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One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by…
The complex dynamics of gene expression in living cells can be well-approximated using Boolean networks. The average sensitivity is a natural measure of stability in these systems: values below one indicate typically stable dynamics…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…
The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations…
Complex systems are often modeled as Boolean networks in attempts to capture their logical structure and reveal its dynamical consequences. Approximating the dynamics of continuous variables by discrete values and Boolean logic gates may,…
Gene regulatory networks (GRNs) play a central role in cellular decision-making. Understanding their structure and how it impacts their dynamics constitutes thus a fundamental biological question. GRNs are frequently modeled as Boolean…
Boolean networks have been proposed as potentially useful models for genetic control. An important aspect of these networks is the stability of their dynamics in response to small perturbations. Previous approaches to stability have assumed…
Biological networks such as gene regulatory networks possess desirable properties. They are more robust and controllable than random networks. This motivates the search for structural and dynamical features that evolution has incorporated…
Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give…
We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we…
Biological processes, including cell differentiation, organism development, and disease progression, can be interpreted as attractors (fixed points or limit cycles) of an underlying networked dynamical system. In this paper, we study the…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…