Relaxed Models for Adversarial Streaming: The Advice Model and the Bounded Interruptions Model

Streaming algorithms are typically analyzed in the oblivious setting, where we assume that the input stream is fixed in advance. Recently, there is a growing interest in designing adversarially robust streaming algorithms that must maintain utility even when the input stream is chosen adaptively and adversarially as the execution progresses. While several fascinating results are known for the adversarial setting, in general, it comes at a very high cost in terms of the required space. Motivated by this, in this work we set out to explore intermediate models that allow us to interpolate between the oblivious and the adversarial models. Specifically, we put forward the following two models: (1) *The advice model*, in which the streaming algorithm may occasionally ask for one bit of advice. (2) *The bounded interruptions model*, in which we assume that the adversary is only partially adaptive. We present both positive and negative results for each of these two models. In particular, we present generic reductions from each of these models to the oblivious model. This allows us to design robust algorithms with significantly improved space complexity compared to what is known in the plain adversarial model

A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Classical streaming algorithms operate under the (not always reasonable) assumption that the input stream is fixed in advance. Recently, there is a growing interest in designing robust streaming algorithms that provide provable guarantees even when the input stream is chosen adaptively as the execution progresses. We propose a new framework for robust streaming that combines techniques from two recently suggested frameworks by Hassidim et al. [NeurIPS 2020] and by Woodruff and Zhou [FOCS 2021]. These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks into a single hybrid framework that obtains the "best of both worlds", thereby solving a question left open by Woodruff and Zhou

Emission of volatile halogenated organic compounds over various landforms at the Dead Sea

Abstract. Volatile halogenated organic compounds (VHOCs), such as methyl halides (CH3X; X = Br, Cl and I) and very short-lived halogenated substances (VSLS; CHBr3, CH2Br2, CHBrCl2, C2HCl3, CHCl3 and CHBr2Cl) are well known for their significant influence on ozone concentrations and oxidation capacity of the troposphere and stratosphere, and for their key role in aerosol formation. Insufficient characterization of the sources and emission rate of VHOCs limits our present ability to understand and assess their impact in both the troposphere and the stratosphere. Over the last two decades several natural terrestrial sources for VHOCs, including soil and vegetation, have been identified, but our knowledge about emission rates from these sources and their responses to changes in ambient conditions remains limited. Here we report measurements of the mixing ratios and the fluxes of several chlorinated and brominated VHOCs from different landforms and vegetated sites at the Dead Sea during different seasons. Fluxes were highly variable but were generally positive (emissive), corresponding with elevated mixing ratios for all of the VHOCs investigated in the four investigated site types – bare soil, coastal, cultivated and natural vegetated sites – except for fluxes of CH3I and C2HCl3 over the vegetated sites. In contrast to previous reports, we also observed emissions of brominated trihalomethanes, with net molar fluxes ordered as follows: CHBr2Cl > CHBr3 > CHBrCl2 > CHCl3. This finding can be explained by the enrichment of soil with Br. Correlation analysis, in agreement with recent studies, indicated common controls for the formation and emission of all the above trihalomethanes but also for CH2Br2. Also in line with previous reports, we observed elevated emissions of CHCl3 and C2HCl3 from mixtures of soil and different salt-deposited structures; the high correlations of flux with methyl halides, and particularly with CH3I, suggested that at least CH3I is also emitted via similar mechanisms or is subjected to similar controls. Overall, our results indicate elevate emission of VHOCs from bare soil under semi-arid conditions. Along with other recent studies, our findings point to the strong emission potential of a suite of VHOCs from saline soils and salt lakes, and call for additional studies of emission rates and mechanisms of VHOCs from saline soils and salt lakes

Emission of volatile halogenated organic compounds over various landforms at the Dead Sea

Abstract. Volatile halogenated organic compounds (VHOCs), such as methyl halides (CH3X; X = Br, Cl and I) and very short-lived halogenated substances (VSLS; CHBr3, CH2Br2, CHBrCl2, C2HCl3, CHCl3 and CHBr2Cl) are well known for their significant influence on ozone concentrations and oxidation capacity of the troposphere and stratosphere, and for their key role in aerosol formation. Insufficient characterization of the sources and emission rate of VHOCs limits our present ability to understand and assess their impact in both the troposphere and the stratosphere. Over the last two decades several natural terrestrial sources for VHOCs, including soil and vegetation, have been identified, but our knowledge about emission rates from these sources and their responses to changes in ambient conditions remains limited. Here we report measurements of the mixing ratios and the fluxes of several chlorinated and brominated VHOCs from different landforms and vegetated sites at the Dead Sea during different seasons. Fluxes were highly variable but were generally positive (emissive), corresponding with elevated mixing ratios for all of the VHOCs investigated in the four investigated site types – bare soil, coastal, cultivated and natural vegetated sites – except for fluxes of CH3I and C2HCl3 over the vegetated sites. In contrast to previous reports, we also observed emissions of brominated trihalomethanes, with net molar fluxes ordered as follows: CHBr2Cl > CHBr3 > CHBrCl2 > CHCl3. This finding can be explained by the enrichment of soil with Br. Correlation analysis, in agreement with recent studies, indicated common controls for the formation and emission of all the above trihalomethanes but also for CH2Br2. Also in line with previous reports, we observed elevated emissions of CHCl3 and C2HCl3 from mixtures of soil and different salt-deposited structures; the high correlations of flux with methyl halides, and particularly with CH3I, suggested that at least CH3I is also emitted via similar mechanisms or is subjected to similar controls. Overall, our results indicate elevate emission of VHOCs from bare soil under semi-arid conditions. Along with other recent studies, our findings point to the strong emission potential of a suite of VHOCs from saline soils and salt lakes, and call for additional studies of emission rates and mechanisms of VHOCs from saline soils and salt lakes