Consistency of Spectral Hypergraph Partitioning under Planted Partition Model

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral graph partitioning under the stochastic block model are well known. In this paper, we present a planted partition model for sparse random non-uniform hypergraphs that generalizes the stochastic block model. We derive an error bound for a spectral hypergraph partitioning algorithm under this model using matrix concentration inequalities. To the best of our knowledge, this is the first consistency result related to partitioning non-uniform hypergraphs.Comment: 35 pages, 2 figures, 1 tabl

Probabilistic Inference of Twitter Users' Age based on What They Follow

Twitter provides an open and rich source of data for studying human behaviour at scale and is widely used in social and network sciences. However, a major criticism of Twitter data is that demographic information is largely absent. Enhancing Twitter data with user ages would advance our ability to study social network structures, information flows and the spread of contagions. Approaches toward age detection of Twitter users typically focus on specific properties of tweets, e.g., linguistic features, which are language dependent. In this paper, we devise a language-independent methodology for determining the age of Twitter users from data that is native to the Twitter ecosystem. The key idea is to use a Bayesian framework to generalise ground-truth age information from a few Twitter users to the entire network based on what/whom they follow. Our approach scales to inferring the age of 700 million Twitter accounts with high accuracy.Comment: 9 pages, 9 figure

Analysis and Control of Socio-Cultural Opinion Evolution in Complex Social Systems

The overarching goal of this thesis is to further our understanding about opinion evolution in networked societies. Such insights can be used in a variety of fields such as economy, marketing, transportation, egress, etc. Three main subjects build up this interdisciplinary research: Sociology, Statistical Mechanics, and Network Sciences. In this thesis, for macrolevel (or society-level) analyses, techniques from statistical mechanics have been borrowed to mathematically model the opinion dynamic on different network topologies based on different interaction models. Also, for micro-level (individual-level) analyses, Individual Decision Making Algorithms (IDMA) have been designed. To account for both macro-level and micro-level dynamics, these two regimes are combined resulting in a more accurate model for opinion propagation. Assessing the controllability of such dynamics through experiments in presence of actual humans is the part of this thesis

Horizontal visibility graphs transformed from fractional Brownian motions: Topological properties versus Hurst index

Nonlinear time series analysis aims at understanding the dynamics of stochastic or chaotic processes. In recent years, quite a few methods have been proposed to transform a single time series to a complex network so that the dynamics of the process can be understood by investigating the topological properties of the network. We study the topological properties of horizontal visibility graphs constructed from fractional Brownian motions with different Hurst index $H\in(0,1)$. Special attention has been paid to the impact of Hurst index on the topological properties. It is found that the clustering coefficient $C$ decreases when $H$ increases. We also found that the mean length $L$ of the shortest paths increases exponentially with $H$ for fixed length $N$ of the original time series. In addition, $L$ increases linearly with respect to $N$ when $H$ is close to 1 and in a logarithmic form when $H$ is close to 0. Although the occurrence of different motifs changes with $H$, the motif rank pattern remains unchanged for different $H$. Adopting the node-covering box-counting method, the horizontal visibility graphs are found to be fractals and the fractal dimension $d_B$ decreases with $H$. Furthermore, the Pearson coefficients of the networks are positive and the degree-degree correlations increase with the degree, which indicate that the horizontal visibility graphs are assortative. With the increase of $H$, the Pearson coefficient decreases first and then increases, in which the turning point is around $H=0.6$. The presence of both fractality and assortativity in the horizontal visibility graphs converted from fractional Brownian motions is different from many cases where fractal networks are usually disassortative.Comment: 12 pages, 8 figure

Singular Structure and Enhanced Friedel Oscillations in the Two-Dimensional Electron Gas

We calculate the leading order corrections (in $r_s$) to the static polarization $\Pi^{*}(q,0,)$, with dynamically screened interactions, for the two-dimensional electron gas. The corresponding diagrams all exhibit singular logarithmic behavior in their derivatives at $q=2 k_F$ and provide significant enhancement to the proper polarization particularly at low densities. At a density of $r_s=3$, the contribution from the leading order {\em fluctuational} diagrams exceeds both the zeroth order (Lindhard) response and the self-energy and exchange contributions. We comment on the importance of these diagrams in two-dimensions and make comparisons to an equivalent three-dimensional electron gas; we also consider the impact these finding have on $\Pi^{*}(q,0)$ computed to all orders in perturbation theory

Impact of edge-removal on the centrality betweenness of the best spreaders

The control of epidemic spreading is essential to avoid potential fatal consequences and also, to lessen unforeseen socio-economic impact. The need for effective control is exemplified during the severe acute respiratory syndrome (SARS) in 2003, which has inflicted near to a thousand deaths as well as bankruptcies of airlines and related businesses. In this article, we examine the efficacy of control strategies on the propagation of infectious diseases based on removing connections within real world airline network with the associated economic and social costs taken into account through defining appropriate quantitative measures. We uncover the surprising results that removing less busy connections can be far more effective in hindering the spread of the disease than removing the more popular connections. Since disconnecting the less popular routes tend to incur less socio-economic cost, our finding suggests the possibility of trading minimal reduction in connectivity of an important hub with efficiencies in epidemic control. In particular, we demonstrate the performance of various local epidemic control strategies, and show how our approach can predict their cost effectiveness through the spreading control characteristics.Comment: 11 pages, 4 figure

Networks in Financial Markets

The thesis applies methods from network sciences to four economic topics: herding in financial markets; corporate board networks; contagion in global financial markets; the Italian overnight loan market