Related papers: Strong modules and asynchronous attractors of Bool…
Boolean Networks (BNs) describe the time evolution of binary states using logic functions on the nodes of a network. They are fundamental models for complex discrete dynamical systems, with applications in various areas of science and…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
Results and tools on discrete interaction networks are often concerned with Boolean variables, whereas considering more than two levels is sometimes useful. Multivalued networks can be converted to partial Boolean maps, in a way that…
Effective control of biological systems can often be achieved through the control of a surprisingly small number of distinct variables. We bring clarity to such results using the formalism of Boolean dynamical networks, analyzing the…
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…
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
Networks (or graphs) are used to model the dyadic relations between entities in a complex system. In cases where there exists multiple relations between the entities, the complex system can be represented as a multilayer network, where the…
We study critical random Boolean networks with two inputs per node that contain only canalyzing functions. We present a phenomenological theory that explains how a frozen core of nodes that are frozen on all attractors arises. This theory…
We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor…
Boolean networks are dynamical models of disease development in which the activation levels of genes are represented by binary variables. Given a Boolean network, controls represent mutations or medical treatments that fix the activation…
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains…
We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
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…
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a…
Random Boolean networks, originally invented as models of genetic regulatory networks, are simple models for a broad class of complex systems that show rich dynamical structures. From a biological perspective, the most interesting networks…