10We relate the second order structure function of a time series with the power spectrum of the original variable, taking an assumption of statistical stationarity. With this approach, we find that the structure function is strongly influenced by the large scales. The large scale contribution and the contribution range are respectively 79% and 1.4 decades for a Kolmogorov -5/3 power spectrum. We show numerically that a single scale influence range, over smaller scales is about 2 decades. We argue that the structure function is not a good method to extract the scaling exponents when the data possess large energetic scales. An alternative methodology, the arbitrary order Hilbert spectral analysis which may constrain this influence within 0.3 decade, is proposed to characterize the scaling property directly in an amplitude-frequency space. An analysis of passive scalar (temperature) turbulence time series is presented to show the influence of large scale structures in real turbulence, and the efficiency of the Hilbert-based methodology. The corresponding scaling exponents ζ θ (q) provided by the Hilbert-based approach indicate that the passive scalar turbulence field may be less intermittent than what was previously believed.
A brain-computer interface (BCI) based on code modulated visual evoked potentials (c-VEP) is among the fastest BCIs that have ever been reported, but it has not yet been given a thorough study. In this study, a pseudorandom binary M sequence and its time lag sequences are utilized for modulation of different stimuli and template matching is adopted as the method for target recognition. Five experiments were devised to investigate the effect of stimulus specificity on target recognition and we made an effort to find the optimal stimulus parameters for size, color and proximity of the stimuli, length of modulation sequence and its lag between two adjacent stimuli. By changing the values of these parameters and measuring classification accuracy of the c-VEP BCI, an optimal value of each parameter can be attained. Experimental results of ten subjects showed that stimulus size of visual angle 3.8°, white, spatial proximity of visual angle 4.8° center to center apart, modulation sequence of length 63 bits and the lag of 4 bits between adjacent stimuli yield individually superior performance. These findings provide a basis for determining stimulus presentation of a high-performance c-VEP based BCI system.
In an existing brain-computer interface (BCI) based on code modulated visual evoked potentials (c-VEP), a method with which to increase the number of targets without increasing code length has not yet been established. In this paper, a novel c-VEP BCI paradigm, namely, grouping modulation with different codes that have good autocorrelation and crosscorrelation properties, is presented to increase the number of targets and information transfer rate (ITR). All stimulus targets are divided into several groups and each group of targets are modulated by a distinct pseudorandom binary code and its circularly shifting codes. Canonical correlation analysis is applied to each group for yielding a spatial filter and templates for all targets in a group are constructed based on spatially filtered signals. Template matching is applied to each group and the attended target is recognized by finding the maximal correlation coefficients of all groups. Based on the paradigm, a BCI with a total of 48 targets divided into three groups was implemented; 12 and 10 subjects participated in an off-line and a simulated online experiments, respectively. Data analysis of the offline experiment showed that the paradigm can massively increase the number of targets from 16 to 48 at the cost of slight compromise in accuracy (95.49% vs. 92.85%). Results of the simulated online experiment suggested that although the averaged accuracy across subjects of all three groups of targets was lower than that of a single group of targets (91.67% vs. 94.9%), the average ITR of the former was substantially higher than that of the later (181 bits/min vs. 135.6 bit/min) due to the large increase of the number of targets. The proposed paradigm significantly improves the performance of the c-VEP BCI, and thereby facilitates its practical applications such as high-speed spelling.
Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.
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