William Wilson

Aquil D. Jones, Gideon Simpson, William Wilson

Weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers, while persisting for all finite time. It has been conjectured by Bourgain that the 2D defocusing nonlinear Schrödinger equation (NLS) on the torus has this dynamic, and several analytical and numerical studies have worked towards addressing this point. In the process of studying the conjecture, Colliander, Keel, Staffilani, Takaoka, and Tao introduced a "toy model" dynamical system as an approximation of NLS, which has been subsequently studied numerically. In this work, we formulate and examine several numerical schemes for integrating this model equation. The model has two invariants, and our schemes aim to conserve at least one of them. We prove convergence in some cases, and our numerical studies show that the schemes compare favorably to others, such as Trapezoidal Rule and fixed step fourth order Runge-Kutta. The preservation of the invariants is particularly important in the study of weak turbulence as the energy transfer tends to occur on long time scales.

William Wilson, Phil Birkin, Uwe Aickelin

The search for patterns or motifs in data represents an area of key interest to many researchers. In this paper we present the Motif Tracking Algorithm, a novel immune inspired pattern identification tool that is able to identify variable length unknown motifs which repeat within time series data. The algorithm searches from a neutral perspective that is independent of the data being analysed and the underlying motifs. In this paper we test the flexibility of the motif tracking algorithm by applying it to the search for patterns in two industrial data sets. The algorithm is able to identify a population of meaningful motifs in both cases, and the value of these motifs is discussed.

William Wilson, Uwe Aickelin

Memory can be defined as the ability to retain and recall information in a diverse range of forms. It is a vital component of the way in which we as human beings operate on a day to day basis. Given a particular situation, decisions are made and actions undertaken in response to that situation based on our memory of related prior events and experiences. By utilising our memory we can anticipate the outcome of our chosen actions to avoid unexpected or unwanted events. In addition, as we subtly alter our actions and recognise altered outcomes we learn and create new memories, enabling us to improve the efficiency of our actions over time. However, as this process occurs so naturally in the subconscious its importance is often overlooked.