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Content available remote Sleep EEG analysis utilizing inter-channel covariance matrices
EN
Background: Sleep is vital for normal body functions as sleep disorders can adversely affect a person. Electroencephalographic (EEG) signals indicate brain functions and have characteristic signatures for various sleep stages. These enable the use of EEG as an effective tool for in-depth studies about sleep. Sleep stages are broadly divided as rapid eye movement (REM) and non-rapid eye movement (NREM). NREM is further divided into 3 stages. The objective of the work is to distinguish the given EEG epoch as wake, NREM1, NREM2, NREM3 and REM. DREAMS Subject Database containing 5 EEG channels is used here. This work focuses on utilizing EEG by exploiting variations in inter-dependencies of different brain regions during sleep. New method: Covariance matrices of the wavelet-decomposed channels are used to obtain the variations in inter-dependencies. The feature sets are: (1) simple matrix properties(MF) like trace, determinant and norm, (2) eigen-values (E1), (3) eigen-vector corresponding to the largest eigen-value (E2) and (4) tangent vectors obtained using Riemann geometry (RG-TS). The features are input to ensemble classifier with bagging. Subject-specific, All-subjects-combined and Leave-one-subject-out methods of analysis are carried out. Results: In all methods of analysis, RG-TS features give maximum accuracy (80.05%, 83.05% and 61.79%), closely followed by E1 (79.49%, 77.14% and 58.34%). Comparison with existing method: The proposed method obtains higher and/or comparable accuracy. This work also ensures no biasing of classifier due to unequal class distribution. Conclusion: The performances of RG-TS and E1 features reveal that the changes in interdependencies of pre-frontal and occipital lobe along with the central lobe can be used to distinguish the different sleep stages.
EN
The DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) was presented in Kaminski (2009). The method has been developed for the determination of displacements and strains of engineering objects in unstable reference systems, as well as for examining the stability of reference points. The DiSTFAG (Gross errors) method presented in the paper is the extension of the DiSTFA method making it robust to gross errors. Theoretical considerations have been supplemented with an example of a practical application on a simulated 3D surveying network.
PL
W niniejszej pracy zaproponowano uodpornienie metody DiSTFA (Displacements and Strains Rusing Transformation and Free Adjustment) na błędy grube. Metodę DiSTFA opracowano do wyznaczania przemieszczeń i odkształceń obiektów inżynierskich w niestabilnych układach odniesienia jak również badania stałości punktów dostosowania. Metoda DiSTFAG jest rozwinięciem metody DiSTFA uwzględniającym w rozwiązaniu obserwacje obarczone błędami grubymi. Teoretyczne rozważania uzupełniono przykładem praktycznego zastosowania na symulowanej, trójwymiarowej osnowie geodezyjnej.
EN
The paper presents the results of research on the DiSTFA method (Displacements and Strains using Transformation and Free Adjustment) for the determination of displacement and strains of a surface determined in unstable reference systems. Additionally, covariance matrices were introduced to assess the accuracy of estimation results. The theoretical discussion includes an example of its application in a simulated, three-dimensional geodetic network. The obtained results encourage further, more detailed analysis of real geodetic networks.
PL
W niniejszej pracy przedstawiono wyniki badań metody DiSTFA (Displacements and Streins with usage Transformation and Free Adjustnent) wyznaczania przemieszczeń i odkształceń powierzchni wyznaczanych w niestabilnych układach odniesienia. Wyprowadzono także macierze kowariancji umożliwiające ocenę dokładności wyników estymacji. Rozważania teoretyczne uzupełniono przykładem zastosowania na symulowanej, trójwymiarowej sieci geodezyjnej. Uzyskane wyniki zachęcają do przeprowadzenia dalszych, bardziej szczegółowych analiz na rzeczywistych sieciach geodezyjnych.
EN
Results of numerical simulations of a portfolio selection model with information cost are presented. Simulations are based on the real data from the Warsaw Stock Exchange. The results show that buying the information according to the presented model may lead to an essential reduction of investment risk depending on the required level of return. If the return level is not too high, reduction of risk really takes place.
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