Related papers: The Dynamics of Canalizing Boolean Networks
Using analytic arguments, we show that dynamical attractor periods in large critical Boolean networks are power-law distributed. Our arguments are based on the method of relevant components, which focuses on the behavior of the nodes that…
This paper focuses on the study of certain classes of Boolean functions that have appeared in several different contexts. Nested canalyzing functions have been studied recently in the context of Boolean network models of gene regulatory…
In systems biology, Boolean networks (BNs) aim at modeling the qualitative dynamics of quantitative biological systems. Contrary to their (a)synchronous interpretations, the Most Permissive (MP) interpretation guarantees capturing all the…
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…
A four-node network consisting of a negative loop controlling a positive one is studied. It models some of the features of the p53 gene network. Using piecewise linear dynamics with thresholds, the allowed dynamical classes are fully…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [Gershenson, 2002] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global…
Because the attractors of biological networks reflect stable behaviors (e.g., cell phenotypes), identifying control interventions that can drive a system towards its attractors (attractor control) is of particular relevance when controlling…
Identifying features of molecular regulatory networks is an important problem in systems biology. It has been shown that the combinatorial logic of such networks can be captured in many cases by special functions called nested canalyzing in…
In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks,…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
The rapid growth of the size and complexity in deep neural networks has sharply increased computational demands, challenging their efficient deployment in real-world scenarios. Boolean networks, constructed with logic gates, offer a…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
A Boolean network is a discrete dynamical system operating on vectors of Boolean variables. The action of a Boolean network can be conveniently expressed as a system of Boolean update functions, computing the new values for each component…
This is the second paper of a series of two about the structural properties that influence the asymptotic dynamics of Random Boolean Networks. Here we study the functionally independent clusters in which the relevant elements, introduced…
Flow networks are essential for both living organisms and enginneered systems. These networks often present complex dynamics controlled, at least in part, by their topology. Previous works have shown that topologically complex networks…
Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and…
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…
It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In the present work, we study the dynamical properties of a neural network designed to store sparsely coded…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…