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Functional principal component analysis (FPCA) has been widely used to capture major modes of variation and reduce dimensions in functional data analysis. However, standard FPCA based on the sample covariance estimator does not work well if the data exhibits heavy‐tailedness or outliers. To address this challenge, a new robust FPCA approach based on a functional pairwise spatial sign (PASS) operator, termed PASS FPCA, is introduced. We propose robust estimation procedures for eigenfunctions and eigenvalues. Theoretical properties of the PASS operator are established, showing that it adopts the same eigenfunctions as the standard covariance operator and also allows recovering ratios between eigenvalues. We also extend the proposed procedure to handle functional data measured with noise. Compared to existing robust FPCA approaches, the proposed PASS FPCA requires weaker distributional assumptions to conserve the eigenspace of the covariance function. Specifically, existing work are often built upon a class of functional elliptical distributions, which requires inherently symmetry. In contrast, we introduce a class of distributions called the weakly functional coordinate symmetry (weakly FCS), which allows for severe asymmetry and is much more flexible than the functional elliptical distribution family. The robustness of the PASS FPCA is demonstrated via extensive simulation studies, especially its advantages in scenarios with nonelliptical distributions. The proposed method was motivated by and applied to analysis of accelerometry data from the Objective Physical Activity and Cardiovascular Health Study, a large‐scale epidemiological study to investigate the relationship between objectively measured physical activity and cardiovascular health among older women. [ABSTRACT FROM AUTHOR]

Verticillium wilt is a severe plant disease that causes massive losses in multiple crops. Increasing the plant resistance to Verticillium wilt is a critical challenge worldwide. Here, we report that the hemibiotrophic Verticillium dahliae -secreted Asp f2-like protein VDAL causes leaf wilting when applied to cotton leaves in vitro but enhances the resistance to V. dahliae when overexpressed in Arabidopsis or cotton without affecting the plant growth and development. VDAL protein interacts with Arabidopsis E3 ligases plant U-box 25 (PUB25) and PUB26 and is ubiquitinated by PUBs in vitro. However, VDAL is not degraded by PUB25 or PUB26 in planta. Besides, the pub25 pub26 double mutant shows higher resistance to V. dahliae than the wild-type. PUBs interact with the transcription factor MYB6 in a yeast two-hybrid screen. MYB6 promotes plant resistance to Verticillium wilt while PUBs ubiquitinate MYB6 and mediate its degradation. VDAL competes with MYB6 for binding to PUBs, and the role of VDAL in increasing Verticillium wilt resistance depends on MYB6. Taken together, these results suggest that plants evolute a strategy to utilize the invaded effector protein VDAL to resist the V. dahliae infection without causing a hypersensitive response (HR); alternatively, hemibiotrophic pathogens may use some effectors to keep plant cells alive during its infection in order to take nutrients from host cells. This study provides the molecular mechanism for plants increasing disease resistance when overexpressing some effector proteins without inducing HR, and may promote searching for more genes from pathogenic fungi or bacteria to engineer plant disease resistance. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) can measure ground motions with a centimetre-level accuracy using only one receiver. It has been widely used in earthquake monitoring and earthquake early warning (EEW) systems. However, traditional PPP highly depends on well-established and robust internet infrastructure for data communication. Along with the broadcast ephemeris, the orbit and clock corrections transmitted by the B2b signals of BeiDou Navigation Satellite System (BDS) can be used to recover the precise products of GPS and BDS. Since the B2b products, namely the satellite state parameter messages, are accessible even without internet infrastructure, PPP with B2b signals is more suitable for real-time applications. This study witnesses the application of PPP with B2b products in seismic monitoring for the first time. The shake table experiments demonstrate that PPP with B2b can reach a millimetre-level accuracy in horizontal in earthquake monitoring for GPS-only, BDS-only and GPS/BDS combination. The application to the 2021 M w 7.4 Maduo earthquake shows that the accuracies of seismic displacements derived from GPS-only PPP with B2b products are 1.7, 2.4 and 1.7 cm in east, north and vertical components, compared with those from GPS-only PPP with final precise products. We therefore conclude that PPP with B2b products has a promising prospect in seismogeodesy and related applications such as EEW and rapid hazard response. [ABSTRACT FROM AUTHOR]

For earthquake and tsunami early warning and emergency response, earthquake magnitude is the crucial parameter to be determined rapidly and correctly. However, a reliable and rapid measurement of the magnitude of an earthquake is a challenging problem, especially for large earthquakes (M > 8). Here, the magnitude is determined based on the GPS displacement waveform derived from real-time precise point positioning (RTPPP). RTPPP results are evaluated with an accuracy of 1 cm in the horizontal components and 2–3 cm in the vertical components, indicating that the RTPPP is capable of detecting seismic waves with amplitude of 1 cm horizontally and 2–3 cm vertically with a confidence level of 95 per cent. In order to estimate the magnitude, the unique information provided by the GPS displacement waveform is the horizontal peak displacement amplitude. We show that the empirical relation of Gutenberg (1945) between peak displacement and magnitude holds up to nearly magnitude 9.0 when displacements are measured with GPS. We tested the proposed method for three large earthquakes. For the 2010 Mw 7.2 El Mayor-Cucapah earthquake, our method provides a magnitude of M7.18 ± 0.18. For the 2011 Mw 9.0 Tohoku-oki earthquake the estimated magnitude is M8.74 ± 0.06, and for the 2010 Mw 8.8 Maule earthquake the value is M8.7 ± 0.1 after excluding some near-field stations. We, therefore, conclude that depending on the availability of high-rate GPS observations, a robust value of magnitude up to 9.0 for a point source earthquake can be estimated within tens of seconds or a few minutes after an event using a few GPS stations close to the epicentre. The rapid magnitude could be as a pre-requisite for tsunami early warning, fast source inversion and emergency response is feasible. [ABSTRACT FROM AUTHOR]