Prophet Inequalities with Limited Information

In the classical prophet inequality, a gambler observes a sequence of stochastic rewards $V_1,...,V_n$ and must decide, for each reward $V_i$, whether to keep it and stop the game or to forfeit the reward forever and reveal the next value $V_i$. The gambler's goal is to obtain a constant fraction of the expected reward that the optimal offline algorithm would get. Recently, prophet inequalities have been generalized to settings where the gambler can choose $k$ items, and, more generally, where he can choose any independent set in a matroid. However, all the existing algorithms require the gambler to know the distribution from which the rewards $V_1,...,V_n$ are drawn. The assumption that the gambler knows the distribution from which $V_1,...,V_n$ are drawn is very strong. Instead, we work with the much simpler assumption that the gambler only knows a few samples from this distribution. We construct the first single-sample prophet inequalities for many settings of interest, whose guarantees all match the best possible asymptotically, \emph{even with full knowledge of the distribution}. Specifically, we provide a novel single-sample algorithm when the gambler can choose any $k$ elements whose analysis is based on random walks with limited correlation. In addition, we provide a black-box method for converting specific types of solutions to the related \emph{secretary problem} to single-sample prophet inequalities, and apply it to several existing algorithms. Finally, we provide a constant-sample prophet inequality for constant-degree bipartite matchings. We apply these results to design the first posted-price and multi-dimensional auction mechanisms with limited information in settings with asymmetric bidders

The VCG Mechanism for Bayesian Scheduling

We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, in which the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O(ln n&frac; ln ln n). This improves significantly on the previously best known bound of O(m/n) for prior-independent mechanisms, given by Chawla et al. [7] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is tight in general, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for m ≥ n ln n i.i.d. tasks. We also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

Societal emotional environments and cross-cultural differences in life satisfaction: A forty-nine country study.

In this paper, we introduce the concept of ‘societal emotional environment’: the emotional climate of a society (operationalized as the degree to which positive and negative emotions are expressed in a society). Using data collected from 12,888 participants across 49 countries, we show how societal emotional environments vary across countries and cultural clusters, and we consider the potential importance of these differences for well-being. Multilevel analyses supported a ‘double-edged sword’ model of negative emotion expression, where expression of negative emotions predicted higher life satisfaction for the expresser but lower life satisfaction for society. In contrast, partial support was found for higher societal life satisfaction in positive societal emotional environments. Our study highlights the potential utility and importance of distinguishing between positive and negative emotion expression, and adopting both individual and societal perspectives in well-being research. Individual pathways to happiness may not necessarily promote the happiness of others

Combinatorial growth with physical constraints: Evidence from electronic miniaturization

In the past sixty years, transistor sizes and weights have decreased by 50 percent every eighteen months, following Moore's Law. Smaller and lighter electronics have increased productivity in virtually every industry and spurred the creation of entirely new sectors of the economy. However, while the effect of the increasing quality of computers and electronics on GDP has been widely studied, the question of how electronic miniaturization affects economic growth has been unexplored. To quantify the effect of electronic miniaturization on GDP, this paper builds an economic growth model that incorporates physical constraints on firms' production sets. This model allows for new types of productivity spillovers that are driven by products' physical characteristics. Not only are there spillovers from changes in industry productivity, but also, there can be "size spillovers," where the miniaturization of one industry's product leads to miniaturization of products that are downstream in the supply chain, reflecting how transistor miniaturization has led to the decrease in size of a large variety of electronic products. Using a new data set of product weights and sizes, we test the predictions of the model and show that Moore's Law accounts for approximately 3.5 percent of all productivity growth in the 1982-2007 period, and for 37.5 percent of the productivity growth in heavy manufacturing industries. The results are robust under multiple specifications, and increase in strength during the 1997-2007 subperiod

Prior independent mechanisms via prophet inequalities with limited information

Prophet inequalities have recently become a fundamental tool in the design of sequential and multi-dimensional mechanisms in Bayesian settings. However, existing mechanisms—as well as the underlying prophet inequalities behind their analysis—require sophisticated information about the distribution from which inputs are drawn. Our goal in this work is to design prior-independent sequential and multi-dimensional mechanisms. To this end, we first design prophet inequalities that require knowing only a single sample from the input distribution. These results come in two forms: the first is via a reduction from single-sample prophet inequalities to secretary algorithms. The second is via novel single-sample prophet inequalities for k-uniform matroids. Leveraging our new prophet inequalities, we construct the first prior-independent sequential mechanisms where the seller does not know the order in which buyers arrive, and buyers may have asymmetric value distributions. We also construct the first prior-independent multi-dimensional mechanism where buyers may have asymmetric value distributions

The financial stability implications of digital assets

The value of assets in the digital ecosystem has grown rapidly amid periods of high volatility. Does the digital financial system create new potential challenges to financial stability? This paper explores this question using the Federal Reserve's framework for analyzing vulnerabilities in the traditional financial system. The digital asset ecosystem has recently proven itself to be highly fragile. However, adverse digital asset market shocks have had limited spillovers to the traditional financial system. Currently, the digital asset ecosystem does not provide significant financial services outside the ecosystem, and it exhibits limited interconnections with the traditional financial system. The paper describes emerging vulnerabilities that could present risks to financial stability in the future if the digital asset ecosystem becomes more systemic, including run risks among large stablecoins, valuation pressures in crypto-assets, fragilities of DeFi platforms, growing interconnectedness, and a general lack of regulation