A comparison between healthy and neurological disorders patients using nonlinear dynamic tools
In this paper, we evaluate the differences between Healthy subjects (HS), Parkinson Disease (PDS) subjects, and Epileptic subjects (EBS - Epileptic subject between seizures and ES - epileptic subjects in seizure) by computing some linear, statistic and non-linear features, such as: correlation dimension, maximum Lyapunov exponent and Hurst coefficient. A comparison is made between PDS, EBS, ES and HS groups using non-linear parameters. The EEG data are wavelet multiresolution decomposed into subbands of interest (alpha 8-12 Hz, beta 13-30 Hz, delta 0-4 Hz, theta 4-8 Hz, gamma 30-60 Hz). We applied rescaled range method to estimate the Hurst coefficient of the decomposed signals, with different types of wavelet transforms. The results obtained using the maximum Lyapunov exponent do not highlight very well differences between the 4 groups analyzed (HS, PDS, EBS and ES) but using Hurst coefficient we can make a very good differentiation of EEG signals. The results show that the Hurst coefficient is significant different for delta and theta rhythms extracted from the EEG signal in case of the healthy subjects compared with PDS or EBS subjects. The Hurst coefficient for healthy subjects has a value higher than 0.5 and for PD subjects or epileptic subject between seizures has a value lower than 0.5. Hence, the non-linear parameters such as Hurst coefficient can help in EEG interpretation and in neurological disorders diagnosis.
Classification of the stages of Parkinson’s disease using novel higher-order statistical features of EEG signals
Parkinson’s disease (PD) is the second most common neurodegenerative disease after Alzheimer’s disease. This progressive disorder is mostly known by its signature symptoms of bradykinesia and rest tremor. The progression of PD is divided into five stages by the Hoehn and Yahr (H&Y) rating scale. The diagnosis of PD and its progress is of utmost importance in providing an effective treatment plan and to manage the disease and maintain quality of life. The goal of this study is to introduce several new higher-order features and use them with a combination of existing lower and higher-order statistical features of EEG signals to diagnose the stages of PD. In this paper, we use the total of 30 higher-order and six lower-order (first and second-order) statistical features extracted from EEG signals of 20 PD patients, along with 20 age-matched healthy control subjects, recorded during rest state, to perform the classification. We use a range of classification methods, and although other methods may have higher overall accuracy, we see that due to our unbalanced dataset, RUS Boosted trees ensemble has the highest sensitivity for this application (highest performance for the late PD class). It is also shown that the accuracy of the classification is improved significantly by using the newly developed features.
Mathematical Modeling of Scour and Deposition
Electronic computers are opening up the field of sedimentation engineering by permitting the analysis of problems which heretofore have required too much time and effort. Movable stream bed profiles are being calculated in addition to water surface profiles. The initial gradation of sediment material in the stream bed may be prescribed to facilitate the calculation of an armor layer. This gradation is continually changed by the computer program in response to sediment particles being deposited on the stream bed and material on the stream bed being removed to satisfy transport capacity. Hydraulic sorting of sediment by grain size is accomodated. The stream bed does not have to be represented by a single grain size. Retardance of motion because of armor layer is calculated.