Despite their relatively low sampling factor, the freely available, randomly sampled status streams of Twitter are very useful sources of geographically embedded social network data. To statistically analyze the information Twitter provides via these streams, we have collected a year's worth of data and built a multi-terabyte relational database from it. The database is designed for fast data loading and to support a wide range of studies focusing on the statistics and geographic features of social networks, as well as on the linguistic analysis of tweets. In this paper we present the method of data collection, the database design, the data loading procedure and special treatment of geo-tagged and multi-lingual data. We also provide some SQL recipes for computing network statistics.

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.

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient quantum optimization algorithm for the graph coloring problem. Our circuits are deeper than the ones of the standard approach. However, the number of required qubits is exponentially reduced in the number of colors. We present extensive numerical simulations demonstrating the performance of our approach. Furthermore, to explore currently available alternatives, we also perform a study of random graph coloring on a quantum annealer to test the limiting factors of that approach, too.

We propose a simple structure for stationary non-Markovian quantum chains in the framework of collisional dynamics of open quantum systems. To this end, we modify the microscopic Markovian system-reservoir model, consider multiple collisions with each of the molecules with an overlap between the collisional time intervals. We show how the equivalent Markovian quantum chain can be constructed with the addition of satellite quantum memory to the system. We distinguish quantum from classical non-Markovianity. Moreover, we define the counts of non-Markovianity by the required number of satellite qubits and bits, respectively. As the particular measure of quantum non-Markovianity the discord of the satellite w.r.t. the system is suggested. Simplest qubit realizations are discussed, and the significance for real system-environment dynamics is also pointed out.

Twitter is a popular public conversation platform with world-wide audience and diverse forms of connections between users. In this paper we introduce the concept of aggregated regional Twitter networks in order to characterize communication between geopolitical regions. We present the study of a follower and a mention graph created from an extensive data set collected during the second half of the year of 2012. With a k-shell decomposition the global core-periphery structure is revealed and by means of a modified Regional-SIR model we also consider basic information spreading properties.adapting a simple information propagation model we can further differentiate the most efficient information sources of the world -as reflected in high volume of individual conversations. Methods Twitter dataWe used a data set collected from the freely available Twitter stream during the second half of the year of 2012 [3]. We refer to Twitter users in this data set allowing public access to their geographical location information as the geousers, and each one is located to a single fixed position [3]. Those that fell into unmapped territories (e.g., oceans) were discarded from further analysis. By means of aggregation of their different forms of connections we create two different communication networks between geopolitical regions: the mention (M) and the follower (F ) networks.For creating the user-level follower graph we used 177, 176, 790 links between 3, 312, 961 geo-users identified as the most active ones. Given their list, the additional follower relations were collected separately [3]. The source of a following link is the followed user while its target is the follower. A network built using the inverse follower relation is also be meaningful, and can be used for showing the direction of interest. To create the user-level mention graph we used 132, 436, 279 mention messages between 5, 381, 565 geo-users. The source of a mention link is the sender while its target is the mentioned user.