A Generalized Approach to Contingency Screening with System Islanding

This paper introduces a generalized contingency analysis approach that can identify critical pairs of contingencies (N-2 contingencies) that result in severe reliability violations or large numbers of islanded system components, bridging the gap between academic research and practical applications. We formulate the practical problem of N-2 contingency analysis in a clear mathematical format. We propose a generalized contingency screening approach compatible with all types of contingencies, including generator failure, load failure, open branches, and their mixtures that can lead to islanding. The proposed approach is demonstrated in a real Texas system, showing its effectiveness in critical contingency identification and its ability to enable possible practical contingency analysis applications

Equilibrium measures in the presence of certain rational external fields

Equilibrium measures in the real axis in the presence of rational external fields are considered. These external fields are called rational since their derivatives are rational functions. We analyze the evolution of the equilibrium measure, and its support, when the size of the measure, $t$, or other parameters in the external field vary. Our analysis is illustrated by studying with detail the case of a generalized Gauss-Penner model, which, in addition to its mathematical relevance, has important physical applications (in the framework of random matrix models). This paper is a natural continuation of \cite{MOR2013}, where equilibrium measures in the presence of polynomial external fields are thoroughly studied

On a new NBUE property in multivariate sense: an application

Since multivariate lifetime data frequently occur in applications, various properties of multivariate distributions have been previously considered to model and describe the main concepts of aging commonly considered in the univariate setting. The generalization of univariate aging notions to the multivariate case involves, among other factors, appropriate definitions of multivariate quantiles and related notions, which are able to correctly describe the intrinsic characteristics of the concepts of aging that should be generalized, and which provide useful tools in the applications. A new multivariate version of the well-known New Better than Used in Expectation univariate aging notion is provided, by means of the concepts of the upper corrected orthant and multivariate excess-wealth function. Some of its properties are described, with particular attention paid to those that can be useful in the analysis of real data sets. Finally, through an example it is illustrated how the new multivariate aging notion influences the final results in the analysis of data on tumor growth from the Comprehensive Cohort Study performed by the German Breast Cancer Study Grou

The Weibull-Exponential Distribution: Its Properties and Applications

A three parameter probability model, the so called Weibull-exponential distribution was proposed using the Weibull Generalized family of distributions. Some important models in the literature were found to be sub models of the new model. Explicit expressions for some of its basic mathematical properties like moments, moment generating function, reliability analysis, limiting behavior and order statistics were derived. The method of maximum likelihood estimation was proposed in estimating its parameters and real life applications were provided to illustrate its flexibility and potentiality over the exponential distribution

Hamiltonian Monte Carlo Acceleration Using Surrogate Functions with Random Bases

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods