Contextual Random Boolean Networks

Abstract

We propose the use of Deterministic Generalized Asynchronous Random Boolean Networks [1] as models of contextual deterministic discrete dynamical systems. We show that changes in the context have drastic effects on the global properties of the same networks, namely the average number of attractors and the average percentage of states in attractors. We introduce the situation where we lack knowledge on the context as a more realistic model for contextual dynamical systems. We notice that this makes the network non-deterministic in a specific way, namely introducing a non-Kolmogorovian quantum-like structure for the modelling of the network [2]. In this case, for example, a state of the network has the potentiality (probability) of collapsing into different attractors, depending on the specific form of lack of knowledge on the context.

The World as Evolving Information

“…A well known example can be seen with cellular automata (Langton, 1990) and random Boolean networks (Kauffman, 1993;Gershenson, 2004b): stable (ordered) dynamics limit considerably or do not allow change of states so information cannot propagate, while variable (chaotic) dynamics change the states too much, losing information. Following the law of information propagation, information will tend to a critical state between stability and variability to maximize its propagation: if it is too stable, it will not propagate, and if it is too variable, it will be transformed.…”

On dynamical genetic programming: simple Boolean networks in learning classifier systems

“…As noted above, traditional RBN consist of N nodes updating synchronously in discrete time steps but asynchronous versions have also been presented, after [Harvey & Bossomaier, 1997], leading to a classification of the space of possible forms of RBN [Gershenson, 2002]. Asynchronous forms of CA have also been explored (e.g., [Nakamura, 1974] [Ingerson & Buvel, 1984] [Bersini & Detour, 1994]) wherein it is often suggested that asynchrony is a more realistic underlying assumption for many natural and artificial systems.…”

“…Asynchrony is here implemented as a randomly chosen node being updated on a given cycle, with as many updates per overall network update cycle as there are nodes in the network before an equivalent cycle to one in the synchronous case is said to have occurred (see [Gershenson, 2002] for alternative schemes).…”

Timescale and Stability in Adaptive Behaviour

“…In general we can think of the ctrnn equation as a re-description of the firing rate of a given neuron (or ensemble) averaged over some window, τ . We will first consider a simple two-node system described by equation (2). To determine the linear stability of this system, we must first calculate the coordinates of its equilibrium point.…”

“…Such models tend to be the subject of various different kinds of question. For example, the generation of different classes of dynamic behaviour (fixed, cyclic, complex, chaotic) has been of interest to CA and RBN researchers, e.g., [1,2] whereas those working with ANNs have been interested in questions of evolvability, problem solving and autonomous agent control, amongst others [3]. Interestingly, in answering these questions, the role of timescale within these systems has often been neglected.…”