Information dissemination in socially aware networks under the linear threshold model

We provide new analytical results concerning the spread of information or influence under the linear threshold social network model introduced by Kempe et al. in, in the information dissemination context. The seeder starts by providing the message to a set of initial nodes and is interested in maximizing the number of nodes that will receive the message ultimately. A node's decision to forward the message depends on the set of nodes from which it has received the message. Under the linear threshold model, the decision to forward the information depends on the comparison of the total influence of the nodes from which a node has received the packet with its own threshold of influence. We derive analytical expressions for the expected number of nodes that receive the message ultimately, as a function of the initial set of nodes, for a generic network. We show that the problem can be recast in the framework of Markov chains. We then use the analytical expression to gain insights into information dissemination in some simple network topologies such as the star, ring, mesh and on acyclic graphs. We also derive the optimal initial set in the above networks, and also hint at general heuristics for picking a good initial set.

Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Maximum likelihood analysis of multi-stress accelerated life test data of series systems with competing log-normal causes of failure

This article presents frequentist inference of accelerated life test data of series systems with independent log-normal component lifetimes. The means of the component log-lifetimes are assumed to depend on the stress variables through a linear stress translation function that can accommodate the standard stress translation functions in the literature. An expectation-maximization algorithm is developed to obtain the maximum likelihood estimates of model parameters. The maximum likelihood estimates are then further refined by bootstrap, which is also used to infer about the component and system reliability metrics at usage stresses. The developed methodology is illustrated by analyzing a real as well as a simulated dataset. A simulation study is also carried out to judge the effectiveness of the bootstrap. It is found that in this model, application of bootstrap results in significant improvement over the simple maximum likelihood estimates.

Fast and slow climate responses to CO2 and solar forcing: A linear multivariate regression model characterizing transient climate change

Climate change in response to a change in external forcing can be understood in terms of fast response to the imposed forcing and slow feedback associated with surface temperature change. Previous studies have investigated the characteristics of fast response and slow feedback for different forcing agents. Here we examine to what extent that fast response and slow feedback derived from time-mean results of climate model simulations can be used to infer total climate change. To achieve this goal, we develop a multivariate regression model of climate change, in which the change in a climate variable is represented by a linear combination of its sensitivity to CO2 forcing, solar forcing, and change in global mean surface temperature. We derive the parameters of the regression model using time-mean results from a set of HadCM3L climate model step-forcing simulations, and then use the regression model to emulate HadCM3L-simulated transient climate change. Our results show that the regression model emulates well HadCM3L-simulated temporal evolution and spatial distribution of climate change, including surface temperature, precipitation, runoff, soil moisture, cloudiness, and radiative fluxes under transient CO2 and/or solar forcing scenarios. Our findings suggest that temporal and spatial patterns of total change for the climate variables considered here can be represented well by the sum of fast response and slow feedback. Furthermore, by using a simple 1-D heat-diffusion climate model, we show that the temporal and spatial characteristics of climate change under transient forcing scenarios can be emulated well using information from step-forcing simulations alone.