The electroencephalogram (EEG) has become a widely used tool for investigating brain function. Brain signal source localization is a process of inverse calculation from sensor information (electric potentials for EEG) to the identification of multiple brain sources to obtain the locations and orientation parameters. In this paper, we describe a combination of the backpropagation neural network (BPNN) with the nonlinear least-square (NLS) method to localize two dipoles with reasonable accuracy and speed from EEG data computerized by two dipoles randomly positioned in the brain. The trained BPNN, obtains the initial values for the two dipoles through fast calculation and also avoids the influence of noise. Then the NLS method (Powell algorithm) is used to accurately estimate the two dipole parameters. In this study, we also obtain the minimum distance between the assumed dipole pair, 0.8 cm, in order to localize two sources from a smaller limited distance between the dipole pair. The present simulation results demonstrate that the combined method can allow us to localize two dipoles with high speed and accuracy, that is, in 20 seconds and with the position error of around 6.5%, and to reduce the influence of noise.

The jaw movements can be measured by estimating the position and orientation of two small permanent magnets attached on the upper and lower jaws. It is a difficult problem to estimate the positions and orientations of the magnets from magnetic field because it is a typical inverse problem. The back propagation neural networks (BPNN) are applicable to solve this problem in short processing time. But its precision is not enough to apply to practical measurement. In the other hand, precise estimation is possible by using the nonlinear least-square (NLS) method. However, it takes long processing time for iterative calculation, and the solutions may be trapped in the local minima. In this paper, we propose a precise and fast measurement system which makes use of the estimation algorithm combining BPNN with NLS method. In this method, the BPNN performs an approximate estimation of magnet parameters in short processing time, and its result is used as the initial value of iterative calculation of NLS method. The cost function is solved by Gauss-Newton iteration algorithm. Precision, processing time and noise immunity were examined by computer simulations. These results shows the proposed system has satisfactory ability to be applied to practical measurement.

Almost all land animals coordinate their behavior with circadian rhythms, matching their functions to the daily cycles of lightness and darkness that result from the rotation of the earth corresponding to 24 hours. Through external stimuli, such as dairy life activities or other sources from our environment may influence the internal rhythmicity of sleep and waking properties. However, the rhythms are regulated to keep their activity constant by homeostasis while fluctuating by incessant influences of external forces. A modeling study has been developed to identify homeostatic dynamics properties underlying a circadian rhythm activity of Sleep and Wake data measured from normal subjects, using an MA (Moving Average) model associated with Backpropagation (BP) algorithm. As results, we found that the neural network can capture the regularity and irregularity components included in the data. The order of MA neural network model depends on subjects behavior, the first two orders are usually dominant in the case of no strong external forces. The adaptive dynamic changes are evaluated by the change of weight vectors, a kind of internal representation of the trained network. The dynamic is kept in a steady state for more than 20 days at most. Identified properties reflect the subject's behavior, and hence may be useful for medical diagnoses of disorders related to circadian rhythms.