LNAI 2801 Critical Values in Asynchronous Random Boolean Networks 1st Edition by Bertrand Mesot, Christof Teuscher ISBN 9783540200574 354020057X

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ISBN 10: 354020057X
ISBN 13: 9783540200574
Author: Bertrand Mesot, Christof Teuscher

Wherever we see life, we see different kinds of complex networks, reason why they are studied across various fields of science. Random Boolean Networks (RBNs) form a special class in which the links between the nodes and the boolean functions are specified at random. Whereas synchronous RBNs were investigated in detail, there has little been done around their asynchronous counterpart, although there is evidence that most living systems are governed by asynchronous updating. Derrida’s annealed approximation predicts a critical connectivity value of K=2 for synchronous RBNs. We present a similar and original approach for asynchronous RBNs and show that they do not possess such a critical connectivity value. The asynchronous and nondeterministic updating scheme introduces perturbations that reach about 25% of the nodes and thus prevents the networks to become stable. Further, our numerical simulations show that asynchronous RBN tend to amplify small and to reduce big perturbations.

LNAI 2801 Critical Values in Asynchronous Random Boolean Networks 1st Edition Table of contents:

Chapter 1: Introduction to Random Boolean Networks

• Defining Random Boolean Networks (RBNs)
• Historical Development of RBNs in Complex Systems
• Overview of Boolean Logic and State Transitions
• Asynchronous vs. Synchronous Boolean Networks

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Chapter 2: Asynchronous Random Boolean Networks

• Key Differences Between Asynchronous and Synchronous Networks
• Defining Asynchronous Update in RBNs
• The Dynamics of Asynchronous Networks
• Stability and Transients in Asynchronous RBNs

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Chapter 3: Critical Values and Phase Transitions in Boolean Networks

• Concept of Criticality in Complex Systems
• Identifying Critical Values in Network Behavior
• Phase Transitions in Boolean Networks
• The Role of Critical Points in Network Dynamics

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Chapter 4: Mathematical Framework for Asynchronous RBNs

• Formalization of Asynchronous Random Boolean Networks
• Analyzing the State Space of aRBNs
• Transition Matrices and Stability Analysis in Asynchronous Networks
• Identifying Critical Values: Techniques and Tools

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Chapter 5: Simulation and Numerical Methods

• Simulation Algorithms for Asynchronous RBNs
• Computational Techniques for Identifying Critical Values
• Exploring Phase Transitions through Simulation Models
• Tools and Software for Simulating Asynchronous RBNs

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Chapter 6: Critical Thresholds in Asynchronous RBNs

• Identifying Thresholds in Asynchronous Networks
• The Impact of Network Size and Connectivity on Criticality
• Experimental Approaches to Investigating Critical Values
• Case Studies on Critical Thresholds in aRBNs

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Chapter 7: Applications of Critical Values in aRBNs

• Critical Values in Biological Systems and Gene Regulatory Networks
• The Role of Criticality in Neural Networks and Cognitive Systems
• aRBNs in Modeling and Simulation of Complex Systems
• The Use of Critical Values in Artificial Intelligence and Evolutionary Algorithms

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Chapter 8: Relationship Between Criticality and Dynamical Properties

• The Role of Critical Points in Network Dynamics
• Analyzing Critical Points and Their Influence on Network Behavior
• The Role of Chaos and Self-Organization at Critical Thresholds
• Critical Transitions and Robustness in Complex Networks

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Chapter 9: Theoretical Insights and Implications

• Theoretical Models of Critical Behavior in Asynchronous RBNs
• Insights into the Role of Critical Values in Dynamical Systems
• Interdisciplinary Approaches to Understanding Criticality in Complex Systems
• Theoretical Advances in Asynchronous Random Boolean Networks

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Chapter 10: Future Directions and Open Problems

• Challenges in Identifying Critical Values in Complex Systems
• Future Research Directions in aRBNs and Criticality
• Expanding the Study of Critical Transitions to Other Network Models
• The Role of Criticality in Understanding Complex System Behavior

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