Related papers: Kauffman networks with threshold functions
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…
This paper provides a collection of mathematical and computational tools for the study of robustness in nonlinear gene regulatory networks, represented by time- and state-discrete dynamical systems taking on multiple states. The focus is on…
A Boolean network (BN) is called observable if any initial state can be uniquely determined from the output sequence. In the existing literature on observability of BNs, there is almost no research on the relationship between the number of…
We show that neural networks with access to randomness can outperform deterministic networks by using amplification. We call such networks Coin-Flipping Neural Networks, or CFNNs. We show that a CFNN can approximate the indicator of a…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
It has been shown \citep{broeck90:physicalreview,patarnello87:europhys} that feedforward Boolean networks can learn to perform specific simple tasks and generalize well if only a subset of the learning examples is provided for learning.…
We determine the average number $ \vartheta (N, K) $, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $ N \gg 1 $, there exists a connectivity critical value $ K_c $ such that $ \vartheta(N,K)…
The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and…
In this paper, we tackle a challenging problem inherent in a series of applications: tracking the influential nodes in dynamic networks. Specifically, we model a dynamic network as a stream of edge weight updates. This general model…
We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and…
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…
In this paper we try to end the debate concerning the suitability of different updating schemes in random Boolean networks (RBNs). We quantify for the first time loose attractors in asyncrhonous RBNs, which allows us to analyze the…
Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
Random Threshold Networks (RTNs) are an idealized model of diluted, non symmetric spin glasses, neural networks or gene regulatory networks. RTNs also serve as an interesting general example of any coordinated causal system. Here we study…
In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
We develop further the consequences of the irreducible-Boolean classification established in Ref. [9]; which have the advantage of allowing strong statistical calculations in disordered Boolean function models, such as the…
Random boolean networks are a model of genetic regulatory networks that has proven able to describe experimental data in biology. They not only reproduce important phenomena in cell dynamics, but they are also extremely interesting from a…