A new model of binary opinion dynamics: coarsening and effect of disorder

We propose a model of binary opinion in which the opinion of the individuals change according to the state of their neighbouring domains. If the neighbouring domains have opposite opinions, then the opinion of the domain with the larger size is followed. Starting from a random configuration, the system evolves to a homogeneous state. The dynamical evolution show novel scaling behaviour with the persistence exponent $\theta \simeq 0.235$ and dynamic exponent $z \simeq1.02 \pm 0.02$. Introducing disorder through a parameter called rigidity coefficient $\rho$ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at $\rho = 0^{+}$ is obtained. Close to $\rho =0$, the equilibrium values of the dynamic variables show power law scaling behaviour with $\rho$. We also discuss the effect of having both quenched and annealed disorder in the system.Comment: 4 pages, 6 figures, Final version of PR

Localized Computation of Newton Updates in Fully-implicit Two-phase Flow Simulation

AbstractFully-Implicit (FI) Methods are often employed in the numerical simulation of large-scale subsurface flows in porous media. At each implicit time step, a Newton-like method is used to solve the FI discrete nonlinear algebraic system. The linear solution process for the Newton updates is the computational workhorse of FI simulations. Empirical observations suggest that the computed Newton updates during FI simulations of multiphase flow are often sparse. Moreover, the level of sparsity observed can vary dramatically from iteration to the next, and across time steps. In several large scale applications, it was reported that the level of sparsity in the Newton update can be as large as 99%. This work develops a localization algorithm that conservatively predetermines the sparsity pattern of the Newton update. Subsequently, only the flagged nonzero components of the system need be solved. The localization algorithm is developed for general FI models of two phase flow. Large scale simulation results of benchmark reservoir models show a 10 to 100 fold reduction in computational cost for homogeneous problems, and a 4 to 10 fold reduction for strongly heterogeneous problems

CovNet: Covariance Networks for Functional Data on Multidimensional Domains

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce "Covariance Networks" (CovNet) as a modeling and estimation tool. The CovNet model is "universal" - it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated by means of an extensive simulation study and an application to resting state fMRI data.Comment: Substantial modification of the previous version. Application to fMRI data added. Theoretical results extended to cover discrete observations with measurement nois

A dermatologist guide to immunogenicity

AbstractDermatologists should be aware that autoantibody formation may occur after the initiation of biologic therapy. This phenomenon has been referred to as immunogenicity and biologic fatigue. Because of this, patients may experience loss of clinical efficacy to a particular drug. To combat this phenomenon, low-dose immunomodulators may be used in hopes of preventing autoantibodies. We review the current literature and provide a basic treatment algorithm for patients with moderate to severe psoriasis

Opinion dynamics model with domain size dependent dynamics: novel features and new universality class

A model for opinion dynamics (Model I) has been recently introduced in which the binary opinions of the individuals are determined according to the size of their neighboring domains (population having the same opinion). The coarsening dynamics of the equivalent Ising model shows power law behavior and has been found to belong to a new universality class with the dynamic exponent $z=1.0 \pm 0.01$ and persistence exponent $\theta \simeq 0.235$ in one dimension. The critical behavior has been found to be robust for a large variety of annealed disorder that has been studied. Further, by mapping Model I to a system of random walkers in one dimension with a tendency to walk towards their nearest neighbour with probability $\epsilon$, we find that for any $\epsilon > 0.5$, the Model I dynamical behaviour is prevalent at long times.Comment: 12 pages, 10 figures. To be published in "Journal of Physics : Conference Series" (2011