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We consider the problem of reconstructing a rank-one matrix from a revealed subset of its entries when some of the revealed entries are corrupted with perturbations that are unknown and can be arbitrarily large. It is not known which revealed entries are corrupted. We propose a new algorithm combining alternating minimization with extreme-value filtering and provide sufficient and necessary conditions to recover the original rank-one matrix. In particular, we show that our proposed algorithm is optimal when the set of revealed entries is given by an Erdos-Renyi random graph. These results are then applied to the problem of classification from crowdsourced data under the assumption that while the majority of the workers are governed by the standard single-coin David-Skene model (i.e., they output the correct answer with a certain probability), some of the workers can deviate arbitrarily from this model. In particular, the adversarial'' workers could even make decisions designed to make the algorithm output an incorrect answer. Extensive experimental results show our algorithm for this problem, based on rank-one matrix completion with perturbations, outperforms all other state-of-the-art methods in such an adversarial scenario. 

Wood formation consumes around 15% of the anthropogenic CO 2 emissions per year and plays a critical role in long-term sequestration of carbon on Earth. However, the exogenous factors driving wood formation onset and the underlying cellular mechanisms are still poorly understood and quantified, and this hampers an effective assessment of terrestrial forest productivity and carbon budget under global warming. Here, we used an extensive collection of unique datasets of weekly xylem tissue formation (wood formation) from 21 coniferous species across the Northern Hemisphere (latitudes 23 to 67°N) to present a quantitative demonstration that the onset of wood formation in Northern Hemisphere conifers is primarily driven by photoperiod and mean annual temperature (MAT), and only secondarily by spring forcing, winter chilling, and moisture availability. Photoperiod interacts with MAT and plays the dominant role in regulating the onset of secondary meristem growth, contrary to its as-yet-unquantified role in affecting the springtime phenology of primary meristems. The unique relationships between exogenous factors and wood formation could help to predict how forest ecosystems respond and adapt to climate warming and could provide a better understanding of the feedback occurring between vegetation and climate that is mediated by phenology. Our study quantifies the role of major environmental drivers for incorporation into state-of-the-art Earth system models (ESMs), thereby providing an improved assessment of long-term and high-resolution observations of biogeochemical cycles across terrestrial biomes.