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Abstract Although microbes are the major agent of wood decomposition - a key component of the carbon cycle - the degree to which microbial community dynamics affect this process is unclear. One key knowledge gap is the extent to which stochastic variation in community assembly, e.g. due to historical contingency, can substantively affect decomposition rates. To close this knowledge gap, we manipulated the pool of microbes dispersing into laboratory microcosms using rainwater sampled across a transition zone between two vegetation types with distinct microbial communities. Because the laboratory microcosms were initially identical this allowed us to isolate the effect of changing microbial dispersal directly on community structure, biogeochemical cycles and wood decomposition. Dispersal significantly affected soil fungal and bacterial community composition and diversity, resulting in distinct patterns of soil nitrogen reduction and wood mass loss. Correlation analysis showed that the relationship among soil fungal and bacterial community, soil nitrogen reduction and wood mass loss were tightly connected. These results give empirical support to the notion that dispersal can structure the soil microbial community and through it ecosystem functions. Future biogeochemical models including the links between soil microbial community and wood decomposition may improve their precision in predicting wood decomposition. 

This work focuses on canonical polyadic decomposition (CPD) for large-scale tensors. Many prior works rely on data sparsity to develop scalable CPD algorithms, which are not suitable for handling dense tensor, while dense tensors often arise in applications such as image and video processing. As an alternative, stochastic algorithms utilize data sampling to reduce per-iteration complexity and thus are very scalable, even when handling dense tensors. However, existing stochastic CPD algorithms are facing some challenges. For example, some algorithms are based on randomly sampled tensor entries, and thus each iteration can only updates a small portion of the latent factors. This may result in slow improvement of the estimation accuracy of the latent factors. In addition, the convergence properties of many stochastic CPD algorithms are unclear, perhaps because CPD poses a hard nonconvex problem and is challenging for analysis under stochastic settings. In this work, we propose a stochastic optimization strategy that can effectively circumvent the above challenges. The proposed algorithm updates a whole latent factor at each iteration using sampled fibers of a tensor, which can quickly increase the estimation accuracy. The algorithm is flexible-many commonly used regularizers and constraints can be easily incorporated in the computational framework. The algorithm is also backed by a rigorous convergence theory. Simulations on large-scale dense tensors are employed to showcase the effectiveness of the algorithm.