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  1. Obtaining solutions to optimal transportation (OT) problems is typically intractable when marginal spaces are continuous. Recent research has focused on approximating continuous solutions with discretization methods based on i.i.d. sampling, and this has shown convergence as the sample size increases. However, obtaining OT solutions with large sample sizes requires intensive computation effort, which can be prohibitive in practice. In this paper, we propose an algorithm for calculating discretizations with a given number of weighted points for marginal distributions by minimizing the (entropy-regularized) Wasserstein distance and providing bounds on the performance. The results suggest that our plans are comparable to those obtained with much larger numbers of i.i.d. samples and are more efficient than existing alternatives. Moreover, we propose a local, parallelizable version of such discretizations for applications, which we demonstrate by approximating adorable images.

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  2. Volatile chemical products (VCPs) and other non-combustion-related sourceshave become important for urban air quality, and bottom-up calculationsreport emissions of a variety of functionalized compounds that remainunderstudied and uncertain in emissions estimates. Using a new instrumentalconfiguration, we present online measurements of oxygenated organiccompounds in a US megacity over a 10 d wintertime sampling period, whenbiogenic sources and photochemistry were less active. Measurements wereconducted at a rooftop observatory in upper Manhattan, New York City, USAusing a Vocus chemical ionization time-of-flight mass spectrometer, withammonium (NH4+) as the reagent ion operating at 1 Hz. The range ofobservations spanned volatile, intermediate-volatility, and semi-volatileorganic compounds, with targeted analyses of ∼150 ions, whoselikely assignments included a range of functionalized compound classes suchas glycols, glycol ethers, acetates, acids, alcohols, acrylates, esters,ethanolamines, and ketones that are found in various consumer, commercial,and industrial products. Their concentrations varied as a function of winddirection, with enhancements over the highly populated areas of the Bronx,Manhattan, and parts of New Jersey, and included abundant concentrations ofacetates, acrylates, ethylene glycol, and other commonly used oxygenatedcompounds. The results provide top-down constraints on wintertime emissionsof these oxygenated and functionalized compounds, with ratios to commonanthropogenic marker compounds and comparisons of their relative abundancesto two regionally resolved emissions inventories used in urban air qualitymodels.

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  3. Abstract

    The primary cell wall is a fundamental plant constituent that is flexible but sufficiently rigid to support the plant cell shape. Although many studies have demonstrated that reactive oxygen species (ROS) serve as important signaling messengers to modify the cell wall structure and affect cellular growth, the regulatory mechanism underlying the spatial-temporal regulation of ROS activity for cell wall maintenance remains largely unclear. Here, we demonstrate the role of the Arabidopsis (Arabidopsis thaliana) multicopper oxidase-like protein skewed 5 (SKU5) and its homolog SKU5-similar 1 (SKS1) in root cell wall formation through modulating ROS homeostasis. Loss of SKU5 and SKS1 function resulted in aberrant division planes, protruding cell walls, ectopic deposition of iron, and reduced nicotinamide adeninedinucleotide phosphate (NADPH) oxidase-dependent ROS overproduction in the root epidermis–cortex and cortex–endodermis junctions. A decrease in ROS level or inhibition of NADPH oxidase activity rescued the cell wall defects of sku5 sks1 double mutants. SKU5 and SKS1 proteins were activated by iron treatment, and iron over-accumulated in the walls between the root epidermis and cortex cell layers of sku5 sks1. The glycosylphosphatidylinositol-anchored motif was crucial for membrane association and functionality of SKU5 and SKS1. Overall, our results identified SKU5 and SKS1 as regulators of ROS at the cell surface for regulation of cell wall structure and root cell growth.

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  5. Abstract

    Although most dramatic structural changes occur in the perinatal period, a growing body of evidences demonstrates that adolescence and early adulthood are also important for substantial neurodevelopment. We were thus motivated to explore brain development during puberty by evaluating functional connectivity network (FCN) differences between childhood and young adulthood using multi‐paradigm task‐based functional magnetic resonance imaging (fMRI) measurements. Different from conventional multigraph based FCN construction methods where the graph network was built independently for each modality/paradigm, we proposed a multigraph learning model in this work. It promises a better fitting to FCN construction by jointly estimating brain network from multi‐paradigm fMRI time series, which may share common graph structures. To investigate the hub regions of the brain, we further conducted graph Fourier transform (GFT) to divide the fMRI BOLD time series of a node within the brain network into a range of frequencies. Then we identified the hub regions characterizing brain maturity through eigen‐analysis of the low frequency components, which were believed to represent the organized structures shared by a large population. The proposed method was evaluated using both synthetic and real data, which demonstrated its effectiveness in extracting informative brain connectivity patterns. We detected 14 hub regions from the child group and 12 hub regions from the young adult group. We show the significance of these findings with a discussion of their functions and activation patterns as a function of age. In summary, our proposed method can extract brain connectivity network more accurately by considering the latent common structures between different fMRI paradigms, which are significant for both understanding brain development and recognizing population groups of different ages.

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