Related papers: Attractor and Basin Entropies of Random Boolean Ne…
The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…
We study information aggregation in networks when agents interact to learn a binary state of the world. Initially each agent privately observes an independent signal which is "correct" with probability $\frac{1}{2}+\delta$ for some $\delta…
Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular,…
Asynchronous Boolean networks are a type of discrete dynamical system in which each variable can take one of two states, and a single variable state is updated in each time step according to pre-selected rules. Boolean networks are popular…
We performed a numerical study on random Boolean networks with power-law rank outdegree distributions to find local structural cause for the emergence of high or low degree of coherence in binary state variables. The degree of randomness…
We consider dissipative periodically forced systems and investigate cases in which having information as to how the system behaves for constant dissipation may be used when dissipation varies in time before settling at a constant final…
We introduce a general methodology of update rules accounting for arbitrary interevent time distributions in simulations of interacting agents. In particular we consider update rules that depend on the state of the agent, so that the update…
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean…
We discuss basic features of emergent complexity in dynamical systems far from equilibrium by focusing on the network structure of their state space. We start by measuring the distributions of avalanche and transient times in Random Boolean…
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…
Neuronal networks can generate burst events. It remains unclear how to analyse interburst periods and their statistics. We study here the phase-space of a mean-field model, based on synaptic short-term changes, that exhibit burst and…
The Kauffman model describes a particularly simple class of random Boolean networks. Despite the simplicity of the model, it exhibits complex behavior and has been suggested as a model for real world network problems. We introduce a novel…
This paper is concerned with the reduction of a noisy synchronous Boolean network to a coarse-grained Markov chain with number of states being equal to the number of attractors of the original network.
Although neuron models have been well studied for their rich dynamics and biological properties, limited research has been done on the complex geometries that emerge from the basins of attraction and basin boundaries of multistable neuron…
The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of…
This article is set in the field of regulation networks modeled by discrete dynamical systems. It focuses on Boolean automata networks. In such networks, there are many ways to update the states of every element. When this is done…
In this work we investigate time varying networks with complex dynamics at the nodes. We consider two scenarios of network change in an interval of time: first, we have the case where each link can change with probability pt, i.e. the…
In this paper, we investigate the evolution of the network entropy for consensus dynamics in classical or quantum networks. We show that in the classical case, the network entropy decreases at the consensus limit if the node initial values…
We consider a node-monitor pair, where updates are generated stochastically (according to a known distribution) at the node that it wishes to send to the monitor. The node is assumed to incur a fixed cost for each transmission, and the…
In a recent article [1] we surveyed advances related to adaptation, learning, and optimization over synchronous networks. Various distributed strategies were discussed that enable a collection of networked agents to interact locally in…