Discrete subgroups of small critical exponent

We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties for any complete pinched negatively curved manifold with critical exponent less than 1.Comment: 20 pages, 6 figures. Comments are welcom

Large deviation principle for reflected SPDE on infinite spatial domain

We study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang ({\it Appl. Math. Optim.} 83: 849-879, 2021) plays an important role in the proof.Comment: 16 page

Reading in the Secondary School: \u27Carbon Dating\u27 Figures of Speech

Teachers usually find that students become enthusiastic and energetic when they are discovering new things for themselves. This article points up some possibilities in teaching students to become detectives, investigating the age and origin of words and phrases used in American simile and metaphor. An end result is sure to be a heightened feeling for literary style, with an increased appreciation for creative writing a possible spinoff. Students may also gain a clearer picture of the cultural settings from which these figures of speech are derived

Learning Personalized Privacy Preference From Public Data

Understanding consumers’ privacy preferences is crucial for firms and policymakers to establish trust and encourage innovation and competition. With the widespread use of digital technologies, individuals generate and share vast amounts of data about themselves in the public domain. Even without knowing a person’s private information, the psychosocial traits revealed in public data can provide valuable insights into their privacy preferences. In this study, we aim to predict personalized privacy preferences using social media posts. Our prediction model shows that psychosocial traits such as personality, lifestyles, risk preference, economic thinking, emotions, etc extracted from posts provide significantly greater predictive power than demographic characteristics. Furthermore, we demonstrate the practical value and impact of our model for business and society through a simulation analysis. Our tool can help platforms and policymakers estimate the impact of privacy policies and prevent potential harms such as discrimination

Using TB-Sized Data to Understand Multi-Device Advertising

In this study, we combine the conversion funnel theory with machine learning methods to understand multi-device advertising. We investigate the important question of how the distribution of ads on multiple devices affects the consumer path to purchase. To handle the sheer volume of TB sized impression data, we develop a MapReduce framework to estimate the non-stationary Hidden Markov Model in parallel. To accommodate the iterative nature of the estimation procedure, we leverage the Apache Spark framework and a corporate cloud computing service. We calibrate the model with hundreds of millions of impressions for 100 advertisers. Our preliminary results show increasing the diversity of device for ads delivery can consistently encourage consumers to become more engaged. In addition, advertiser heterogeneity plays an important role in the variety of the conversion process

Fake It Till You Make It: An Empirical Investigation of Sales Fraud in E-commerce

The competition on e-commerce platforms has become more and more fierce. Among all the different promotion strategies, sales fraud, which is a practice inflating sale volume by using fictitious transactions, is an open secret among e-commerce sellers. Sales fraud will fundamentally undermine the credibility of sales volume, which is one of the major information source for decision making in online purchasing. To shed light on this phenomenon, we empirically investigate circumstance under which sales fraud will take place, using a comprehensive dataset from a mainstream ecommerce website in China. We find that sales cheating is more likely to take place for those products with lower price, from lower-level shops, in their early stages, but with good sales potential. Our empirical findings provide important contributions to the literature on e-commerce, and offer critical managerial implications to online retailers, e-commerce platforms, and consumers

Mechanism Design for Efficient Nash Equilibrium in Oligopolistic Markets

This paper investigates the efficiency loss in social cost caused by strategic bidding behavior of individual participants in a supply-demand balancing market, and proposes a mechanism to fully recover equilibrium social optimum via subsidization and taxation. We characterize the competition among supply-side firms to meet given inelastic demand, with linear supply function bidding and the proposed efficiency recovery mechanism. We show that the Nash equilibrium of such a game exists under mild conditions, and more importantly, it achieves the underlying efficient supply dispatch and the market clearing price that reflects the truthful system marginal production cost. Further, the mechanism can be tuned to guarantee self-sufficiency, i.e., taxes collected counterbalance subsidies needed. Extensive numerical case studies are run to validate the equilibrium analysis, and we employ individual net profit and a modified version of Lerner index as two metrics to evaluate the impact of the mechanism on market outcomes by varying its tuning parameter and firm heterogeneity