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Summary Latent space models are frequently used for modelling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well developed for more complex network structures, which are becoming increasingly common in practice. In this article we propose a new latent space model for multiplex networks, i.e., multiple heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of the proposed model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear-norm penalty, and prove a guarantee of recovery for the latent positions provided there is sufficient separation between the shared and the individual latent subspaces. We compare the model with competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products. 

Abstract The relationship between extreme precipitation intensity and temperature has been comprehensively studied over different regions worldwide. However, the effect of temperature on the spatiotemporal organization of precipitation, which can have a significant impact on precipitation intensity, has not been adequately studied or understood. In this study, we propose a novel approach to quantifying the spatial and temporal concentration of precipitation at the event level and study how the concentration varies with temperature. The results based on rain gauge data from 843 stations in the Ganzhou county, a humid region in south China, show that rain events tend to be more concentrated both temporally and spatially at higher temperature, and this increase in concentration qualitatively holds for events of different precipitation amounts and durations. The effects of temperature on precipitation organization in space and in time differ at high temperatures. The temporal concentration increases with temperature up to a threshold (approximately 24°C) beyond which it plateaus, whereas the spatial concentration keeps rising with temperature. More concentrated precipitation, in addition to a projected increase of extreme precipitation, would intensify flooding in a warming world, causing more detrimental effects. 

The discovery of two-dimensional systems hosting intrinsic magnetic order represents a seminal addition to the rich landscape of van der Waals materials. CrI₃is an archetypal example, where the interdependence of structure and magnetism, along with strong light-matter interactions, provides a new platform to explore the optical control of magnetic and vibrational degrees of freedom at the nanoscale. However, the nature of magneto-structural coupling on its intrinsic ultrafast timescale remains a crucial open question. Here, we probe magnetic and vibrational dynamics in bulk CrI₃using ultrafast optical spectroscopy, revealing spin-flip scattering-driven demagnetization and strong transient exchange-mediated interactions between lattice vibrations and spin oscillations. The latter yields a coherent spin-coupled phonon mode that is highly sensitive to the driving pulse’s helicity in the magnetically ordered phase. Our results elucidate the nature of ultrafast spin-lattice coupling in CrI₃and highlight its potential for applications requiring high-speed control of magnetism at the nanoscale.

 

Since its publication, the authors of Wang et al. (2021) have brought to our attention an error in their article. A grant awarded by the National Science Foundation (grant no. MCB 1817985) to author Elizabeth Vierling was omitted from the Acknowledgements section. The correct Acknowledgements section is shown below. Acknowledgements We thank Suiwen Hou (Lanzhou University) and Zhaojun Ding (Shandong University) for providing the seeds used in this study. We thank Xiaoping Gou (Lanzhou University) and Ravishankar Palanivelu (University of Arizona) for critically reading the manuscript and for suggestions regarding the article. This work was supported by grants from National Natural Science Foundation of China (31870298) to SX, the US Department of Agriculture (USDA-CSREES-NRI-001030) and the National Science Foundation (MCB 1817985) to EV, and the Youth 1000-Talent Program of China (A279021801) to LY. 

We propose an end-to-end optimized adversarial deep compressed imaging modality. This method exploits the adversarial duality of the sensing basis and sparse representation basis in compressed sensing framework and shows solid super-resolution results.