Related papers: Boolean nested canalizing functions: a comprehensi…
This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, the evolution equation of each gene switches among a collection of candidate…
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…
Boolean networks may be viewed as idealizations of biological genetic networks, where each node is represented by an on-off switch which is a function of the binary output from some other nodes. We evolve connectivity in a single Boolean…
Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we…
The global dynamics of gene regulatory networks are known to show robustness to perturbations in the form of intrinsic and extrinsic noise, as well as mutations of individual genes. One molecular mechanism underlying this robustness has…
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…
Boolean functions and networks are commonly used in the modeling and analysis of complex biological systems, and this paradigm is highly relevant in other important areas in data science and decision making, such as in the medical field and…
Models of biochemical networks are frequently high-dimensional and complex. Reduction methods that preserve important dynamical properties are therefore essential in their study. Interactions between the nodes in such networks are…
Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean…
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…
Floating-point neural networks dominate modern machine learning but incur substantial inference costs, motivating emerging interest in Boolean networks for resource-constrained deployments. Since Boolean networks use only Boolean…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
In previous works, we introduced the notion of dominant vertices in the context of dynamical systems on networks. This is a set of nodes in the underlying network whose evolution determines the whole network's dynamics after a transient…
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…
Dynamic processes of interacting units on a network are out of equilibrium in general. In the case of a directed tree, the dynamic cavity method provides an efficient tool that characterises the dynamic trajectory of the process for the…
Boolean networks have been widely used in many areas of science and engineering to represent various dynamical behaviour. In systems biology, they became useful tools to study the dynamical characteristics of large-scale biomolecular…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
Discrete modelling frameworks of Biological networks can be divided in two distinct categories: Boolean and Multi-valued. Although Multi-valued networks are more expressive for qualifying the regulatory behaviours modelled by more than two…
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…
The dynamics of Boolean networks (the N-K model) with scale-free topology are studied here. The existence of a phase transition governed by the value of the scale-free exponent of the network is shown analytically by analyzing the overlap…