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The most important result of Shaw et al. [1969] is the representation of each component of the vertical-deflection vector as a homogeneous nonisotropic random process when starting from a homogeneous and isotropic random process of gravity anomaly via the fiat Vening-Meinesz formula. Here our purpose is to show that all formulas of Shaw et al. are correct but that the

The difficulty associated with processing and understanding the high dimensionality of electroencephalogram (EEG) data requires developing efficient and robust compression algorithms. In this paper, different lossless compression techniques of single and multichannel EEG data, including Huffman coding, arithmetic coding, Markov predictor, linear predictor, context-based error modeling, multivariate autoregression (MVAR), and a low complexity bivariate model have been examined and their performances have been compared. Furthermore, a high compression algorithm named general MVAR and a modified context-based error modeling for multichannel EEG have been proposed. The resulting compression algorithm produces a higher relative compression ratio of 70.64% on average compared with the existing methods, and in some cases, it goes up to 83.06%. The proposed methods are designed to compress a large amount of multichannel EEG data efficiently so that the data storage and transmission bandwidth can be effectively used. These methods have been validated using several experimental multichannel EEG recordings of different subjects and publicly available standard databases. The satisfactory parametric measures of these methods, namely percent-root-mean square distortion, peak signal-to-noise ratio, root-mean-square error, and cross correlation, show their superiority over the state-of-the-art compression methods.

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