Related papers: The Dynamics of Canalizing Boolean Networks
Previous work in Boolean dynamical networks has suggested that the number of components that must be controlled to select an existing attractor is typically set by the number of attractors admitted by the dynamics, with no dependence on the…
We study Boolean networks which are simple spatial models of the highly conserved Delta-Notch system. The models assume the inhibition of Delta in each cell by Notch in the same cell, and the activation of Notch in presence of Delta in…
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…
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…
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…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
Our formal understanding of the inductive bias that drives the success of convolutional networks on computer vision tasks is limited. In particular, it is unclear what makes hypotheses spaces born from convolution and pooling operations so…
This research addresses the challenge of characterizing the complexity and unpredictability of basins within various dynamical systems. The main focus is on demonstrating the efficiency of convolutional neural networks (CNNs) in this field.…
Boolean networks, widely used to model gene regulation, exhibit a phase transition between regimes in which small perturbations either die out or grow exponentially. We show and numerically verify that this phase transition in the dynamics…
The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational…
We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional…
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\lambda$, and we…
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…
The description of gene interactions that constantly occur in the cellular environment is an extremely challenging task due to an immense number of degrees of freedom and incomplete knowledge about microscopic details. Hence, a…
We introduce a numerical method to study random Boolean networks with asynchronous stochas- tic update. Each node in the network of states starts with equal occupation probability and this probability distribution then evolves to a steady…
The control of biological systems presents interesting applications such as cell reprogramming or drug target identification. A common type of control strategy consists in a set of interventions that, by fixing the values of some variables,…
This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
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…
Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on…