scholarly journals Relationship Between the Reprogramming Determinants of Boolean Networks and Their Interaction Graph

2016 ◽  
pp. 113-127 ◽  
Author(s):  
Hugues Mandon ◽  
Stefan Haar ◽  
Loïc Paulevé
Keyword(s):  
Boolean Networks ◽  
Interaction Graph

scholarly journals On the Rank and Periodic Rank of Finite Dynamical Systems

10.37236/7017 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Maximilien Gadouleau
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Periodic Points ◽  
Boolean Networks ◽  
Finite Alphabet ◽  
Interaction Graph ◽  
Maximum Rank ◽  
Local Functions ◽  
Finite Dynamical Systems ◽  
Finite Dynamical System

A finite dynamical system is a function $f : A^n \to A^n$ where $A$ is a finite alphabet, used to model a network of interacting entities. The main feature of a finite dynamical system is its interaction graph, which indicates which local functions depend on which variables; the interaction graph is a qualitative representation of the interactions amongst entities on the network. The rank of a finite dynamical system is the cardinality of its image; the periodic rank is the number of its periodic points. In this paper, we determine the maximum rank and the maximum periodic rank of a finite dynamical system with a given interaction graph over any non-Boolean alphabet. The rank and the maximum rank are both computable in polynomial time. We also obtain a similar result for Boolean finite dynamical systems (also known as Boolean networks) whose interaction graphs are contained in a given digraph. We then prove that the average rank is relatively close (as the size of the alphabet is large) to the maximum. The results mentioned above only deal with the parallel update schedule. We finally determine the maximum rank over all block-sequential update schedules and the supremum periodic rank over all complete update schedules.

scholarly journals A fixed point theorem for Boolean networks expressed in terms of forbidden subnetworks

2011 ◽  
Vol DMTCS Proceedings vol. AP,... (Proceedings) ◽  
Author(s):  
Adrien Richard
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Adjacency Matrix ◽  
Jacobian Matrix ◽  
Unique Fixed Point ◽  
Boolean Networks ◽  
Directed Cycle ◽  
Interaction Graph ◽  
International Audience

International audience We are interested in fixed points in Boolean networks, $\textit{i.e.}$ functions $f$ from $\{0,1\}^n$ to itself. We define the subnetworks of $f$ as the restrictions of $f$ to the hypercubes contained in $\{0,1\}^n$, and we exhibit a class $\mathcal{F}$ of Boolean networks, called even or odd self-dual networks, satisfying the following property: if a network $f$ has no subnetwork in $\mathcal{F}$, then it has a unique fixed point. We then discuss this "forbidden subnetworks theorem''. We show that it generalizes the following fixed point theorem of Shih and Dong: if, for every $x$ in $\{0,1\}^n$, there is no directed cycle in the directed graph whose the adjacency matrix is the discrete Jacobian matrix of $f$ evaluated at point $x$, then $f$ has a unique fixed point. We also show that $\mathcal{F}$ contains the class $\mathcal{F'}$ of networks whose the interaction graph is a directed cycle, but that the absence of subnetwork in $\mathcal{F'}$ does not imply the existence and the uniqueness of a fixed point.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

2019 ◽  
Vol 19 (6) ◽  
pp. 413-425 ◽  
Author(s):  
Athanasios Alexiou ◽  
Stylianos Chatzichronis ◽  
Asma Perveen ◽  
Abdul Hafeez ◽  
Ghulam Md. Ashraf
Keyword(s):  
Protein Interactions ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Review Paper ◽  
Boolean Networks ◽  
Diagnostic Tools ◽  
Complex Nature ◽  
Cellular Interactions ◽  
Protein Protein Interactions ◽  
Deterministic Models

Background:Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.Objective:Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.Methods:Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.Results:GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.Conclusion:In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

Optimal output tracking of switched Boolean networks

2021 ◽  
Author(s):  
Yuzhi Chen ◽  
Pengfei Sun ◽  
Tao Sun ◽  
Madini O. Alassafi ◽  
Adil M. Ahmad
Keyword(s):  
Boolean Networks ◽  
Output Tracking ◽  
Optimal Output

Controllability of Boolean networks with intermittent disturbances

2020 ◽  
Vol 34 (28) ◽  
pp. 2050309
Author(s):  
Tao You ◽  
Hailun Zhang ◽  
Mingyu Yang ◽  
Xiao Wang ◽  
Yangming Guo
Keyword(s):  
Gene Expression ◽  
Boolean Network ◽  
Boolean Networks ◽  
Genetic Mutations ◽  
Intermittent Control ◽  
Mathematical Tool ◽  
Pulse Control ◽  
Expression Of Genes ◽  
Complicated Process ◽  
Living Being

In biological systems, gene expression is an important subject. In order to clarify the specific process of gene expression, mathematical tools are needed to simulate the process. The Boolean network (BN) is a good mathematical tool. In this paper, we study a Boolean network with intermittent perturbations. This is of great significance for studying genetic mutations in bioengineering. The expression of genes in the internal system of a living being is a very complicated process, and it is clear that the process is trans-ageal for humans. Through the intermittent control and pulse control of the BN, we can obtain the trajectory of gene expression better and faster, which will provide a very important theoretical basis for our next research.

scholarly journals Hybrid Boolean Networks as Physically Unclonable Functions

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Noeloikeau Charlot ◽  
Daniel Canaday ◽  
Andrew Pomerance ◽  
Daniel J. Gauthier
Keyword(s):  
Boolean Networks ◽  
Physically Unclonable Functions
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