It is an intersecting fact to not that to date the notion of dynamic networks refers to either one of two different concepts. First the pattern of Links, in a network topology evolves dynamically in time. Second the nodes can be individual dynamic systems coupled by static links [5, 6, 10, 22 24].
Adaptive networks are not new. Nearly all real world networks are to an extent adaptive and adaptive networks occurs in multiple disciplines today [12, 13, and 18]. What is new is that in recent years adaptive networks have become a focal point of extensive investigation using simple conceptual models. Revealing new mechanisms and phenomenons. In [1] by (Gross and Sayama) Adaptive networks based on simple local rules can organise themselves robustly towards transitional phases and highly complex topologies consequently distinct classes of nodes emerge spontaneously for populations that were homogeneous in nature and complex dynamics emerge as a consequence of phase transition and bifurcation in that involve locate as well as topological degrees of freedom [1].
in [4] (Galstyan and Lerman ) consider a network of Boolean agents competing for limited resource, using agent playing a Generalized Minority Game. (The Authors) study properties such a system for varying values of mean connectivity K of the network, and demonstrate that the system K = 2 indicating high degree of coordinated Large size variations of the capacity level. [4]
Algorithms for Search attractors in RBNs
In [7] (Guo et al) Models a genetic regulatory network as a boolean network and proposes a solving algorithm, tackling the attractor finding problem by partitioning the boolean networks into several units comprised of strongly connected entities and according to their gradient, and described the connection between units as decision nodes [7]
Wuensche in [8] uses a computer software called “Discrete Dynamic Lab” to examine simple networks ranging from Random Boolean network (RBN) to cellular automata (CA) provided by attractor basins, to search for general principles that underlay their dynamics. The study moved to new areas where findings from attractor basins combined with findings of local dynamics to shed light on memory and self organisation.[8]
(Liang et al) in [11] studies the Kauffman net, Showing the effects of distribution on the localization property of the net. Showing that nets with N > 1000 to be difficult. (Authors) also determine scaling properties of attractor and transients with net size [11].
There is use of numerical means in [9] to investigate structural circuits in Kauffman networks and suggest that exponential growth of the number of structural circuits puts a lower bound on complexity growth of Boolean dependency loops and consequently the number of attractors. (Hawick et al) use an exact and fast circuit enumeration method not relying on sampling trajectories, [9] also explores the role of structural self-inputs, or self-edged in the NK-model and study how they affect structural circuits number and hence of attractors. Structural [9].
Information processing in RBNs
Using networks of autonomous noisy elements with fluctuating timing and study conditions for overall system behaviour being reproducible in presence of noise. (Klemm and Bornhold) in [13] seek to answer how to make network of unreliable elements perform in a reliable manner, considering that living cells and organisms are largely based on very reliable function of their networks. [13]
looking into ensembles of RBN, [14] find that the basin entropy scales with system size only in critical regimes, suggesting that informationally optimal partition of state space is achieved the system operates at the critical boundary between the disordered and ordered phases. [14]
Authors in [15] propose a hierarchical adaptive HARBN as a system comprised of distinctive ARBNs – sub-networks – connected by a unit of permanent interlinks. (Authors) investigate mean edge information and mean node information, as well as mean node degree. Internal subnetworks topology and Information measures of HARBN coevolve and reach steady-states that are specific to particular network structure. The main natural feature of ARBNs, The mean information processed in a node or a link increases with the number of interlinks introduced in to the system. The modular network shows external values of it observations when subnetworks connect with a density few times less than mean density of all links [15]
Mitchell in [16] proposes four general principles of adaptive information processing in decentralized systems together with relevance of network thinking to artificial intelligence and vice versa is the subject. [16]. [17] investigate a well known phase transition between chaotic and behaviour in RBNs in the context of the distributed computation carried out by nodes. Finding maximizations in information storage and information transfer that is coherent both sides of the critical point, explaining phase transition in in RBNs in regard to intrinsic distribution computations being undertaken [17].
Parallel algorithms for RBNs
[19] Expounds Kauffman’s description of a parallel RBN algorithm. RBN is comprised of N nodes each node i at time t has binary valued state Ci,t Є B[19]. Each node with k inputs assigned randomly from K of the N nodes, the wiring pattern is static throughout the lifetime of the network. The wiring defines neighbourhood state of a node, Vi Є Nk.[19]
References
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