The active selfish herd.

The selfish herd hypothesis provides an explanation for group aggregation via the selfish avoidance of predators. Conceptually, and as was first proposed, this movement should aim to minimise the danger domain of each individual. Whilst many reasonable proxies have been proposed, none have directly sought to reduce the danger domain. In this work we present a two dimensional stochastic model that actively optimises these domains. The individuals' dynamics are determined by sampling the space surrounding them and moving to achieve the largest possible domain reduction. Two variants of this idea are investigated with sampling occurring either locally or globally. We simulate our models and two of the previously proposed benchmark selfish herd models: k-nearest neighbours (kNN); and local crowded horizon (LCH). The resulting positions are analysed to determine the benefit to the individual and the group's ability to form a compact group. To do this, the group level metric of packing fraction and individual level metric of domain size are observed over time for a range of noise levels. With these measures we show a clear stratification of the four models when noise is not included. kNN never resulted in centrally compacted herd, while the local active selfish model and LCH did so with varying levels of success. The most centralised groups were achieved with our global active selfish herd model. The inclusion of noise improved aggregation in all models. This was particularly so with the local active selfish model with a change to ordering of performance so that it marginally outperformed LCH in aggregation. By more closely following Hamilton's original conception and aligning the individual's goal of a reduced danger domain with the movement it makes increased cohesion is observed, thus confirming his hypothesis, however, these findings are dependent on noise. Moreover, many features originally conjectured by Hamilton are also observed in our simulations.

Optimal Shadowing Filter for a Positioning and Tracking Methodology with Limited Information.

Positioning and tracking a moving target from limited positional information is a frequently-encountered problem. For given noisy observations of the target's position, one wants to estimate the true trajectory and reconstruct the full phase space including velocity and acceleration. The shadowing filter offers a robust methodology to achieve such an estimation and reconstruction. Here, we highlight and validate important merits of this methodology for real-life applications. In particular, we explore the filter's performance when dealing with correlated or uncorrelated noise, irregular sampling in time and how it can be optimised even when the true dynamics of the system are not known.