We propose an alternative B-spline approach for empirical mode decompositions for nonlinear and nonstationary signals. Motivated by this new approach, we derive recursive formulas of the Hilbert transform of B-splines and discuss Euler splines as spline intrinsic mode functions in the decomposition. We also develop the Bedrosian identity for signals having vanishing moments. We present numerical implementations of the B-spline algorithm for an earthquake signal and compare the numerical performance of this approach with that given by the standard empirical mode decomposition. Finally, we discuss several open mathematical problems related to the empirical mode decomposition.

Cardiovascular diseases (CVDs) are the leading causes of death worldwide, and defects in mitochondrial function contribute largely to the occurrence of CVDs. Recent studies suggest that sirtuin 3 (SIRT3), the mitochondrial NAD+-dependent deacetylase, may regulate mitochondrial function and biosynthetic pathways such as glucose and fatty acid metabolism and the tricarboxylic acid (TCA) cycle, oxidative stress, and apoptosis by reversible protein lysine deacetylation. SIRT3 regulates glucose and lipid metabolism and maintains myocardial ATP levels, which protects the heart from metabolic disturbances. SIRT3 can also protect cardiomyocytes from oxidative stress-mediated cell damage and block the development of cardiac hypertrophy. Recent reports show that SIRT3 is involved in the protection of several heart diseases. This review discusses the progress in SIRT3-related research and the role of SIRT3 in the prevention and treatment of CVDs.

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Abstract-As an effective method for copyright protection of digital products against illegal usage, watermarking in wavelet domain has recently received considerable attention due to the desirable multiresolution property of wavelet transform. In general, images can be represented with different resolutions by the wavelet decomposition, analogous to the human visual system (HVS). Usually, human eyes are insensitive to image singularities revealed by different high frequency subbands of wavelet decomposed images. Hence, adding watermarks into these singularities will improve the imperceptibility that is a desired property of a watermarking scheme. That is, the capability for revealing singularities of images plays a key role in designing wavelet-based watermarking algorithms. Unfortunately, the existing wavelets have a limited ability in revealing singularities in different directions. This motivates us to construct new wavelet filter banks that can reveal singularities in all directions. In this paper, we utilize special symmetric matrices to construct the new nontensor product wavelet filter banks, which can capture the singularities in all directions. Empirical studies will show their advantages of revealing singularities in comparison with the existing wavelets. Based upon these new wavelet filter banks, we, therefore, propose a modified significant difference watermarking algorithm. Experimental results show its promising results.Index Terms-Nontensor product wavelet filter, singularities, watermarking.

Nitrification inhibitors (NIs) 3,4-dimethylpyrazole phosphate (DMPP) and dicyandiamide (DCD) have been used extensively to improve nitrogen fertilizer utilization in farmland. However, their comparative effects on ammonia-oxidizing bacteria (AOB) and ammonia-oxidizing archaea (AOA) in agricultural soils are still unclear. Here, we compared the impacts of these two inhibitors on soil nitrification, AOA and AOB abundance as well as their community structure in a vegetable soil by using real-time PCR and terminal restriction fragment length polymorphism (T-RFLP). Our results showed that urea application significantly increased the net nitrification rates, but were significantly inhibited by both NIs, and the inhibitory effect of DMPP was significantly greater than that of DCD. AOB growth was more greatly inhibited by DMPP than by DCD, and the net nitrification rate was significantly related to AOB abundance, but not to AOA abundance. Application of urea and NIs to soil did not change the diversity of the AOA community, with the T-RFs remaining in proportions that were similar to control soils, while the community structure of AOB exhibited obvious shifts within all different treatments compared to the control. Phylogenetic analysis showed that all AOA sequences fell within group 1.1a and group 1.1b, and the AOB community consisted of Nitrosospira cluster 3, cluster 0, and unidentified species. These results suggest that DMPP exhibited a stronger inhibitory effect on nitrification than DCD by inhibiting AOB rather than AOA.