A note on computing with Kolmogorov Superpositions without iterations

We extend Kolmogorov's Superpositions to approximating arbitrary continuous functions with a noniterative approach that can be used by any neural network that uses these superpositions. Our approximation algorithm uses a modified dimension reducing function that allows for an increased number of summands to achieve an error bound commensurate with that of r iterations for any r. This new variant of Kolmogorov's Superpositions improves upon the original parallelism inherent in them by performing highly distributed parallel computations without synchronization. We note that this approach makes implementation much easier and more efficient on networks of modern parallel hardware, and thus makes it a more practical tool.

Reducing complexity in an agent based reaction model-Benefits and limitations of simplifications in relation to run time and system level output

Agent based modelling is a methodology for simulating a variety of systems across a broad spectrum of fields. However, due to the complexity of the systems it is often impossible or impractical to model them at a one to one scale. In this paper we use a simple reaction rate model implemented using the FLAME framework to test the impact of common methods for reducing model complexity such as reducing scale, increasing iteration duration and reducing message overheads. We demonstrate that such approaches can have significant impact on simulation runtime albeit with increasing risk of aberrant system behaviour and errors, as the complexity of the model is reduced.