An alternative solution to the model structure selection problem

An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model

On Overparameterization of Nonlinear Discrete Systems

One of the subjects which has received a great deal of attention is the overparameterization problem. It is known that the dynamical performance of the model representations deteriorates if the respective model structure is too complex. This paper investigates the problem of model overparameterization. Two new types of overparameterization, fixed-point and dimension overparameterization are introduced and based upon this a new procedure for improving structure detection of nonlinear models is developed. This procedure uses all the information from the cluster cancellation and the location of the fixed points. Numerous examples are given to illustrate the ideas

Smoothing data with Local Instabilities for the Identification of Chaotic Systems.

Chaotic systems are characterised by local divergence of nearby orbits in state space. This provokes sensitive dependence on initial conditions and in turn drastically limits the accuracy of long term predictions. This has important implications in the filtering of data generated by such systems. In the present paper, the use of global smoothers for chaotic data is investigated. The ultimate objective is to be able to identify dynamically valid models from smoothed data when the identification from the original noisy data has completely failed. The objective is to produce identified models which faithfully reproduce the dynamical invariants of the original system such as the geometry of the attractors in state space, the largest Lyapunov exponent, fractal dimensions and Poincare sections. Numerical examples are included which illustrate the main points of the paper

Fine-Tuning Solution for Hybrid Inflation in Dissipative Chaotic Dynamics

We study the presence of chaotic behavior in phase space in the pre-inflationary stage of hybrid inflation models. This is closely related to the problem of initial conditions associated to these inflationary type of models. We then show how an expected dissipative dynamics of fields just before the onset of inflation can solve or ease considerably the problem of initial conditions, driving naturally the system towards inflation. The chaotic behavior of the corresponding dynamical system is studied by the computation of the fractal dimension of the boundary, in phase space, separating inflationary from non-inflationary trajectories. The fractal dimension for this boundary is determined as a function of the dissipation coefficients appearing in the effective equations of motion for the fields.Comment: 10 pages, 4 eps figures (uses epsf), Revtex. Replaced with version to match one in press Physical Review

Professionalism, Golf Coaching and a Master of Science Degree: A commentary

As a point of reference I congratulate Simon Jenkins on tackling the issue of professionalism in coaching. As he points out coaching is not a profession, but this does not mean that coaching would not benefit from going through a professionalization process. As things stand I find that the stimulus article unpacks some critically important issues of professionalism, broadly within the context of golf coaching. However, I am not sure enough is made of understanding what professional (golf) coaching actually is nor how the development of a professional golf coach can be facilitated by a Master of Science Degree (M.Sc.). I will focus my commentary on these two issues