Monotonicity Testing for Boolean Functions over Graph Products

We establish a directed analogue of Chung and Tetali's isoperimetric inequality for graph products. We use this inequality to obtain new bounds on the query complexity for testing monotonicity of Boolean-valued functions over products of general posets

From Competition to Complementarity: Comparative Influence Diffusion and Maximization

Influence maximization is a well-studied problem that asks for a small set of influential users from a social network, such that by targeting them as early adopters, the expected total adoption through influence cascades over the network is maximized. However, almost all prior work focuses on cascades of a single propagating entity or purely-competitive entities. In this work, we propose the Comparative Independent Cascade (Com-IC) model that covers the full spectrum of entity interactions from competition to complementarity. In Com-IC, users' adoption decisions depend not only on edge-level information propagation, but also on a node-level automaton whose behavior is governed by a set of model parameters, enabling our model to capture not only competition, but also complementarity, to any possible degree. We study two natural optimization problems, Self Influence Maximization and Complementary Influence Maximization, in a novel setting with complementary entities. Both problems are NP-hard, and we devise efficient and effective approximation algorithms via non-trivial techniques based on reverse-reachable sets and a novel "sandwich approximation". The applicability of both techniques extends beyond our model and problems. Our experiments show that the proposed algorithms consistently outperform intuitive baselines in four real-world social networks, often by a significant margin. In addition, we learn model parameters from real user action logs.Comment: An abridged of this work is to appear in the Proceedings of VLDB Endowment (PVDLB), Vol 9, No 2. Also, the paper will be presented in the VLDB 2016 conference in New Delhi, India. This update contains new theoretical and experimental results, and the paper is now in single-column format (44 pages

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

The Need for Theoretically Consistent Efficiency Frontiers

The availability of efficiency estimation software freely distributed via the internet and relatively easy to use recently inflated the number of corresponding applications. The resulting efficiency estimates are often used without a critical assessment with respect to the literature on theoretical consistency, flexibility and the choice of the appropriate functional form. The robustness of policy suggestions based on inferences from efficiency measures nevertheless crucially depends on theoretically well-founded estimates. This paper addresses stochastic efficiency measurement by critically reviewing the theoretical consistency of recently published technical efficiency estimates. The results confirm the need for a posteriori checking the regularity of the estimated frontier by the researcher and, if necessary, the a priori imposition of the theoretical requirements.functional form, stochastic efficiency analysis, theoretical consistency, Research and Development/Tech Change/Emerging Technologies, C51, D24, Q12,

Strategic Entry Deterrence and the Behavior of Pharmaceutical Incumbents Prior to Patent Expiration

This paper develops a new approach to testing for strategic entry deterrence and applies it to the behavior of pharmaceutical incumbents just before they lose patent protection. The approach involves looking at a cross-section of markets and examining whether behavior is nonmonotonic in the size of the market. Under certain conditions, investment levels will be monotone in market size if firms are not influenced by a desire to deter entry. Strategic investments, however, may be nonmonotone because entry deterrence is unnecessary in very small markets and impossible in very large ones, resulting in overall nonmonotonic investment. The pharmaceutical data contain advertising, product proliferation, and pricing information for a sample of drugs which lost patent protection between 1986 and 1992. Among the findings consistent with an entry deterrence motivation are that incumbents in markets of intermediate size have lower levels of advertising and are more likely to reduce advertising immediately prior to patent expiration.

Stochastic efficiency measurement: The curse of theoretical consistency

The availability of efficiency estimation software – freely distributed via the internet and relatively easy to use – recently inflated the number of corresponding applications. The resulting efficiency estimates are used without a critical assessment with respect to the literature on theoretical consistency, flexibility and the choice of the appropriate functional form. The robustness of policy suggestions based on inferences from efficiency measures nevertheless crucially depends on theoretically well-founded estimates. This paper adresses stochastic efficiency measurement by critically reviewing the theoretical consistency of recently published technical efficiency estimates. The results confirm the need for a posteriori checking the regularity of the estimated frontier by the researcher and, if necessary, the a priori imposition of the theoretical requirements.functional form, stochastic efficiency analysis, theoretical consistency