Related papers: Phase transitions and memory effects in the dynami…
We demonstrate the advantages of feedforward loops using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical behaviors of network embedded feedback and…
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…
In this paper we study the phase transitions of different types of Random Boolean networks. These differ in their updating scheme: synchronous, semi-synchronous, or asynchronous, and deterministic or non-deterministic. It has been shown…
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…
Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply…
Different Boolean networks may reveal similar dynamics although their definition differs, then preventing their distinction from the observations. This raises the question about the sufficiency of a particular Boolean network for properly…
Boolean networks, first developed in the late 1960s as a tool for studying complex disordered dynamical systems, consist of nodes governed by Boolean functions whose evolution is entirely deterministic in that the state of the network at a…
Recent developments in Omics-technologies revolutionized the investigation of biology by producing molecular data in multiple dimensions and scale. This breakthrough in biology raises the crucial issue of their interpretation based on…
Probabilistic Boolean Networks have been proposed for estimating the behaviour of dynamical systems as they combine rule-based modelling with uncertainty principles. Inferring PBNs directly from gene data is challenging however, especially…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…
A growing body of research indicates that structural plasticity mechanisms are crucial for learning and memory consolidation. Starting from a simple phenomenological model, we exploit a mean-field approach to develop a theoretical framework…
We consider a model for heterogeneous 'gene regulatory networks' that is a generalization of the model proposed by Chatterjee and Durrett (2011) as an "annealed approximation" of Kauffmann's (1969) random Boolean networks. In this model,…
Many recent generative models make use of neural networks to transform the probability distribution of a simple low-dimensional noise process into the complex distribution of the data. This raises the question of whether biological networks…
We investigate the expressive power of neural networks from the point of view of descriptive complexity. We study neural networks that use floating-point numbers and piecewise polynomial activation functions from two perspectives: 1) the…
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…
Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…
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…