Community detection in multiplex networks using locally adaptive random walks

Multiplex networks, a special type of multilayer networks, are increasingly applied in many domains ranging from social media analytics to biology. A common task in these applications concerns the detection of community structures. Many existing algorithms for community detection in multiplexes attempt to detect communities which are shared by all layers. In this article we propose a community detection algorithm, LART (Locally Adaptive Random Transitions), for the detection of communities that are shared by either some or all the layers in the multiplex. The algorithm is based on a random walk on the multiplex, and the transition probabilities defining the random walk are allowed to depend on the local topological similarity between layers at any given node so as to facilitate the exploration of communities across layers. Based on this random walk, a node dissimilarity measure is derived and nodes are clustered based on this distance in a hierarchical fashion. We present experimental results using networks simulated under various scenarios to showcase the performance of LART in comparison to related community detection algorithms

Nodal Quasiparticle Lifetimes in Cuprate Superconductors

A new generation of angular-resolved photoemission spectroscopy (ARPES) measurements on the cuprate superconductors offer the promise of enhanced momentum and energy resolution. In particular, the energy and temperature dependence of the on-shell nodal (k_x=k_y) quasiparticle scattering rate can be studied. In the superconducting state, low temperature transport measurements suggest that one can describe nodal quasiparticles within the framework of a BCS d-wave model by including forward elastic scattering and spin-fluctuation inelastic scattering. Here, using this model, we calculate the temperature and frequency dependence of the on-shell nodal quasiparticle scattering rate in the superconducting state which determines the momentum width of the ARPES momentum distribution curves. For a zero-energy quasiparticle at the nodal momentum k_N, both the elastic and inelastic scattering rate show a sudden decrease as the temperature drops below Tc, reflecting the onset of the gap amplitude. At low temperatures the scattering rate decreases as T^3 and approaches a zero temperature value determined by the elastic impurity scattering. For T>T_c, we find a quasilinear dependence on T. At low reduced temperatures, the elastic scattering rate for the nodal quasiparticles exhibits a quasilinear increase at low energy which arises from elastic scattering processes. The inelastic spin-fluctuation scattering leads to a low energy omega^3 dependence which, for omega>~Delta_0, crosses over to a quasilinear behavior.Comment: 8 pages, 7 figures, minor revision