The inverse CDFs of IMFs, (A) IMF 2 of X and of the added noise channel; (B) IMF 5 of Z and of the added noise channel.

<p>Note that the IMF 5 of Z refers to the sine wave component of 26 Hz. It is clear that the significant information-bearing component (red solid in (B)) is clearly different from the IMF obtained from the noise reference (blue dash in (B)) in terms of inverse CDF, whereas the IMF without significant information content (red solid in (A)) almost completely overlaps with the noise IMF (blue dash in (A)).</p

Discrimination of two perpetual conditions based on the identified information-bearing IMFs by (A) the proposed approach and (B) the method in [12].

<p>It is clear that the IMF 6 in both methods show the most significant difference in power of two conditions, yet with a larger separation for the proposed method (<i>p</i><0.01). The error bars denote the SEM.</p

Performance of the proposed approach at different signal-noise-ratios (SNRs).

<p>SNR is systematically varied by changing the variance of the white noise superimposed in the trivariate data. At each SNR level, a data set of 100 trials is generated. The proposed method is applied to each trial to measure the signal identification performance, as quantified by both Type I error and Type II error.</p

Statistical significance of first six IMFs for synthetic time series [X Y Z] by MEMD based on the method in [12].

<p>In each panel, the energy of IMFs is plotted as a function of the logarithm of period, where the two dotted curves indicate 95% confidence intervals, corresponding to the upper and lower boundaries of the energy spread function, and each symbol ‘*’ refers to an IMF. The false identifications frequently occur in all three channels, e.g. all IMFs are identified significant in three channels.</p

Statistical identification of significant IMFs by the proposed method when the pink noise (1/f) in the data is different from the white noise in the reference channels.

<p>Our results show that the designed components (in bold) are all still correctly identified.</p

MEMD decomposition of composite time series consisting of the original 3-channel synthetic data [X Y Z] and noise reference channels.

<p>For the purpose of clarity, only one noise channel is shown. All the sine waves with distinct frequencies (red) are correctly obtained via MEMD. At the same time, the IMFs obtained from the added noise channel provide the reference for statistical identification of significant IMFs.</p

MEMD decomposition of the trivariate dada, consisting of three noise time series: the white noise (left top), the noise with positive long-range dependence (left middle) and the noise with negative long-range dependence (left bottom).

<p>The left panels show the power spectra of IMFs from the each noise (the sampling rate of 1000 Hz), in which the number denotes the order of IMF components. The right panel shows the inverse CDFs of IMF 3 from three different noise time series. Thanks to the rank-order statistics used in the estimation, there is an excellent match among three inverse CDFs, indicating that our approach is robust to the different types of noises.</p

Examples of decomposition from two trials of LFP time series, one is from the invisible condition (Left), and another from the visible condition (Right).

<p>0 indicates the surrounding onset. Our approach is able to identify the information-bearing IMFs, which are highlighted in red.</p

Organic Fouling of Graphene Oxide Membranes and Its Implications for Membrane Fouling Control in Engineered Osmosis

This study provides experimental evidence to mechanistically understand some contradicting effects of the characteristic properties of graphene oxide (GO), such as the high hydrophilicity, negative charge, strong adsorption capability, and large surface area, on the antifouling properties of GO membranes. Furthermore, this study demonstrates the effectiveness of forming a dense GO barrier layer on the back (i.e., porous) side of an asymmetric membrane for fouling control in pressure-retarded osmosis (PRO), an emerging engineered osmosis process whose advancement has been much hindered due to the severe irreversible fouling that occurs as foulants accumulate inside the porous membrane support. In the membrane fouling experiments, protein and alginate were used as model organic foulants. When operated in forward osmosis mode, the GO membrane exhibited fouling performance comparable with that of a polyamide (PA) membrane. Analysis of the membrane adsorption capacity showed that, likely due to the presence of hydrophobic regions in the GO basal plane, the GO membrane has an affinity toward organic foulants 4 to 5 times higher than the PA membrane. Such a high adsorption capacity along with a large surface area, however, did not noticeably aggravate the fouling problem. Our explanation for this phenomenon is that organic foulants are adsorbed mainly on the basal plane of GO nanosheets, and water enters the GO membrane primarily around the oxidized edges of GO, making foulant adsorption not create much hindrance to water flux. When operated in PRO mode, the GO membrane exhibited much better antifouling performance than the PA membrane. This is because unlike the PA membrane for which foulants can be easily trapped inside the porous support and hence cause severe irreversible fouling, the GO membrane allows the foulants to accumulate primarily on its surface due to the sealing effect of the GO layer assembled on the porous side of the asymmetric membrane support. Results from the physical cleaning experiments further showed that the water flux of GO membranes operated in PRO mode can be sufficiently restored toward its initial prefouling level

Fabrication of Graphene-Based Xerogels for Removal of Heavy Metal Ions and Capacitive Deionization

With a rapid increase of population, delivering clean and potable water to humans has been an impending challenge. Here, we report a green method for the preparation of graphene–chitosan–Mn₃O₄ (Gr–Cs–Mn₃O₄) composites, where Gr–Cs hydrogels are first prepared from the self-assembly of chitosan with graphene oxide (GO) nanosheets; then Gr–Cs–Mn₃O₄ composites are obtained by oxidizing Mn­(II) ions which are adsorbed by Gr–Cs hydrogels. The effects of pH and mass ratio of GO to Cs on sorption of different ions are investigated. Enhanced capacitive deionization performance of Gr–Cs–Mn₃O₄ composites was also demonstrated. The resultant Gr–Cs–Mn₃O₄ composites exhibit a hierarchical porous structure with a specific surface area of 240 m²/g and excellent specific capacity of 190 F/g, much higher than those of pristine reduced graphene oxide electrodes. Distinguished electrochemical capacity and low inner resistance endow Gr–Cs–Mn₃O₄ composites with outstanding specific electrosorptive capacity of 12.7 mg/g