Review of Nonlinear Methods and Modelling

Borg F . Chydenius Institute - Hur Lab - 03/04/02 Biosignal Nonlinear Modelling.
Review of Nonlinear Methods and Modelling I.
Introduction.
Basic theoretical concepts.
Dynamic systems.
Continuous systems.
Discrete systems.
Chaos and attractors.
Lyapunov exponents.
Poincaré sections.
Fractal dimensions.
Entropies.
Geometry from time series.
Embedding.
The Grassberger-Procaccia algorithm.
Approximate Entropy (ApEn).
Nonlinear prediction and modelling.
Noise reduction.
Detrended fluctuation analysis (DFA).
Disgression: Fourier transform and power laws.
Surrogate data.
Diks' estimator.
Case studies.
Human balance.
Force plate design.
COP versus CM.
Stiffness hypothesis.
Random walk in quiet standing.
Disgression: Random walk with relaxation.
Analysis of EMG (ElectroMyoGram).
Neuromuscular Basics.
Modelling EMG.
Model of IAP.
The volume conductor model.
A four-layer model.
Bibliography.