Identifying communities by influence dynamics in social networks

Communities are not static; they evolve, split and merge, appear and disappear, i.e. they are product of dynamical processes that govern the evolution of the network. A good algorithm for community detection should not only quantify the topology of the network, but incorporate the dynamical processes that take place on the network. We present a novel algorithm for community detection that combines network structure with processes that support creation and/or evolution of communities. The algorithm does not embrace the universal approach but instead tries to focus on social networks and model dynamic social interactions that occur on those networks. It identifies leaders, and communities that form around those leaders. It naturally supports overlapping communities by associating each node with a membership vector that describes node's involvement in each community. This way, in addition to overlapping communities, we can identify nodes that are good followers to their leader, and also nodes with no clear community involvement that serve as a proxy between several communities and are equally as important. We run the algorithm for several real social networks which we believe represent a good fraction of the wide body of social networks and discuss the results including other possible applications.Comment: 10 pages, 6 figure

Spatial unification of coupling interactions between EGFR and PTPs establishes a growth factor sensing network

Cells continuously sense and respond to stimuli from the non-stationary environment. For this, they optimise processing of the perceived signals while maintaining continuous responsiveness. Cell surface receptors, such as the receptor tyrosine kinases, comprise the first layer of sensing. They translate the extracellular signal into internal activity using the protein interaction networks in which they are embedded. The proto-oncogenic epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase whose sensitivity to epidermal growth factor (EGF) and signalling duration determines cellular behaviour. In the canonical view, signal processing occurs through the ligand-induced dimer formation mechanism and subsequent trans-phosphorylation. However, it has been also established recently that signal amplification via the unliganded EGFR monomers through an autocatalytic mechanism enhances the phosphorylation response of EGFR. In this thesis, I demonstrate how autocatalytic phosphorylation of EGFR in concert with the coupling interactions with the protein tyrosine phosphatases (PTPs) shape the response dynamics of EGFR. Single cell dose-response analysis revealed that a toggle switch between autocatalytically activated monomeric EGFR and the tumour suppressor PTPRG at the plasma membrane (PM) shapes the sensitivity of EGFR to EGF dose. As the system exhibits switch-like activation due to the bistable regime of operation, irreversible activation occurs as an adversary side effect. To ensure continuous growth factor sensing, the system is positioned outside of the bistable regime by the PM-localised PTPRJ, which negatively regulates EGFR phosphorylation. On the other hand, a spatially-distributed negative feedback with the ER-bound PTPN2 that is established by vesicular trafficking resets the phosphorylation state of monomeric EGFR on the plasma membrane. The distinct recycling route of the unliganded receptor, as opposed to the unidirectional degradation route towards the perinuclear area of the liganded receptor, enables it to repopulate the plasma membrane and thus maintain sensitivity to upcoming stimuli. In this manner, the coupling interactions between EGFR and the PTPs on different membranes are spatially unified in a network that enables sensing of time-varying EGF signals. The signal processing capabilities of this network are optimised by the system organisation, as its parameters are poised at the criticality point, just outside the bistable regime of operation. In this region, the EGFR response is characterised by prolonged but reversible phosphorylation, enabling the cell to maintain a balance between preserving a transient memory of previous EGF stimulations, while still remaining responsive to upcoming stimuli

State diagram of a node for the model.

<p>The diagram shows the dynamics of a single node. Curvy arrows depict state change due to contact with the neighbors, while less curvy arrows depict spontaneous state change.</p

State diagram of a node for the altered model that operates only with the contact-based mechanism.

<p>The diagram shows the dynamics of a single node. Curvy arrows depict state change due to contact with the neighbors.</p

Modeling the Spread of Multiple Concurrent Contagions on Networks

<div><p>Many contagions spread over various types of communication networks and their spreading dynamics have been extensively studied in the literature. Here we propose a general model for the concurrent spread of an arbitrary number of contagions in complex networks. The model is stochastic and runs in discrete time, and includes two widely used mechanisms by which a node can change its state. The first, termed the spontaneous state change mechanism, describes spontaneous transition to another state, while the second, termed the contact-induced state change mechanism, describes acquiring other contagions due to contact with the neighbors. We consider reactive discrete-time spreading processes of multiple concurrent contagions where time steps are of finite size without neglecting the possibility of multiple infecting events in a single time step. An essential element for making the model numerically tractable is the use of an approximation for the probability that a node transits to a specific state given any set of neighboring states. Different transmission probabilities may be present between each pair of states. We also derive corresponding continuous–time equations that are simple and intuitive. The model includes many well-known epidemic and rumor spreading models as a special case and it naturally captures spreading processes in multiplex networks.</p></div

A multiplex network.

<p>Different link types correspond to different layers in the multiplex network. We assume that transmission probabilities depend on the link type, i.e. each contagion or state propagates differently over each layer. This is depicted by coloring the contact-induced transition mechanism links differently for each separate layer. In the adaptation of the model for multiplex networks both contagions spread only on their respective layers. Hence, we have and .</p

Comparison of the macroscopic behavior simulated by the approximated and non-approximated stochastic version of the model.

<p>Percentage of nodes in each of the states is displayed for each time step. The left panel shows the comparison results on a lattice network with periodic boundary conditions of 16384 () nodes. The right panel shows the comparison results on a power grid network of 4941 nodes and 13188 links, whose highest degree is 19. The results were produced by averaging over 1000 executions. The markers display the execution results of the approximated version, while the lines display the results of the non-approximated version, i.e. the actual model simulations. For brevity only 40 markers are displayed for each state.</p

Comparison of the macroscopic fixed point values produced by the approximated and non-approximated version of the discrete-time generalization of the model.

<p>The norm of the error vector, whose components are the differences between the macroscopic fixed point values (percentage of nodes in each state) of both versions, is calculated for each combination of the parameters and . and parameters are fixed at and , respectively. Three different graphs are examined with three random initial state assignments of the nodes: a complete and a star graph with 6 nodes, and a lattice graph with periodic boundary conditions of 9 nodes. Our approximated version produces the same fixed points as the non-approximated version, except for the line that depicts the area where there is no clear winner.</p

State diagram for the SIR model.

<p>The diagram shows the dynamics of a single node. A susceptible node can become infected by contacting its infected neighbors, with transmission probability . On the other hand, infected nodes spontaneously recover with probability and they remain permanently immune to the infection. The contact-induced transition mechanism is represented by a curvy arrow, whereas the spontaneous transition mechanism is represented by a less curvy arrow.</p

State diagram for the SIS model.

<p>The diagram shows the dynamics of a single node. A susceptible node can become infected by contacting its infected neighbors, with probability . On the other hand, infected nodes spontaneously recover with probability , and become susceptible again. The contact-induced transition mechanism is represented by a curvy arrow, whereas the spontaneous transition mechanism is represented by a less curvy arrow.</p