Twitter event networks and the Superstar model

Condensation phenomenon is often observed in social networks such as Twitter where one "superstar" vertex gains a positive fraction of the edges, while the remaining empirical degree distribution still exhibits a power law tail. We formulate a mathematically tractable model for this phenomenon that provides a better fit to empirical data than the standard preferential attachment model across an array of networks observed in Twitter. Using embeddings in an equivalent continuous time version of the process, and adapting techniques from the stable age-distribution theory of branching processes, we prove limit results for the proportion of edges that condense around the superstar, the degree distribution of the remaining vertices, maximal nonsuperstar degree asymptotics and height of these random trees in the large network limit.Comment: Published at http://dx.doi.org/10.1214/14-AAP1053 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A High-Order Radial Basis Function (RBF) Leray Projection Method for the Solution of the Incompressible Unsteady Stokes Equations

A new projection method based on radial basis functions (RBFs) is presented for discretizing the incompressible unsteady Stokes equations in irregular geometries. The novelty of the method comes from the application of a new technique for computing the Leray-Helmholtz projection of a vector field using generalized interpolation with divergence-free and curl-free RBFs. Unlike traditional projection methods, this new method enables matching both tangential and normal components of divergence-free vector fields on the domain boundary. This allows incompressibility of the velocity field to be enforced without any time-splitting or pressure boundary conditions. Spatial derivatives are approximated using collocation with global RBFs so that the method only requires samples of the field at (possibly scattered) nodes over the domain. Numerical results are presented demonstrating high-order convergence in both space (between 5th and 6th order) and time (up to 4th order) for some model problems in two dimensional irregular geometries.Comment: 34 pages, 8 figure

Pulsed Ultrasound Does Not Affect Recovery From Delayed Onset Muscle Soreness

Aim: To investigate the effects of pulsed Ultrasound (US) in recovery from Delayed Onset Muscle Soreness (DOMS). Methods: Twelve healthy male athletes (mean age 23.83±1.697 year) performed an eccentric exercise protocol of non-dominant elbow flexors to induce muscle soreness on 2 occasions separated by 3 weeks. Subjects in experimental group received pulsed US (1 MHz, intensity 0.8 W/cm2, mark space ratio 1:10), whereas control group received sham US after 24 h, 48 h and 72 h. Perception of muscle soreness, active ROM and muscle strength were the parameters measured at 0 h, 24 h, 48 h and 72 h with the help of VAS, manual goniometer and JONEX muscles master instrument respectively. Results: Post hoc t test analysis revealed significant differences (p <0.05) between 0 h and 72 h in the parameter of ROM (t = 6.18) and muscle power (t = 2.54) as well as between 24 h and 48 h in the parameter of muscle soreness (t = 3.13) in control group. Similar differences were also observed in the experimental group. No significant inter-group differences at α level of 0.05 was observed in any parameter at any level. Conclusion: The pattern of recovery from DOMS was not influenced by the application of pulsed Ultrasound at the parameters discussed here

Topological Sound and Flocking on Curved Surfaces

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady state due to the constraints imposed by the topology of the underlying surface. In the presence of spontaneous flow the system additionally supports long-wavelength propagating sound modes which get gapped by the curvature of the underlying substrate. We analytically compute the steady state profile of an active polar flock on a two-sphere and a catenoid, and show that curvature and active flow together result in symmetry protected topological modes that get localized to special geodesics on the surface (the equator or the neck respectively). These modes are the analogue of edge states in electronic quantum Hall systems and provide unidirectional channels for information transport in the flock, robust against disorder and backscattering.Comment: 15 pages, 6 figure

Meson Masses and Mixing Angles in 2+1 Flavor Polyakov Quark Meson Sigma Model and Symmetry Restoration Effects

The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized 2+1 flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare 2+1 quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in quark meson linear sigma model together with the presence of axial anomaly, triggers an early and significant melting of the strange condensate. We have examined how the inclusion of the Polyakov loop qualitatively and quantitatively affects the convergence in the masses of the chiral partners in pseudoscalar ($\pi$, $\eta$, $\eta'$, $K$) and scalar ($\sigma$, $a_0$, $f_0$,$\kappa$) meson nonets as the temperature is varied on the reduced temperature scale. The role of $U_A(1)$ anomaly in determining the isoscalar masses and mixing angles for the pseudoscalar ($\eta$ and $\eta'$) and scalar ($\sigma$ and $f_0$)meson complex, has also been investigated in the Polyakov quark meson linear sigma model. The interplay of chiral symmetry restoration effects and the setting up of $U_A(1)$ restoration trend has been discussed and analyzed in the framework of the presented model calculations.Comment: 15 pages, 8 figures, 4 table

A Statistical Semi-Empirical Model: Satellite galaxies in Groups and Clusters

We present STEEL a STatistical sEmi-Empirical modeL designed to probe the distribution of satellite galaxies in groups and clusters. Our fast statistical methodology relies on tracing the abundances of central and satellite haloes via their mass functions at all cosmic epochs with virtually no limitation on cosmic volume and mass resolution. From mean halo accretion histories and subhalo mass functions the satellite mass function is progressively built in time via abundance matching techniques constrained by number densities of centrals in the local Universe. By enforcing dynamical merging timescales as predicted by high-resolution N-body simulations, we obtain satellite distributions as a function of stellar mass and halo mass consistent with current data. We show that stellar stripping, star formation, and quenching play all a secondary role in setting the number densities of massive satellites above $M_*\gtrsim 3\times 10^{10}\, M_{\odot}$. We further show that observed star formation rates used in our empirical model over predict low-mass satellites below $M_*\lesssim 3\times 10^{10}\, M_{\odot}$, whereas, star formation rates derived from a continuity equation approach yield the correct abundances similar to previous results for centrals.Comment: 21 pages, 17 Figures. MNRAS, in pres