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  1. Airborne bacteria are an influential component of the Earth’s microbiomes, but their community structure and biogeographic distribution patterns have yet to be understood. We analyzed the bacterial communities of 370 air particulate samples collected from 63 sites around the world and constructed an airborne bacterial reference catalog with more than 27 million nonredundant 16S ribosomal RNA (rRNA) gene sequences. We present their biogeographic pattern and decipher the interlacing of the microbiome co-occurrence network with surface environments of the Earth. While the total abundance of global airborne bacteria in the troposphere (1.72 × 10 24 cells) is 1 to 3 orders of magnitude lower than that of other habitats, the number of bacterial taxa (i.e., richness) in the atmosphere (4.71 × 10 8 to 3.08 × 10 9 ) is comparable to that in the hydrosphere, and its maximum occurs in midlatitude regions, as is also observed in other ecosystems. The airborne bacterial community harbors a unique set of dominant taxa (24 species); however, its structure appears to be more easily perturbed, due to the more prominent role of stochastic processes in shaping community assembly. This is corroborated by the major contribution of surface microbiomes to airborne bacteria (averaging 46.3%), while atmospheric conditions such as meteorological factors and air quality also play a role. Particularly in urban areas, human impacts weaken the relative importance of plant sources of airborne bacteria and elevate the occurrence of potential pathogens from anthropogenic sources. These findings serve as a key reference for predicting planetary microbiome responses and the health impacts of inhalable microbiomes with future changes in the environment. 
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  2. Abstract

    The max‐p‐compact‐regions problem involves the aggregation of a set of small areas into an unknown maximum number (p) of compact, homogeneous, and spatially contiguous regions such that a regional attribute value is higher than a predefined threshold. The max‐p‐compact‐regions problem is an extension of the max‐p‐regions problem accounting for compactness. The max‐p‐regions model has been widely used to define study regions in many application cases since it allows users to specify criteria and then to identify a regionalization scheme. However, the max‐p‐regions model does not consider compactness even though compactness is usually a desirable goal in regionalization, implying ideal accessibility and apparent homogeneity. This article discusses how to integrate a compactness measure into the max‐pregionalization process by constructing a multiobjective optimization model that maximizes the number of regions while optimizing the compactness of identified regions. An efficient heuristic algorithm is developed to address the computational intensity of the max‐p‐compact‐regions problem so that it can be applied to large‐scale practical regionalization problems. This new algorithm will be implemented in the open‐source Python Spatial Analysis Library. One hypothetical and one practical application of the max‐p‐compact‐regions problem are introduced to demonstrate the effectiveness and efficiency of the proposed algorithm.

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