Toward Order-of-Magnitude Cascade Prediction

When a piece of information (microblog, photograph, video, link, etc.) starts to spread in a social network, an important question arises: will it spread to "viral" proportions -- where "viral" is defined as an order-of-magnitude increase. However, several previous studies have established that cascade size and frequency are related through a power-law - which leads to a severe imbalance in this classification problem. In this paper, we devise a suite of measurements based on "structural diversity" -- the variety of social contexts (communities) in which individuals partaking in a given cascade engage. We demonstrate these measures are able to distinguish viral from non-viral cascades, despite the severe imbalance of the data for this problem. Further, we leverage these measurements as features in a classification approach, successfully predicting microblogs that grow from 50 to 500 reposts with precision of 0.69 and recall of 0.52 for the viral class - despite this class comprising under 2\% of samples. This significantly outperforms our baseline approach as well as the current state-of-the-art. Our work also demonstrates how we can tradeoff between precision and recall.Comment: 4 pages, 15 figures, ASONAM 2015 poster pape

Dynamic modeling of Terahertz Quantum cascade lasers

In this paper, the influence of the simplifications made in the four-equation-based set of rate equations describing the dynamic behavior of a Quantum Cascade Laser (QCL) is studied. Numerical simulations based on the set of four rate equations has been developed, enabling the theoretical study of the influence of different parameters on the direct modulation response of the laser. These equations have been then linearized in order to deduce a set of state system equations, which was written in a matrix formalism. Finally, an approximate second order transfer function has been derived with the linearized dependence of its times constant

Recurrent flow analysis in spatiotemporally chaotic 2-dimensional Kolmogorov flow

Motivated by recent success in the dynamical systems approach to transitional flow, we study the efficiency and effectiveness of extracting simple invariant sets (recurrent flows) directly from chaotic/turbulent flows and the potential of these sets for providing predictions of certain statistics of the flow. Two-dimensional Kolmogorov flow (the 2D Navier-Stokes equations with a sinusoidal body force) is studied both over a square [0, 2{\pi}]2 torus and a rectangular torus extended in the forcing direction. In the former case, an order of magnitude more recurrent flows are found than previously (Chandler & Kerswell 2013) and shown to give improved predictions for the dissipation and energy pdfs of the chaos via periodic orbit theory. Over the extended torus at low forcing amplitudes, some extracted states mimick the statistics of the spatially-localised chaos present surprisingly well recalling the striking finding of Kawahara & Kida (2001) in low-Reynolds-number plane Couette flow. At higher forcing amplitudes, however, success is limited highlighting the increased dimensionality of the chaos and the need for larger data sets. Algorithmic developments to improve the extraction procedure are discussed

Scaling and Linear Response in the GOY Turbulence model

The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, $\nu$, is small the model has a qualitative behavior which is similar to the Kolmogorov theories of turbulence. Here a static solution to the model is examined, and a linear stability analysis is performed to obtain response eigenvalues and eigenfunctions. Both the static behavior and the linear response show an inertial range with a relatively simple scaling structure. Our main results are: (i) The response frequencies cover a wide range of scales, with ratios which can be understood in terms of the frequency scaling properties of the model. (ii) Even small viscosities play a crucial role in determining the model's eigenvalue spectrum. (iii) As a parameter within the model is varied, it shows a ``phase transition'' in which there is an abrupt change in many eigenvalues from stable to unstable values. (iv) The abrupt change is determined by the model's conservation laws and symmetries. This work is thus intended to add to our knowledge of the linear response of a stiff dynamical systems and at the same time to help illuminate scaling within a class of turbulence models.Comment: 25 pages, figures on reques

Simulations of Incompressible MHD Turbulence

We simulate incompressible MHD turbulence in the presence of a strong background magnetic field. Our major conclusions are: 1) MHD turbulence is most conveniently described in terms of counter propagating shear Alfven and slow waves. Shear Alfven waves control the cascade dynamics. Slow waves play a passive role and adopt the spectrum set by the shear Alfven waves, as does a passive scalar. 2) MHD turbulence is anisotropic with energy cascading more rapidly along k_perp than along k_parallel, where k_perp and k_parallel refer to wavevector components perpendicular and parallel to the local magnetic field. Anisotropy increases with increasing k_perp. 3) MHD turbulence is generically strong in the sense that the waves which comprise it suffer order unity distortions on timescales comparable to their periods. Nevertheless, turbulent fluctuations are small deep inside the inertial range compared to the background field. 4) Decaying MHD turbulence is unstable to an increase of the imbalance between the flux of waves propagating in opposite directions along the magnetic field. 5) Items 1-4 lend support to the model of strong MHD turbulence by Goldreich & Sridhar (GS). Results from our simulations are also consistent with the GS prediction gamma=2/3. The sole notable discrepancy is that 1D power law spectra, E(k_perp) ~ k_perp^{-alpha}, determined from our simulations exhibit alpha ~ 3/2, whereas the GS model predicts alpha = 5/3.Comment: 56 pages, 30 figures, submitted to ApJ 59 pages, 31 figures, accepted to Ap