Time complexity analysis of the stochastic diffusion search

The Stochastic Diffusion Search algorithm -an integral part of Stochastic Search Networks is investigated. Stochastic Diffusion Search is an alternative solution for invariant pattern recognition and focus of attention. It has been shown that the algorithm can be modelled as an ergodic, finite state Markov Chain under some non-restrictive assumptions. Sub-linear time complexity for some settings of parameters has been formulated and proved. Some properties of the algorithm are then characterised and numerical examples illustrating some features of the algorithm are presented.

Learning in neural networks and stochastic approximation methods with averaging

The problem of adjusting the weights (learning) in multilayer feedforward neural networks (NN) is known to be of a high importance when utilizing NN techniques in various practical applications. The learning procedure is to be performed as fast as possible and in a simple computational fashion, the two requirements which are usually not satisfied practically by the methods developed so far. Moreover, the presence of random inaccuracies are usually not taken into account. In view of these three issues, an alternative stochastic approximation approach discussed in the paper, seems to be very promising.

Stability criteria for the contextual emergence of macrostates in neural networks

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations of their microstates. We compare their stochastic stability criterion with a deterministic stability criterion based on the ergodic theory of dynamical systems, recently proposed for the scheme of contextual emergence and applied to particular inter-level relations in neuroscience. Stochastic and deterministic stability criteria for macrostates rely on macro-level contexts, which make them sensitive to differences between different macro-levels.

Small-world effects in lattice stochastic diffusion search

Stochastic Diffusion Search is an efficient probabilistic bestfit search technique, capable of transformation invariant pattern matching. Although inherently parallel in operation it is difficult to implement efficiently in hardware as it requires full inter-agent connectivity. This paper describes a lattice implementation, which, while qualitatively retaining the properties of the original algorithm, restricts connectivity, enabling simpler implementation on parallel hardware. Diffusion times are examined for different network topologies, ranging from ordered lattices, over small-world networks to random graphs.

Competing edge networks

We introduce a model for a pair of nonlinear evolving networks, defined over a common set of vertices, sub ject to edgewise competition. Each network may grow new edges spontaneously or through triad closure. Both networks inhibit the other’s growth and encourage the other’s demise. These nonlinear stochastic competition equations yield to a mean field analysis resulting in a nonlinear deterministic system. There may be multiple equilibria; and bifurcations of different types are shown to occur within a reduced parameter space. This situation models competitive peer-to-peer communication networks such as BlackBerry Messenger displacing SMS; or instant messaging displacing emails.

Interventions in social networks: impact on mood and network dynamics

Results from two studies on longitudinal friendship networks are presented, exploring the impact of a gratitude intervention on positive and negative affect dynamics in a social network. The gratitude intervention had been previously shown to increase positive affect and decrease negative affect in an individual but dynamic group effects have not been considered. In the first study the intervention was administered to the whole network. In the second study two social networks are considered and in each only a subset of individuals, initially low/high in negative affect respectively received the intervention as `agents of change'. Data was analyzed using stochastic actor based modelling techniques to identify resulting network changes, impact on positive and negative affect and potential contagion of mood within the group. The first study found a group level increase in positive and a decrease in negative affect. Homophily was detected with regard to positive and negative affect but no evidence of contagion was found. The network itself became more volatile along with a fall in rate of change of negative affect. Centrality measures indicated that the best broadcasters were the individuals with the least negative affect levels at the beginning of the study. In the second study, the positive and negative affect levels for the whole group depended on the initial levels of negative affect of the intervention recipients. There was evidence of positive affect contagion in the group where intervention recipients had low initial level of negative affect and contagion in negative affect for the group where recipients had initially high level of negative affect.