Martínez
Website
Guest Editor
Department of Mathematics, University of Castilla‐La Mancha, Plza. de la Universidad, 3, 02071‐Albacete, Spain
Interests: discrete mathematics; Boolean networks; mathematics education

Special Issue Information

Dear Colleagues,

As a generalization of other notions like cellular automata or Kauffman networks appeared in the last quarter of the twentieth century, the notion of Boolean networks has undergone a special development in the last decades. This is mainly due to its applications in Science and Engineering.

In this sense, several research groups of mathematicians are working and obtaining relevant results in this area that can be applied in other fields. We invite them to submit their latest research to our Special Issue, “Boolean Networks Models in Science and Engineering”, in the reputed journal Mathematics.

We hope to collect novel and interesting papers, both theoretical and practical, in this field. Submissions are welcome presenting new theoretical results, new algorithmic as well as new models or applications in Science and Engineering.

Potential topics include, but are not limited to:

  • Dynamics of Boolean network models
  • Algorithms, methods, and software for the study of Boolean network models
  • Boolean network models applied in science and engineering

Prof. Dr. Jose C. Valverde
Prof. Dr. Juan A. Aledo
Prof. Dr. Silvia Martínez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Boolean network models
  • Combinatorial dynamics
  • Algorithms, methods and software
  • Application of Boolean algebra
  • Boolean functions

Published Papers (2 papers)

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Research

Open AccessArticle
On the Periodic Structure of Parallel Dynamical Systems on Generalized Independent Boolean Functions
Mathematics 2020, 8(7), 1088; https://doi.org/10.3390/math8071088 - 03 Jul 2020
Abstract
In this paper, based on previous results on AND-OR parallel dynamical systems over directed graphs, we give a more general pattern of local functions that also provides fixed point systems. Moreover, by considering independent sets, this pattern is also generalized to get systems [...] Read more.
In this paper, based on previous results on AND-OR parallel dynamical systems over directed graphs, we give a more general pattern of local functions that also provides fixed point systems. Moreover, by considering independent sets, this pattern is also generalized to get systems in which periodic orbits are only fixed points or 2-periodic orbits. The results obtained are also applicable to homogeneous systems. On the other hand, we study the periodic structure of parallel dynamical systems given by the composition of two parallel systems, which are conjugate under an invertible map in which the inverse is equal to the original map. This allows us to prove that the composition of any parallel system on a maxterm (or minterm) Boolean function and its conjugate one by means of the complement map is a fixed point system, when the associated graph is undirected. However, when the associated graph is directed, we demonstrate that the corresponding composition may have points of any period, even if we restrict ourselves to the simplest maxterm OR and the simplest minterm AND. In spite of this general situation, we prove that, when the associated digraph is acyclic, the composition of OR and AND is a fixed point system. Full article
(This article belongs to the Special Issue Boolean Networks Models in Science and Engineering)
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Open AccessArticle
On the Lyapunov Exponent of Monotone Boolean Networks
Mathematics 2020, 8(6), 1035; https://doi.org/10.3390/math8061035 - 24 Jun 2020
Abstract
Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive [...] Read more.
Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd. Full article
(This article belongs to the Special Issue Boolean Networks Models in Science and Engineering)
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