Directionality is a crucial ingredient in many complex networks in which information, energy or influence are transmitted. In such directed networks, analysing flows (and not only the strength of connections) is crucial to reveal important features of the network that might go undetected if the orientation of connections is ignored. We showcase here a flow-based approach for community detection through the study of the network of the most influential Twitter users during the 2011 riots in England. Firstly, we use directed Markov Stability to extract descriptions of the network at different levels of coarseness in terms of interest communities, i.e. groups of nodes within which flows of information are contained and reinforced. Such interest communities reveal user groupings according to location, profession, employer and topic. The study of flows also allows us to generate an interest distance, which affords a personalized view of the attention in the network as viewed from the vantage point of any given user. Secondly, we analyse the profiles of incoming and outgoing long-range flows with a combined approach of role-based similarity and the novel relaxed minimum spanning tree algorithm to reveal that the users in the network can be classified into five roles. These flow roles go beyond the standard leader/follower dichotomy and differ from classifications based on regular/structural equivalence. We then show that the interest communities fall into distinct informational organigrams characterized by a different mix of user roles reflecting the quality of dialogue within them. Our generic framework can be used to provide insight into how flows are generated, distributed, preserved and consumed in directed networks.

We exploit flow propagation on the directed neuronal network of the nematode C. elegans to reveal dynamically relevant features of its connectome. We find flow-based groupings of neurons at different levels of granularity, which we relate to functional and anatomical constituents of its nervous system. A systematic in silico evaluation of the full set of single and double neuron ablations is used to identify deletions that induce the most severe disruptions of the multi-resolution flow structure. Such ablations are linked to functionally relevant neurons, and suggest potential candidates for further in vivo investigation. In addition, we use the directional patterns of incoming and outgoing network flows at all scales to identify flow profiles for the neurons in the connectome, without pre-imposing a priori categories. The four flow roles identified are linked to signal propagation motivated by biological input-response scenarios.

Abstract-We present a framework to cluster nodes in directed networks according to their roles by combining Role-Based Similarity (RBS) and Markov Stability, two techniques based on flows. First we compute the RBS matrix, which contains the pairwise similarities between nodes according to the scaled number of in-and out-directed paths of different lengths. The weighted RBS similarity matrix is then transformed into an undirected similarity network using the Relaxed MinimumSpanning Tree (RMST) algorithm, which uses the geometric structure of the RBS matrix to unblur the network, such that edges between nodes with high, direct RBS are preserved. Finally, we partition the RMST similarity network into role-communities of nodes at all scales using Markov Stability to find a robust set of roles in the network. We showcase our framework through a biological and a man-made network.

Social media are being increasingly used for health promotion, yet the landscape of users, messages and interactions in such fora is poorly understood. Studies of social media and diabetes have focused mostly on patients, or public agencies addressing it, but have not looked broadly at all of the participants or the diversity of content they contribute. We study Twitter conversations about diabetes through the systematic analysis of 2.5 million tweets collected over 8 months and the interactions between their authors. We address three questions. (1) What themes arise in these tweets? (2) Who are the most influential users? (3) Which type of users contribute to which themes? We answer these questions using a mixed-methods approach, integrating techniques from anthropology, network science and information retrieval such as thematic coding, temporal network analysis and community and topic detection. Diabetes-related tweets fall within broad thematic groups: health information, news, social interaction and commercial. At the same time, humorous messages and references to popular culture appear consistently, more than any other type of tweet. We classify authors according to their temporal ‘hub’ and ‘authority’ scores. Whereas the hub landscape is diffuse and fluid over time, top authorities are highly persistent across time and comprise bloggers, advocacy groups and NGOs related to diabetes, as well as for-profit entities without specific diabetes expertise. Top authorities fall into seven interest communities as derived from their Twitter follower network. Our findings have implications for public health professionals and policy makers who seek to use social media as an engagement tool and to inform policy design.

BackgroundStomata are tiny pores in plant leaves that regulate gas and water exchange between the plant and its environment. Abscisic acid and ethylene are two well-known elicitors of stomatal closure when acting independently. However, when stomata are presented with a combination of both signals, they fail to close.ResultsToshed light on this unexplained behaviour, we have collected time course measurements of stomatal aperture and hydrogen peroxide production in Arabidopsis thaliana guard cells treated with abscisic acid, ethylene, and a combination of both. Our experiments show that stomatal closure is linked to sustained high levels of hydrogen peroxide in guard cells. When treated with a combined dose of abscisic acid and ethylene, guard cells exhibit increased antioxidant activity that reduces hydrogen peroxide levels and precludes closure. We construct a simplified model of stomatal closure derived from known biochemical pathways that captures the experimentally observed behaviour.ConclusionsOur experiments and modelling results suggest a distinct role for two antioxidant mechanisms during stomatal closure: a slower, delayed response activated by a single stimulus (abscisic acid ‘or’ ethylene) and another more rapid ‘and’ mechanism that is only activated when both stimuli are present. Our model indicates that the presence of this rapid ‘and’ mechanism in the antioxidant response is key to explain the lack of closure under a combined stimulus.

Motivation Even within well studied organisms, many genes lack useful functional annotations. One way to generate such functional information is to infer biological relationships between genes/proteins, using a network of gene coexpression data that includes functional annotations. However, the lack of trustworthy functional annotations can impede the validation of such networks. Hence, there is a need for a principled method to construct gene coexpression networks that capture biological information and are structurally stable even in the absence of functional information. Results We introduce the concept of signed distance correlation as a measure of dependency between two variables, and apply it to generate gene coexpression networks. Distance correlation offers a more intuitive approach to network construction than commonly used methods such as Pearson correlation and mutual information. We propose a framework to generate self-consistent networks using signed distance correlation purely from gene expression data, with no additional information. We analyse data from three different organisms to illustrate how networks generated with our method are more stable and capture more biological information compared to networks obtained from Pearson correlation or mutual information. Supplementary information Supplementary Information and code are available at Bioinformatics and https://github.com/javier-pardodiaz/sdcorGCN online.

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

Network theory is a useful framework for studying interconnected systems of interacting agents. Many networked systems evolve continuously in time, but most existing methods for the analysis of time-dependent networks rely on discrete or discretized time. In this paper, we propose an approach for studying networks that evolve in continuous time by distinguishing between interactions, which we model as discrete contacts, and ties, which represent strengths of relationships as functions of time. To illustrate our tie-decay network formulation, we adapt the well-known Page-Rank centrality score to the tie-decay framework in a mathematically tractable and computationally efficient way. We demonstrate our framework on a synthetic example and then use it to study a network of retweets during the 2012 National Health Service controversy in the United Kingdom. Our work also provides guidance for similar generalizations of other tools from network theory to continuous-time networks with tie decay, including for applications to streaming data.