AN ADAPTIVE EXTENDED KALMAN FILTERING APPROACH TO NONLINEAR DYNAMIC GENE REGULATORY NETWORKS VIA SHORT GENE EXPRESSION TIME SERIES

Abstract

Sleep spindles, which are believed to have important role of re- inforcing the sleep duration, are the characteristic wave shapes that are seen in non-REM sleep stage. Detecting and analyzing the wave forms of spin- dles as well as determining the areas and durations of sleep spindles are quite important to understand the sleeping process thoroughly. However, the fact that spindles have temporary regime features and lower amplitudes compared to the background EEG signals makes resolving and distinguishing between them difficult. Although there have been extensive research on the decompo- sition of EEG signals and about the general characteristics of the spindles, the existing studies do not decompose the components in a dynamic fashion. This study takes this argument as its starting point and comes up with a methodol- ogy to detect the spindles in the sleep EEG. In particular, this study separates EEG signals into trend and cycle components via frequency analysis, where the methodology allows for system parameters and the components to be es- timated simultaneously. Since the methodology allows for the parameters to vary over time, observing the time patterns of the estimated parameters have the potential to reveal further information about the sleep process.