相关论文: Analysis of random Boolean networks using the aver…

Understanding the inductive bias of neural networks is critical to explaining their ability to generalise. Here, for one of the simplest neural networks -- a single-layer perceptron with n input neurons, one output neuron, and no threshold…

Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…

We determine stability and attractor properties of random Boolean genetic network models with canalyzing rules for a variety of architectures. For all power law, exponential, and flat in-degree distributions, we find that the networks are…

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…

Standard Random Boolean Networks display an order-disorder phase transition. We add to the standard Random Boolean Networks a disconnection rule which couples the control and order parameters. By this way, the system is driven to the…

This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…

Fixed points are fundamental states in any dynamical system. In the case of gene regulatory networks (GRNs) they correspond to stable genes profiles associated to the various cell types. We use Kauffman's approach to model GRNs with random…

In a balancing network each processor has an initial collection of unit-size jobs (tokens) and in each round, pairs of processors connected by balancers split their load as evenly as possible. An excess token (if any) is placed according to…

We consider random graphs with uniformly bounded edges on a Poisson point process conditioned to contain the origin. In particular we focus on the random connection model, the Boolean model and Miller-Abrahams random resistor network with…

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…

Threshold networks are used as models for neural or gene regulatory networks. They show a rich dynamical behaviour with a transition between a frozen and a chaotic phase. We investigate the phase diagram of randomly connected threshold…

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a…

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…

The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations.…

Characterization of the differences between biological and random networks can reveal the design principles that enable the robust realization of crucial biological functions including the establishment of different cell types. Previous…

We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically…

A variety of problems in distributed control involve a networked system of autonomous agents cooperating to carry out some complex task in a decentralized fashion, e.g., orienting a flock of drones, or aggregating data from a network of…

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive…

We derive analytically the scaling behavior in the thermodynamic limit of the number of nonfrozen and relevant nodes in the most general class of critical Kauffman networks for any number of inputs per node, and for any choice of the…

We investigate the evolution of Boolean networks subject to a selective pressure which favors robustness against noise, as a model of evolved genetic regulatory systems. By mapping the evolutionary process into a statistical ensemble and…