We propose modeling signed networks by considering two layers in a social network for generation of positive and negative links where both the layers comprise of identical set of nodes. The growth process is modeled based on preferential attachment, formation of links probabilistically asserting structural balance of local groups, and internal growth which happens without addition of new nodes. We prove that the degree distribution of a generated network follows a power-law whose exponent depends on the largest eigenvalue of a matrix which governs the dynamics of growth of degrees of nodes with respect to positive and negative links. A computable formula for average degree and lower-bounds for the number of balanced and unbalanced triads of modelled networks are also obtained. A method for structural reconstruction of real signed networks is formulated through estimation the values of the model parameters to generate the network that can inherit different structural properties of the corresponding real network. Experimental results show that our model which we term as 2L-SNM can replicate properties of several real world signed networks much more robustly than competitive state-of-the-art techniques.

The digital media and TV - which is increasingly digitized, have amassed and generating enormous amount of data. While extremely useful, the big data generated by these platforms poses unique challenges for Data Scientists working on developing measurement framework and metrics. Most practitioners optimize speed and scale at the expense of accuracy, which is critical for any measurement. And, the trade-off between bias and variance is not in consideration. In this paper, we will demonstrate how Nielsen is combining proprietary ground truth data and methodologies with Big Data to address the accuracy and bias/variance challenges. We argue that high quality ground truth or training set is pre-requisite to deploying Big Data for high quality media measurement. To illustrate the point, we will share how Nielsen is combining its proprietary high quality panels with Set Top Box for TV measurement in the U.S.

This paper considers the problem of assessing the reliability of a software system that can be decomposed into a finite number of modules. It uses a Markovian model for the transfer of control between modules in order to develop the system reliability expression in terms of the module reliabilities. An operational test procedure is considered in which only the individual modules are tested and the system is considered acceptable if, and only if, no failures are observed. The minimum number of tests required of each module is determined such that the probability of accepting a system whose reliability falls below a specified value R/sub 0/ is less than a specified small fraction /spl beta/. This sample size determination problem is formulated as a two-stage mathematical program and an algorithm is developed for solving this problem. Two examples from the literature are considered to demonstrate the procedure.

Acceptance testing is analyzed for a series system of n components, each having an unknown, different, constant failure rate. Components are tested individually, and tests are terminated when a preassigned number of failures is observed for each component. The total time-on-test for each component is noted, and a statistic is constructed using observed test times and the number of failures of the components; the statistic is based on the maximum likelihood estimation of system reliability. This statistic is then used in specifying a decision rule for accepting or rejecting the entire system. The design of the test plan is stated as an optimization problem which minimizes test costs while ensuring that specified consumer and producer risks on system reliability are not exceeded. Numerical examples are provided, and implications of the test plan are discussed.