Related papers: A reduction method for noisy Boolean networks
Previous preliminary results on the application of knowledge networks to noise reduction in stationary harmonic and weakly chaotic signals are extended to more general cases. The formalism gives a novel algorithm from which statistical…
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…
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…
We consider the discrete-time filtering problem in scenarios where the observation noise is degenerate or low. More precisely, one is given access to a discrete time observation sequence which at any time $k$ depends only on the state of an…
Echo state networks are a recently developed type of recurrent neural network where the internal layer is fixed with random weights, and only the output layer is trained on specific data. Echo state networks are increasingly being used to…
Chaos control in Random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. This paper…
We study the synchronization behavior of discrete-time Markov chains on countable state spaces. Representing a Markov chain in terms of a random dynamical system, which describes the collective dynamics of trajectories driven by the same…
Noisy network coding, which elegantly combines the conventional compress-and-forward relaying strategy and ideas from network coding, has recently drawn much attention for its simplicity and optimality in achieving to within constant gap of…
Given a Boolean network BN and a subset A of attractors of BN, we study the problem of identifying a minimal subset C of vertices of BN, such that the dynamics of BN can reach from a state s in any attractor As in A to any attractor At in A…
We survey information-theoretic approaches to the reduction of Markov chains. Our survey is structured in two parts: The first part considers Markov chain coarse graining, which focuses on projecting the Markov chain to a process on a…
We address the problem of retrieving information from a noisy version of the ``knowledge networks'' introduced by Maslov and Zhang. We map this problem onto a disordered statistical mechanics model, which opens the door to many analytical…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
We study classes of dynamical systems that can be obtained by constructing recursive networks with monotone Boolean functions. Stack filters in nonlinear signal processing are special cases of such systems. We show an analytical connection…
This paper explores the problem of training a recurrent neural network from noisy data. While neural network based dynamic predictors perform well with noise-free training data, prediction with noisy inputs during training phase poses a…
It is an increasingly important problem to study conditions on the structure of a network that guarantee a given behavior for its underlying dynamical system. In this paper we report that a Boolean network may fall within the chaotic…
We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…
Boolean networks are special types of finite state time-discrete dynamical systems. A Boolean network can be described by a function from an n-dimensional vector space over the field of two elements to itself. A fundamental problem in…
Boolean networks at the critical point have been a matter of debate for many years as, e.g., scaling of number of attractor with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a…
We propose a new analytical method to study stochastic, binary-state models on complex networks. Moving beyond the usual mean-field theories, this alternative approach is based on the introduction of an annealed approximation for…