Perturbation bounds for singular spaces, in particular Wedin’s sin Θ theorem, are a fundamental tool in many fields including high-dimensional statistics, machine learning and applied mathematics. In ...this paper, we establish separate perturbation bounds, measured in both spectral and Frobenius sin Θ distances, for the left and right singular subspaces. Lower bounds, which show that the individual perturbation bounds are rate-optimal, are also given.
The new perturbation bounds are applicable to a wide range of problems. In this paper, we consider in detail applications to low-rank matrix denoising and singular space estimation, high-dimensional clustering and canonical correlation analysis (CCA). In particular, separate matching upper and lower bounds are obtained for estimating the left and right singular spaces. To the best of our knowledge, this is the first result that gives different optimal rates for the left and right singular spaces under the same perturbation.
PM2.5 pollution has become one of the most serious air pollution in China. The cross-correlations between PM2.5 concentration and meteorological factors (i.e., temperature, air pressure, relative ...humidity and wind speed) in Beijing and Hong Kong are discussed in this paper. We use the multifractal detrended cross-correlation analysis (MF-DCCA) to analyze the cross-correlations, and study further the asymmetric characteristics of cross-correlations by multifractal asymmetric detrended cross-correlation analysis (MF-ADCCA). The experimental results show that the cross-correlations between PM2.5 concentration and four meteorological factors are multifractal and anti-persistent, and the strength of multifractality of Beijing is stronger than that of Hong Kong. Meanwhile, the cross-correlations between PM2.5 concentration and meteorological factors are asymmetric, and the asymmetric cross-correlations are multifractal.
•The cross-correlations between PM2.5 and meteorological factors are discussed by MF-DCCA and MF-ADCCA.•The cross-correlations are significant and display the property of anti-persistent.•The cross-correlations are asymmetric, and the asymmetric cross-correlations are multifractal.•The cross-correlations are useful for detecting relations in environmental system.
This letter investigates the secrecy performance of the classical Wyner’s wiretap model, where the main channel and eavesdropper channel experience correlated Formula Omitted-Formula Omitted fading. ...Novel and exact expressions for the average secrecy capacity and secrecy outage probability are derived for the considered realistic scenario. The effect of correlation has been studied on the secrecy performance. Useful insights into the system performance are obtained through the asymptotic analysis.
Hybrid lateral closed-wedge high tibial osteotomy (HBHTO) carries certain advantages over medial open-wedge high tibial osteotomy (OWHTO). We investigated the potential difference in the required ...correction angle between HBHTO and OWHTO to achieve an equal amount of whole lower-extremity alignment correction, retrospectively analyzing the preoperative plain radiographic images of 100 patients. The medial proximal tibial angle (MPTA), joint line convergence angle (JLCA), mechanical lateral distal femoral angle (mLDFA), hip–knee–ankle axis (HKA), length of the tibia, width of the tibial plateau, length of the lower limb (leg length), and location of the center of deformity (CD) were measured. Differences in the required correction angle at the hinge point between the two techniques (CAD) were compared, and correlation analysis was performed to reveal the influential factors. The mean difference in CAD between HBHTO and OWHTO was 0.78 ± 0.22 (0.4~1.5)°, and mean WBL position change per correction angle was 3.9 ± 0.3 (3.0~4.6)% in HBHTO and 4.1 ± 0.3 (3.1~4.7)% in OWHTO. Correlation analysis revealed a strong positive correlation between CAD and HKA. mLDFA, JLCA, MPTA, leg length, OWCD, HBCD, and HCD were also significantly correlated with CAD. HBHTO required a 5.6% larger correction angle at the hinge point to achieve the same amount of alignment correction as OWHTO.
•Exogenous sucrose promoted grape berry ripening.•Sugar metabolism in grape berry was altered by exogenous application of sucrose.•Hexokinase inhibitor had a similar function to sucrose in modifying ...berry composition.•Sucrose application promotes anthocyanin and proanthocyanidin repartitioning during grape ripening.
Sugar and its metabolism play a critical role in fruit quality and determine the accumulation characteristics of secondary metabolites. In this study, the dynamic changes in anthocyanin and proanthocyanidin (PA) accumulation during exogenous sugar application were investigated throughout the grape ripening stage, and the underlying biosynthesis mechanism was monitored. Results showed that exogenous sucrose and N-acetyl-d-glucosamine (hexokinase inhibitor, HI) promoted grape berry ripening. Exogenous application of sucrose and HI significantly increased the levels of soluble sugars and anthocyanins, while significantly decreased the levels of acids and PAs in grape berries. Exogenous sucrose and HI activated the transcription of the VvSPS, VvAI and VvNI genes but inhibited the transcription of VvHXK gene to alter sugar metabolism. Notably, the accumulation of anthocyanin compounds, particularly peonidin derivatives, significantly increased in the sucrose- and HI-treated berries by upregulating the transcription of anthocyanin biosynthesis genes, including VvCHS2, VvF3′H, VvDFR, VvLDOX, and VvUFGT, whereas the accumulation of PA units, such as (‒)-epicatechin, (+)-gallocatechin, and (‒)-epigallocatechin, was repressed by downregulating the transcription of the VvLAR2 and VvANR genes, which boosted anthocyanin and PA reprogramming. These results provide preliminary information on how to modulate the biosynthesis and accumulation of anthocyanins and PAs in grape berries by the exogenous application of sucrose and thus, to modify berry composition.
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