A comparative study on global wavelet and polynomial models for nonlinear regime-switching systems

A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems

Time-varying parametric modelling and time-dependent spectral characterisation with applications to EEG signals using multi-wavelets

A new time-varying autoregressive (TVAR) modelling approach is proposed for nonstationary signal processing and analysis, with application to EEG data modelling and power spectral estimation. In the new parametric modelling framework, the time-dependent coefficients of the TVAR model are represented using a novel multi-wavelet decomposition scheme. The time-varying modelling problem is then reduced to regression selection and parameter estimation, which can be effectively resolved by using a forward orthogonal regression algorithm. Two examples, one for an artificial signal and another for an EEG signal, are given to show the effectiveness and applicability of the new TVAR modelling method

The economic basis of periodic enzyme dynamics

Periodic enzyme activities can improve the metabolic performance of cells. As an adaptation to periodic environments or by driving metabolic cycles that can shift fluxes and rearrange metabolic processes in time to increase their efficiency. To study what benefits can ensue from rhythmic gene expression or posttranslational modification of enzymes, I propose a theory of optimal enzyme rhythms in periodic or static environments. The theory is based on kinetic metabolic models with predefined metabolic objectives, scores the effects of harmonic enzyme oscillations, and determines amplitudes and phase shifts that maximise cell fitness. In an expansion around optimal steady states, the optimal enzyme profiles can be computed by solving a quadratic optimality problem. The formulae show how enzymes can increase their efficiency by oscillating in phase with their substrates and how cells can benefit from adapting to external rhythms and from spontaneous, intrinsic enzyme rhythms. Both types of behaviour may occur different parameter regions of the same model. Optimal enzyme profiles are not passively adapted to existing substrate rhythms, but shape them actively to create opportunities for further fitness advantage: in doing so, they reflect the dynamic effects that enzymes can exert in the network. The proposed theory combines the dynamics and economics of metabolic systems and shows how optimal enzyme profiles are shaped by network structure, dynamics, external rhythms, and metabolic objectives. It covers static enzyme adaptation as a special case, reveals the conditions for beneficial metabolic cycles, and predicts optimally combinations of gene expression and posttranslational modification for creating enzyme rhythms

Identification of time-varying systems using multiresolution wavelet models

Identification of linear and nonlinear time-varying systems is investigated and a new wavelet model identification algorithm is introduced. By expanding each time-varying coefficient using a multiresolution wavelet expansion, the time-varying problem is reduced to a time invariant problem and the identification reduces to regressor selection and parameter estimation. Several examples are included to illustrate the application of the new algorithm