In this paper we introduce a mathematical model that captures some of the salient features of recommender systems that are based on popularity and that try to exploit social ties among the users. We show that, under very general conditions, the market always converges to a steady state, for which we are able to give an explicit form. Thanks to this we can tell rather precisely how much a market is altered by a recommendation system, and determine the power of users to influence others. Our theoretical results are complemented by experiments with real world social networks showing that social graphs prevent large market distortions in spite of the presence of highly influential users. †

Online communities like Reddit feature intensive discussions on political topics, engaging many users who give and receive votes for their posts and comments. Prior work has focused on detecting controversial discussions and analyzing the role of troll-like users. This paper provides a systematic analysis of the characteristics of user actions, like replies and votes, in discussion threads, identifying different patterns that refine the notion of controversies into disputes, disruptions and discrepancies. Most importantly, our study connects the dimension of user actions with a rich feature space comprising also the sentiments expressed in post contents and the topical variation across the posts and replies. We use this framework to gain insight on the traits of different archetypes of discussions, and to statistically test a variety of hypotheses on expected and abnormal behavior.

We introduce Tiered Sampling, a novel technique for approximate counting sparse motifs in massive graphs whose edges are observed in a stream. Our technique requires only a single pass on the data and uses a memory of fixed size M , which can be magnitudes smaller than the number of edges.Our methods addresses the challenging task of counting sparse motifs -sub-graph patterns that have low probability to appear in a sample of M edges in the graph, which is the maximum amount of data available to the algorithms in each step. To obtain an unbiased and low variance estimate of the count we partition the available memory to tiers (layers) of reservoir samples. While the base layer is a standard reservoir sample of edges, other layers are reservoir samples of sub-structures of the desired motif. By storing more frequent sub-structures of the motif, we increase the probability of detecting an occurrence of the sparse motif we are counting, thus decreasing the variance and error of the estimate.We demonstrate the advantage of our method in the specific applications of counting sparse 4 and 5cliques in massive graphs. We present a complete analytical analysis and extensive experimental results using both synthetic and real-world data. Our results demonstrate the advantage of our method in obtaining high-quality approximations for the number of 4 and 5-cliques for large graphs using a very limited amount of memory, significantly outperforming the single edge sample approach for counting sparse motifs in large scale graphs.

Given a notion of pairwise similarity between objects, locality sensitive hashing (LSH) aims to construct a hash function family over the universe of objects such that the probability two objects hash to the same value is their similarity. LSH is a powerful algorithmic tool for large scale applications and much work has been done to understand LSHable similarities, i.e., similarities that admit an LSH. In this paper we focus on similarities that are provably non-LSHable and propose a notion of distortion to capture the approximation of such a similarity by an LSHable similarity. We consider several well-known non-LSHable similarities and show tight upper and lower bounds on their distortion.