For each positive integer n ≥ 4, we give an inequality satisfied by rank functions of arrangements of n subspaces. When n = 4 we recover Ingleton’s inequality; for higher n the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the “cone of realizable polymatroids” are also...

Social network sites have become an important medium for people to receive information anytime anywhere. Users of social network sites share information by posting updates. The updates shared by friends form social update streams that provide people with up-to-date information. To receive novel information, users of social network sites are encouraged to establish social relations. However, hav...

In this paper, we explore a geo-spatial learning-to-rank framework for identifying local experts. Three of the key features of the proposed approach are: (i) a learning-based framework for integrating multiple factors impacting local expertise that leverages the fine-grained GPS coordinates of millions of social media users; (ii) a location-sensitive random walk that propagates crowd knowledge ...

Most Twitter search systems generally treat a tweet as a plain text when modeling relevance. However, a series of conventions allows users to tweet in structural ways using combination of different blocks of texts. These blocks include plain texts, hashtags, links, mentions, etc. Each block encodes a variety of communicative intent and sequence of these blocks captures changing discourse. Previ...

Social class reflects more than the material conditions of people’s lives. Objective resources (e.g., income) shape cultural practices and behaviors that signal social class. These signals create cultural identities among upperand lower-class individuals— identities that are rooted in subjective perceptions of social-class rank vis-à-vis others. Empirical studies find that perceptions of social...

This paper presents an algorithm that solves optimization problems on a matrix manifold M ⊆ Rm×n with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted low-rank approximation problem is use...

In animal societies, some stressful events can lead to higher levels of physiological stress. Such stressors, like social rank, also predict an increased vulnerability to an array of diseases. However, the physiological relationship between social rank and stress varies between different species, as well as within groups of a single species. For example, dominant individuals are more socially s...

The Machiavellian/Social Intelligence Hypothesis proposes that a complex social environment selected for advanced cognitive abilities in vertebrates. In primates it has been proposed that sophisticated social strategies like obtaining suitable coalition partners are an important component of social intelligence. Knowing the rank relationships between group members is a basic requirement for the...

Abstract In this work, we consider the issue of unveiling unknown links in a social network, one of the difficulties of this problem being the small number of unobserved links in comparison of the total number of pairs of nodes. We define a simple supervised learning-to-rank framework, called RankMerging, which aims at combining information provided by various unsupervised rankings. As an illus...