Graph coarse-graining reveals differences in the module-level structure of functional brain networks.

Networks have become a standard tool for analyzing functional magnetic resonance imaging (fMRI) data. In this approach, brain areas and their functional connections are mapped to the nodes and links of a network. Even though this mapping reduces the complexity of the underlying data, it remains challenging to understand the structure of the resulting networks due to the large number of nodes and links. One solution is to partition networks into modules and then investigate the modules' composition and relationship with brain functioning. While this approach works well for single networks, understanding differences between two networks by comparing their partitions is difficult and alternative approaches are thus necessary. To this end, we present a coarse-graining framework that uses a single set of data-driven modules as a frame of reference, enabling one to zoom out from the node- and link-level details. As a result, differences in the module-level connectivity can be understood in a transparent, statistically verifiable manner. We demonstrate the feasibility of the method by applying it to networks constructed from fMRI data recorded from 13 healthy subjects during rest and movie viewing. While independently partitioning the rest and movie networks is shown to yield little insight, the coarse-graining framework enables one to pinpoint differences in the module-level structure, such as the increased number of intra-module links within the visual cortex during movie viewing. In addition to quantifying differences due to external stimuli, the approach could also be applied in clinical settings, such as comparing patients with healthy controls.

Inferring human mobility using communication patterns.

Understanding the patterns of mobility of individuals is crucial for a number of reasons, from city planning to disaster management. There are two common ways of quantifying the amount of travel between locations: by direct observations that often involve privacy issues, e.g., tracking mobile phone locations, or by estimations from models. Typically, such models build on accurate knowledge of the population size at each location. However, when this information is not readily available, their applicability is rather limited. As mobile phones are ubiquitous, our aim is to investigate if mobility patterns can be inferred from aggregated mobile phone call data alone. Using data released by Orange for Ivory Coast, we show that human mobility is well predicted by a simple model based on the frequency of mobile phone calls between two locations and their geographical distance. We argue that the strength of the model comes from directly incorporating the social dimension of mobility. Furthermore, as only aggregated call data is required, the model helps to avoid potential privacy problems.

Effects of temporal correlations on cascades: threshold models on temporal networks.

A person's decision to adopt an idea or product is often driven by the decisions of peers, mediated through a network of social ties. A common way of modeling adoption dynamics is to use threshold models, where a node may become an adopter given a high enough rate of contacts with adopted neighbors. We study the dynamics of threshold models that take both the network topology and the timings of contacts into account, using empirical contact sequences as substrates. The models are designed such that adoption is driven by the number of contacts with different adopted neighbors within a chosen time. We find that while some networks support cascades leading to network-level adoption, some do not: the propagation of adoption depends on several factors from the frequency of contacts to burstiness and timing correlations of contact sequences. More specifically, burstiness is seen to suppress cascade sizes when compared to randomized contact timings, while timing correlations between contacts on adjacent links facilitate cascades.

Author Impact Factor: tracking the dynamics of individual scientific impact.

The impact factor (IF) of scientific journals has acquired a major role in the evaluations of the output of scholars, departments and whole institutions. Typically papers appearing in journals with large values of the IF receive a high weight in such evaluations. However, at the end of the day one is interested in assessing the impact of individuals, rather than papers. Here we introduce Author Impact Factor (AIF), which is the extension of the IF to authors. The AIF of an author A in year t is the average number of citations given by papers published in year t to papers published by A in a period of Δt years before year t. Due to its intrinsic dynamic character, AIF is capable to capture trends and variations of the impact of the scientific output of scholars in time, unlike the h-index, which is a growing measure taking into account the whole career path.

Contextual analysis framework for bursty dynamics.

To understand the origin of bursty dynamics in natural and social processes we provide a general analysis framework in which the temporal process is decomposed into subprocesses and then the bursts in subprocesses, called contextual bursts, are combined to collective bursts in the original process. For the combination of subprocesses, it is required to consider the distribution of different contexts over the original process. Based on minimal assumptions for interevent time statistics, we present a theoretical analysis for the relationship between contextual and collective interevent time distributions. Our analysis framework helps to exploit contextual information available in decomposable bursty dynamics.

World citation and collaboration networks: uncovering the role of geography in science.

Modern information and communication technologies, especially the Internet, have diminished the role of spatial distances and territorial boundaries on the access and transmissibility of information. This has enabled scientists for closer collaboration and internationalization. Nevertheless, geography remains an important factor affecting the dynamics of science. Here we present a systematic analysis of citation and collaboration networks between cities and countries, by assigning papers to the geographic locations of their authors' affiliations. The citation flows as well as the collaboration strengths between cities decrease with the distance between them and follow gravity laws. In addition, the total research impact of a country grows linearly with the amount of national funding for research & development. However, the average impact reveals a peculiar threshold effect: the scientific output of a country may reach an impact larger than the world average only if the country invests more than about 100,000 USD per researcher annually.

Time-varying priority queuing models for human dynamics.

Queuing models provide insight into the temporal inhomogeneity of human dynamics, characterized by the broad distribution of waiting times of individuals performing tasks. We theoretically study the queuing model of an agent trying to execute a task of interest, the priority of which may vary with time due to the agent's "state of mind." However, its execution is disrupted by other tasks of random priorities. By considering the priority of the task of interest either decreasing or increasing algebraically in time, we analytically obtain and numerically confirm the bimodal and unimodal waiting time distributions with power-law decaying tails, respectively. These results are also compared to the updating time distribution of papers in arXiv.org and the processing time distribution of papers in Physical Review journals. Our analysis helps to understand human task execution in a more realistic scenario.

The evolution of interdisciplinarity in physics research.

Science, being a social enterprise, is subject to fragmentation into groups that focus on specialized areas or topics. Often new advances occur through cross-fertilization of ideas between sub-fields that otherwise have little overlap as they study dissimilar phenomena using different techniques. Thus to explore the nature and dynamics of scientific progress one needs to consider the organization and interactions between different subject areas. Here, we study the relationships between the sub-fields of Physics using the Physics and Astronomy Classification Scheme (PACS) codes employed for self-categorization of articles published over the past 25 years (1985-2009). We observe a clear trend towards increasing interactions between the different sub-fields. The network of sub-fields also exhibits core-periphery organization, the nucleus being dominated by Condensed Matter and General Physics. However, over time Interdisciplinary Physics is steadily increasing its share in the network core, reflecting a shift in the overall trend of Physics research.

Path lengths, correlations, and centrality in temporal networks.

In temporal networks, where nodes interact via sequences of temporary events, information or resources can only flow through paths that follow the time ordering of events. Such temporal paths play a crucial role in dynamic processes. However, since networks have so far been usually considered static or quasistatic, the properties of temporal paths are not yet well understood. Building on a definition and algorithmic implementation of the average temporal distance between nodes, we study temporal paths in empirical networks of human communication and air transport. Although temporal distances correlate with static graph distances, there is a large spread, and nodes that appear close from the static network view may be connected via slow paths or not at all. Differences between static and temporal properties are further highlighted in studies of the temporal closeness centrality. In addition, correlations and heterogeneities in the underlying event sequences affect temporal path lengths, increasing temporal distances in communication networks and decreasing them in the air transport network.

Emergence of bursts and communities in evolving weighted networks.

Understanding the patterns of human dynamics and social interaction and the way they lead to the formation of an organized and functional society are important issues especially for techno-social development. Addressing these issues of social networks has recently become possible through large scale data analysis of mobile phone call records, which has revealed the existence of modular or community structure with many links between nodes of the same community and relatively few links between nodes of different communities. The weights of links, e.g., the number of calls between two users, and the network topology are found correlated such that intra-community links are stronger compared to the weak inter-community links. This feature is known as Granovetter's "The strength of weak ties" hypothesis. In addition to this inhomogeneous community structure, the temporal patterns of human dynamics turn out to be inhomogeneous or bursty, characterized by the heavy tailed distribution of time interval between two consecutive events, i.e., inter-event time. In this paper, we study how the community structure and the bursty dynamics emerge together in a simple evolving weighted network model. The principal mechanisms behind these patterns are social interaction by cyclic closure, i.e., links to friends of friends and the focal closure, links to individuals sharing similar attributes or interests, and human dynamics by task handling process. These three mechanisms have been implemented as a network model with local attachment, global attachment, and priority-based queuing processes. By comprehensive numerical simulations we show that the interplay of these mechanisms leads to the emergence of heavy tailed inter-event time distribution and the evolution of Granovetter-type community structure. Moreover, the numerical results are found to be in qualitative agreement with empirical analysis results from mobile phone call dataset.

Using explosive percolation in analysis of real-world networks.

We apply a variant of the explosive percolation procedure to large real-world networks and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural properties of the network, as well as the number of unoccupied links considered for comparison in our procedure. We observe that in our social networks, the percolation clusters close to the critical point are related to the community structure. This relationship is further highlighted by applying the procedure to model networks with predefined communities.

Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system.

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. The coordination of many different co-occurring processes at this level underlies the command and control of overall network activity. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations such as, optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Even including information about the genetic relatedness of the cells cannot account for the observed modular structure. Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.

Phase of Ising spins on modular networks analogous to social polarization.

Coordination processes in complex systems can be related to the problem of collective ordering in networks, many of which have modular organization. Investigating the order-disorder transition for Ising spins on modular random networks, corresponding to consensus formation in society, we observe two distinct phases: (i) ordering within each module at a critical temperature followed by (ii) global ordering at a lower temperature. This indicates polarization of society into groups having contrary opinions can persist indefinitely even when mutual interactions between agents favor consensus.

Modular networks emerge from multiconstraint optimization.

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.

Collective behavior of stock price movements in an emerging market.

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intrasector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.