Using Robust PCA to estimate regional characteristics of language use from geo-tagged Twitter messages

Principal component analysis (PCA) and related techniques have been successfully employed in natural language processing. Text mining applications in the age of the online social media (OSM) face new challenges due to properties specific to these use cases (e.g. spelling issues specific to texts posted by users, the presence of spammers and bots, service announcements, etc.). In this paper, we employ a Robust PCA technique to separate typical outliers and highly localized topics from the low-dimensional structure present in language use in online social networks. Our focus is on identifying geospatial features among the messages posted by the users of the Twitter microblogging service. Using a dataset which consists of over 200 million geolocated tweets collected over the course of a year, we investigate whether the information present in word usage frequencies can be used to identify regional features of language use and topics of interest. Using the PCA pursuit method, we are able to identify important low-dimensional features, which constitute smoothly varying functions of the geographic location

The effect of network structure on phase transitions in queuing networks

Recently, De Martino et al have presented a general framework for the study of transportation phenomena on complex networks. One of their most significant achievements was a deeper understanding of the phase transition from the uncongested to the congested phase at a critical traffic load. In this paper, we also study phase transition in transportation networks using a discrete time random walk model. Our aim is to establish a direct connection between the structure of the graph and the value of the critical traffic load. Applying spectral graph theory, we show that the original results of De Martino et al showing that the critical loading depends only on the degree sequence of the graph -- suggesting that different graphs with the same degree sequence have the same critical loading if all other circumstances are fixed -- is valid only if the graph is dense enough. For sparse graphs, higher order corrections, related to the local structure of the network, appear.Comment: 12 pages, 7 figure

Spatial Fingerprints of Community Structure in Human Interaction Network for an Extensive Set of Large-Scale Regions

Human interaction networks inferred from country-wide telephone activity recordings were recently used to redraw political maps by projecting their topological partitions into geographical space. The results showed remarkable spatial cohesiveness of the network communities and a significant overlap between the redrawn and the administrative borders. Here we present a similar analysis based on one of the most popular online social networks represented by the ties between more than 5.8 million of its geo-located users. The worldwide coverage of their measured activity allowed us to analyze the large-scale regional subgraphs of entire continents and an extensive set of examples for single countries. We present results for North and South America, Europe and Asia. In our analysis we used the well- established method of modularity clustering after an aggregation of the individual links into a weighted graph connecting equal- area geographical pixels. Our results show fingerprints of both of the opposing forces of dividing local conflicts and of uniting cross-cultural trends of globalization

Short-time behavior of continuous-time quantum walks on graphs

Dynamical evolution of systems with sparse Hamiltonians can always be recognized as continuous-time quantum walks (CTQWs) on graphs. In this paper, we analyze the short-time asymptotics of CTQWs. In recent studies, it was shown that for the classical diffusion process the short-time asymptotics of the transition probabilities follows power laws whose exponents are given by the usual combinatorial distances of the nodes. Inspired by this result, we perform a similar analysis for CTQWs in both closed and open systems, including time-dependent couplings. For time-reversal symmetric coherent quantum evolutions, the short-time asymptotics of the transition probabilities is completely determined by the topology of the underlying graph analogously to the classical case, but with a doubled power-law exponent. Moreover, this result is robust against the introduction of on-site potential terms. However, we show that time-reversal symmetry-breaking terms and noncoherent effects can significantly alter the short-time asymptotics. The analytical formulas are checked against numerics, and excellent agreement is found. Furthermore, we discuss in detail the relevance of our results for quantum evolutions on particular network topologies

Communities formed in Switzerland.

<p>These are clusters formed within the European continent’s regional subgraph, focusing on the single country of <i>Switzerland</i>. Each cluster of geo-pixels has a different unique color. The <i>red</i> and the <i>purple</i> correspond to the communities concentrated in <i>France</i> and in <i>Italy</i> respectively. The subnational boundaries are marked with thinner lines, depicting the administrative units of this graph.</p