Sequential Posted Price Mechanisms with Correlated Valuations

We study the revenue performance of sequential posted price mechanisms and some natural extensions, for a general setting where the valuations of the buyers are drawn from a correlated distribution. Sequential posted price mechanisms are conceptually simple mechanisms that work by proposing a take-it-or-leave-it offer to each buyer. We apply sequential posted price mechanisms to single-parameter multi-unit settings in which each buyer demands only one item and the mechanism can assign the service to at most k of the buyers. For standard sequential posted price mechanisms, we prove that with the valuation distribution having finite support, no sequential posted price mechanism can extract a constant fraction of the optimal expected revenue, even with unlimited supply. We extend this result to the the case of a continuous valuation distribution when various standard assumptions hold simultaneously. In fact, it turns out that the best fraction of the optimal revenue that is extractable by a sequential posted price mechanism is proportional to ratio of the highest and lowest possible valuation. We prove that for two simple generalizations of these mechanisms, a better revenue performance can be achieved: if the sequential posted price mechanism has for each buyer the option of either proposing an offer or asking the buyer for its valuation, then a Omega(1/max{1,d}) fraction of the optimal revenue can be extracted, where d denotes the degree of dependence of the valuations, ranging from complete independence (d=0) to arbitrary dependence (d=n-1). Moreover, when we generalize the sequential posted price mechanisms further, such that the mechanism has the ability to make a take-it-or-leave-it offer to the i-th buyer that depends on the valuations of all buyers except i's, we prove that a constant fraction (2-sqrt{e})/4~0.088 of the optimal revenue can be always be extracted.Comment: 29 pages, To appear in WINE 201

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Received 22 April 1988 Published 23 January 2021 Issue Date September 1988Peer reviewe

Analogy Training Multilingual Encoders

Language encoders encode words and phrases in ways that capture their local semantic relatedness, but are known to be globally inconsistent. Global inconsistency can seemingly be corrected for, in part, by leveraging signals from knowledge bases, but previous results are partial and limited to monolingual English encoders. We extract a large-scale multilingual, multi-word analogy dataset from Wikidata for diagnosing and correcting for global inconsistencies and implement a four-way Siamese BERT architecture for grounding multilingual BERT (mBERT) in Wikidata through analogy training. We show that analogy training not only improves the global consistency of mBERT, as well as the isomorphism of language-specific subspaces, but also leads to significant gains on downstream tasks such as bilingual dictionary induction and sentence retrieval

Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Evaluating regional emission estimates using the TRACE-P observations

Measurements obtained during the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) experiment are used in conjunction with regional modeling analysis to evaluate emission estimates for Asia. A comparison between the modeled values and the observations is one method to evaluate emissions. Based on such analysis it is concluded that the inventory performs well for the light alkanes, CO, ethyne, SO2, and NOₓ. Furthermore, based on model skill in predicting important photochemical species such as O₃, HCHO, OH, HO₂, and HNO₃, it is found that the emissions inventories are of sufficient quality to support preliminary studies of ozone production. These are important finding in light of the fact that emission estimates for many species (such as speciated NMHCs and BC) for this region have only recently been estimated and are highly uncertain. Using a classification of the measurements built upon trajectory analysis, we compare observed species distributions and ratios of species to those modeled and to ratios estimated from the emissions inventory. It is shown that this technique can reconstruct a spatial distribution of propane/benzene that looks remarkably similar to that calculated from the emissions inventory. A major discrepancy between modeled and observed behavior is found in the Yellow Sea, where modeled values are systematically underpredicted. The integrated analysis suggests that this may be related to an underestimation of emissions from the domestic sector. The emission is further tested by comparing observed and measured species ratios in identified megacity plumes. Many of the model derived ratios (e.g., BC/CO, SOₓ/C₂H₂) fall within ∼25% of those observed and all fall outside of a factor of 2.5. (See Article file for details of the abstract.)Department of Civil and Environmental EngineeringAuthor name used in this publication: Wang, T

Analysis of the atmospheric distribution, sources, and sinks of oxygenated volatile organic chemicals based on measurements over the Pacific during TRACE-P

Airborne measurements of a large number of oxygenated volatile organic chemicals (OVOC) were carried out in the Pacific troposphere (0.1 - 12 km) in winter/spring of 2001 (24 February to 10 April). Specifically, these measurements included acetone (CH3COCHA3), methylethyl ketone (CH3COC2H5, MEK), methanol (CH3OH), ethanol (C2H5OH), acetaldehyde (CH3CHO), propionaldehyde C2H 5CHO), peroxyacylnitrates (PANs) (CnH 2n+1COO2NO2), and organic nitrates (CnH2n+1ONO2). Complementary measurements of formaldehyde (HCHO), methyl hydroperoxide (CH 3OOH), and selected tracers were also available. OVOC were abundant in the clean troposphere and were greatly enhanced in the outflow regions from Asia. Background mixing ratios were typically highest in the lower troposphere and declined toward the upper troposphere and the lowermost stratosphere. Their total abundance (ΣOVOC) was nearly twice that of nonmethane hydrocarbons (Σ C2-C8 NMHC. Throughout the troposphere, the OH reactivity of OVOC is comparable to that of methane and far exceeds that of NMHC. A comparison of these data with western Pacific observations collected some 7 years earlier (February-March 1994) did not reveal significant differences. Mixing ratios of OVOC were strongly correlated with each other as well as with tracers of fossil and biomass/biofuel combustion. Analysis of the relative enhancement of selected OVOC with respect to CH 3Cl and CO in 12 plumes originating from fires and sampled in the free troposphere (3-11 km) is used to assess their primary and secondary emissions from biomass combustion. The composition of these plumes also indicates a large shift of reactive nitrogen into the PAN reservoir thereby limiting ozone formation. A three-dimensional global model that uses state of the art chemistry and source information is used to compare measured and simulated mixing ratios of selected OVOC. While there is reasonable agreement in many cases, measured aldehyde concentrations are significantly larger than predicted. At their observed levels, acetaldehyde mixing ratios are shown to be an important source of HCHO (and HOx) and PAN in the troposphere. On the basis of presently known chemistry, measured mixing ratios of aldehydes and PANs are mutually incompatible. We provide rough estimates of the global sources of several OVOC and conclude that collectively these are extremely large (150-500 Tg C yr-1) but remain poorly quantified. Copyright 2004 by the American Geophysical Union