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Abstract Nucleation and subsequent growth of new aerosol particles in the atmosphere is a major source of cloud condensation nuclei and persistent large uncertainty in climate models. Newly formed particles need to grow rapidly to avoid scavenging by pre-existing aerosols and become relevant for the climate and air quality. In the continental atmosphere, condensation of oxygenated organic molecules is often the dominant mechanism for rapid growth. However, the huge variety of different organics present in the continental boundary layer makes it challenging to predict nanoparticle growth rates from gas-phase measurements. Moreover, recent studies have shown that growth rates of nanoparticles derived from particle size distribution measurements show surprisingly little dependency on potentially condensable vapors observed in the gas phase. Here, we show that the observed nanoparticle growth rates in the sub-10 nm size range can be predicted in the boreal forest only for springtime conditions, even with state-of-the-art mass spectrometers and particle sizing instruments. We find that, especially under warmer conditions, observed growth is slower than predicted from gas-phase condensation. We show that only a combination of simple particle-phase reaction schemes, phase separation due to non-ideal solution behavior, or particle-phase diffusion limitations can explain the observed lower growth rates. Our analysis provides first insights as to why atmospheric nanoparticle growth rates above 10 nm h⁻¹are rarely observed. Ultimately, a reduction of experimental uncertainties and improved sub-10 nm particle hygroscopicity and chemical composition measurements are needed to further investigate the occurrence of such a growth rate-limiting process. 

For S ⊆ 𝔽ⁿ, consider the linear space of restrictions of degree-d polynomials to S. The Hilbert function of S, denoted h_S(d,𝔽), is the dimension of this space. We obtain a tight lower bound on the smallest value of the Hilbert function of subsets S of arbitrary finite grids in 𝔽ⁿ with a fixed size |S|. We achieve this by proving that this value coincides with a combinatorial quantity, namely the smallest number of low Hamming weight points in a down-closed set of size |S|. Understanding the smallest values of Hilbert functions is closely related to the study of degree-d closure of sets, a notion introduced by Nie and Wang (Journal of Combinatorial Theory, Series A, 2015). We use bounds on the Hilbert function to obtain a tight bound on the size of degree-d closures of subsets of 𝔽_qⁿ, which answers a question posed by Doron, Ta-Shma, and Tell (Computational Complexity, 2022). We use the bounds on the Hilbert function and degree-d closure of sets to prove that a random low-degree polynomial is an extractor for samplable randomness sources. Most notably, we prove the existence of low-degree extractors and dispersers for sources generated by constant-degree polynomials and polynomial-size circuits. Until recently, even the existence of arbitrary deterministic extractors for such sources was not known. 

A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Past research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case of learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019]. We explore prediction as an alternative to learning. A predictor answers a stream of classification queries instead of outputting a hypothesis. Earlier work has considered a private prediction model with a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and in a manner that cannot rely solely on the training set. We introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions over infinite domains, for which (traditional) private learning is known to be impossible. 

Abstract Haze in Beijing is linked to atmospherically formed secondary organic aerosol, which has been shown to be particularly harmful to human health. However, the sources and formation pathways of these secondary aerosols remain largely unknown, hindering effective pollution mitigation. Here we have quantified the sources of organic aerosol via direct near-molecular observations in central Beijing. In winter, organic aerosol pollution arises mainly from fresh solid-fuel emissions and secondary organic aerosols originating from both solid-fuel combustion and aqueous processes, probably involving multiphase chemistry with aromatic compounds. The most severe haze is linked to secondary organic aerosols originating from solid-fuel combustion, transported from the Beijing–Tianjing–Hebei Plain and rural mountainous areas west of Beijing. In summer, the increased fraction of secondary organic aerosol is dominated by aromatic emissions from the Xi’an–Shanghai–Beijing region, while the contribution of biogenic emissions remains relatively small. Overall, we identify the main sources of secondary organic aerosol affecting Beijing, which clearly extend beyond the local emissions in Beijing. Our results suggest that targeting key organic precursor emission sectors regionally may be needed to effectively mitigate organic aerosol pollution. 

Abstract A key challenge in aerosol pollution studies and climate change assessment is to understand how atmospheric aerosol particles are initially formed^1,2. Although new particle formation (NPF) mechanisms have been described at specific sites^3–6, in most regions, such mechanisms remain uncertain to a large extent because of the limited ability of atmospheric models to simulate critical NPF processes^1,7. Here we synthesize molecular-level experiments to develop comprehensive representations of 11 NPF mechanisms and the complex chemical transformation of precursor gases in a fully coupled global climate model. Combined simulations and observations show that the dominant NPF mechanisms are distinct worldwide and vary with region and altitude. Previously neglected or underrepresented mechanisms involving organics, amines, iodine oxoacids and HNO₃probably dominate NPF in most regions with high concentrations of aerosols or large aerosol radiative forcing; such regions include oceanic and human-polluted continental boundary layers, as well as the upper troposphere over rainforests and Asian monsoon regions. These underrepresented mechanisms also play notable roles in other areas, such as the upper troposphere of the Pacific and Atlantic oceans. Accordingly, NPF accounts for different fractions (10–80%) of the nuclei on which cloud forms at 0.5% supersaturation over various regions in the lower troposphere. The comprehensive simulation of global NPF mechanisms can help improve estimation and source attribution of the climate effects of aerosols. 

Isoprene affects new particle formation rates in environments and experiments also containing monoterpenes. 

Abstract Exposure to anthropogenic atmospheric aerosol is a major health issue, causing several million deaths per year worldwide. The oxidation of aromatic hydrocarbons from traffic and wood combustion is an important anthropogenic source of low-volatility species in secondary organic aerosol, especially in heavily polluted environments. It is not yet established whether the formation of anthropogenic secondary organic aerosol involves mainly rapid autoxidation, slower sequential oxidation steps or a combination of the two. Here we reproduced a typical urban haze in the ‘Cosmics Leaving Outdoor Droplets’ chamber at the European Organization for Nuclear Research and observed the dynamics of aromatic oxidation products during secondary organic aerosol growth on a molecular level to determine mechanisms underlying their production and removal. We demonstrate that sequential oxidation is required for substantial secondary organic aerosol formation. Second-generation oxidation decreases the products’ saturation vapour pressure by several orders of magnitude and increases the aromatic secondary organic aerosol yields from a few percent to a few tens of percent at typical atmospheric concentrations. Through regional modelling, we show that more than 70% of the exposure to anthropogenic organic aerosol in Europe arises from second-generation oxidation. 

Gas-phase oxygenated organic molecules (OOMs) can contribute significantly to both atmospheric new particle growth and secondary organic aerosol formation. Precursor apportionment of atmospheric OOMs connects them with volatile organic compounds (VOCs). Since atmospheric OOMs are often highly functionalized products of multistep reactions, it is challenging to reveal the complete mapping relationships between OOMs and their precursors. In this study, we demonstrate that the machine learning method is useful in attributing atmospheric OOMs to their precursors using several chemical indicators, such as O/C ratio and H/C ratio. The model is trained and tested using data acquired in controlled laboratory experiments, covering the oxidation products of four main types of VOCs (isoprene, monoterpenes, aliphatics, and aromatics). Then, the model is used for analyzing atmospheric OOMs measured in both urban Beijing and a boreal forest environment in southern Finland. The results suggest that atmospheric OOMs in these two environments can be reasonably assigned to their precursors. Beijing is an anthropogenic VOC dominated environment with ∼64% aromatic and aliphatic OOMs, and the other boreal forested area has ∼76% monoterpene OOMs. This pilot study shows that machine learning can be a promising tool in atmospheric chemistry for connecting the dots.