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Functional data have received significant attention as they frequently appear in modern applications, such as functional magnetic resonance imaging (fMRI) and natural language processing. The infinite-dimensional nature of functional data makes it necessary to use dimension reduction techniques. Most existing techniques, however, rely on the covariance operator, which can be affected by heavy-tailed data and unusual observations. Therefore, in this paper, we consider a robust sliced inverse regression for multivariate elliptical functional data. For that reason, we introduce a new statistical linear operator, called the conditional spatial sign Kendall’s tau covariance operator, which can be seen as an extension of the multivariate Kendall’s tau to both the conditional and functional settings. The new operator is robust to heavy-tailed data and outliers, and hence can provide a robust estimate of the sufficient predictors. We also derive the convergence rates of the proposed estimators for both completely and partially observed data. Finally, we demonstrate the finite sample performance of our estimator using simulation examples and a real dataset based on fMRI. 

Abstract Many natural faults are believed to consist of velocity weakening (VW) patches surrounded by velocity strengthening (VS) sections. Numerical studies routinely employ this framework to study earthquake sequences including repeating earthquakes. In this laboratory study, we made a VW asperity, of lengthL, from a bare Poly(methyl methacrylate) PMMA frictional interface and coated the surrounding interface with Teflon to make VS fault sections. Behavior of this isolated asperity was studied as a function ofL(ranging from 100 to 400 mm) and the critical nucleation length, , which is inversely proportional to the applied normal stress (2–16 MPa). Consistent with recent numerical simulations, we observed aseismic slip for  < 2, periodic slip for 2 <  < 6, and non‐periodic slip for 10 < . Furthermore, we compared the experiments whereLwas contained by VS material to standard stick‐slip events whereLwas bounded by free surfaces (i.e.,L = the total sample length). The free surface case produced ∼10 times larger slip during stick‐slip events compared to the contained fault ruptures, even with identical . This disparity highlights how standard, complete‐rupture stick‐slip events differ from contained events expected in nature, due to both the free surface conditions and the heterogeneous normal stress along the fault near the free ends, as confirmed by Digital Image Correlation analysis. This study not only introduces the Teflon coating experimental technique for containing laboratory earthquake ruptures, but also highlights the utility of as a predictive parameter for earthquake behavior. 

Two-dimensional (2D) hexagonal boron nitride (h-BN) is one of the few materials showing great promise for light emission in the far ultraviolet (UV)-C wavelength, which is more effective and safer in containing the transmission of microbial diseases than traditional UV light. In this report, we observed that h-BN, despite having an indirect energy bandgap, exhibits a remarkably high room-temperature quantum efficiency (∼60%), which is orders of magnitude higher than that of other indirect bandgap material, and is enabled by strong excitonic effects and efficient exciton-phonon interactions. This study offers a new approach for the design and development of far UV-C optoelectronic devices as well as quantum photonic devices employing 2D semiconductor active regions. 

Ru-Ni diatomic sites can effectively catalyze alkaline hydrogen oxidation with high activity, CO tolerance, and stability.