Abstract Correlated binary data are prevalent in a wide range of scientific disciplines, including healthcare and medicine. The generalized estimating equations (GEEs) the multivariate probit (MP) model two popular methods for analyzing such data. However, both have some significant drawbacks. GEEs may not an underlying likelihood MP fail to generate distribution with specified marginals bivari...

In this paper, we consider approximation algorithms for optimizing a generic multivariate polynomial function in discrete (typically binary) variables. Such models have natural applications in graph theory, neural networks, error-correcting codes, among many others. In particular, we focus on three types of optimization models: (1) maximizing a homogeneous polynomial function in binary variable...

Unlike the classical deterministic digital circuit analysis, we consider a Monte Carlo simulation in the context of uncertain digital circuits. In other words, given a binary function of n uncertain input binary variables, we express the probability of this binary function in terms of the probabilities of the corresponding input binary variables. This in turn, allows us to estimate appropriate ...

Unlike the classical deterministic digital circuit analysis, we consider the analysis of uncertain digital circuits defined as follows. Given a binary function of n uncertain input binary variables, we express the probability of this binary function in terms of the probabilities of the corresponding input binary variables. This in turn, allows us to estimate appropriate probabilistic measure of...

We study the use of binary variables in reformulating general mixed-integer linear programs. We show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching. We also give computational results on the performance of such reformulations in solving the mixed-integer programs, which support our...

A variety of formulations for the Travelling Salesman Problem as Mixed Integer Program have been proposed. They contain either non-binary variables or the number of constraints and variables is large. We want to give a new formulation that consists solely of binary variables; the number of variables is of order O(n ln(n)) and the number of constraints is of order O(n ln(n)).